'form' ************** MAGMA ***************** Host form (140.247.29.178) Time: Mon Oct 11 18:18:05 2004 Input: 2+2 Output: Magma V2.11-6 Mon Oct 11 2004 18:18:04 on modular [Seed = 1866803342] ------------------------------------- 4 Total time: 0.190 seconds, Total memory usage: 3.50MB '141.223' ************** MAGMA ***************** Host 141.223.66.12 (141.223.66.12) Time: Mon Oct 11 22:39:49 2004 Input: F:=GF(4); A:=GL(2,F)![a,a^2,a,0]; Order(A); Output: Magma V2.11-6 Mon Oct 11 2004 22:39:44 on modular [Seed = 3370306079] ------------------------------------- 5 Total time: 0.190 seconds, Total memory usage: 3.56MB '141.223' ************** MAGMA ***************** Host 141.223.66.12 (141.223.66.12) Time: Mon Oct 11 22:40:30 2004 Input: F:=GF(4); A:=GL(2,F)![a,a^2,a,0]; for i:=1 to 5 print A^i;end for; Output: Magma V2.11-6 Mon Oct 11 2004 22:40:29 on modular [Seed = 990985728] ------------------------------------- >> print A^i;end for;; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.56MB '141.223' ************** MAGMA ***************** Host 141.223.66.12 (141.223.66.12) Time: Mon Oct 11 22:40:43 2004 Input: F:=GF(4); A:=GL(2,F)![a,a^2,a,0]; for i:=1 to 5; print A^i;end for; Output: Magma V2.11-6 Mon Oct 11 2004 22:40:43 on modular [Seed = 136449285] ------------------------------------- >> for i:=1 to 5; ^ User error: bad syntax >> print A^i;end for;; ^ User error: Identifier 'i' has not been declared or assigned >> print A^i;end for;; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.56MB '141.223' ************** MAGMA ***************** Host 141.223.66.12 (141.223.66.12) Time: Mon Oct 11 22:41:26 2004 Input: F:=GF(4); A:=GL(2,F)![a,a^2,a,0]; A^2;A^3;A^4;A^5; Output: Magma V2.11-6 Mon Oct 11 2004 22:41:26 on modular [Seed = 1901818881] ------------------------------------- [ a 1] [a^2 1] [ 1 1] [a^2 a] [ 0 a^2] [ a a] [ 1 0] [ 0 1] Total time: 0.190 seconds, Total memory usage: 3.56MB '128.250' ************** MAGMA ***************** Host 128.250.6.244 (128.250.6.244) Time: Tue Oct 12 04:26:36 2004 Input: p:=10572822555107569377414458344863414771024962571611471661140895426298657901541993790458548786498590099500325953831948304724404616568348787497941868467363057; f_p2 := GF(p,2); k:=PrimitiveElement(f_p2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Oct 12 2004 04:25:54 on modular [Seed = 2595245730] ------------------------------------- Errors: /bin/sh: line 1: 27568 Killed nice -n 19 /usr/local/bin/magma '128.250' ************** MAGMA ***************** Host 128.250.6.244 (128.250.6.244) Time: Tue Oct 12 04:27:36 2004 Input: p:=10572822555107569377414458344863414771024962571611471661140895426298657901541993790458548786498590099500325953831948304724404616568348787497941868467363057; f_p2 := GF(p,2); k:=PrimitiveElement(f_p2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Oct 12 2004 04:26:45 on modular [Seed = 2461550333] ------------------------------------- Errors: /bin/sh: line 1: 27576 Killed nice -n 19 /usr/local/bin/magma '128.250' ************** MAGMA ***************** Host 128.250.6.244 (128.250.6.244) Time: Tue Oct 12 04:28:00 2004 Input: p:=10572822555107569377414458344863414771024962571611471661140895426298657901541993790458548786498590099500325953831948304724404616568348787497941868467363057; f_p2 := GF(p,2); k:=PrimitiveElement(f_p2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Oct 12 2004 04:27:09 on modular [Seed = 2495496419] ------------------------------------- Errors: /bin/sh: line 1: 27582 Killed nice -n 19 /usr/local/bin/magma '128.250' ************** MAGMA ***************** Host 128.250.6.244 (128.250.6.244) Time: Tue Oct 12 04:28:07 2004 Input: p:=10572822555107569377414458344863414771024962571611471661140895426298657901541993790458548786498590099500325953831948304724404616568348787497941868467363057; f_p2 := GF(p,2); k:=PrimitiveElement(f_p2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Oct 12 2004 04:27:07 on modular [Seed = 2444969440] ------------------------------------- Errors: /bin/sh: line 1: 27579 Killed nice -n 19 /usr/local/bin/magma '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:18:36 2004 Input: EulerPhi(100) Output: Magma V2.11-6 Tue Oct 12 2004 10:18:36 on modular [Seed = 2444965662] ------------------------------------- 40 Total time: 0.210 seconds, Total memory usage: 3.50MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:06 2004 Input: eulerphi(100) Output: Magma V2.11-6 Tue Oct 12 2004 10:19:05 on modular [Seed = 2359700070] ------------------------------------- >> eulerphi(100); ^ User error: Identifier 'eulerphi' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:29 2004 Input: EulerPhi(100) Output: Magma V2.11-6 Tue Oct 12 2004 10:19:29 on modular [Seed = 4191379259] ------------------------------------- 40 Total time: 0.200 seconds, Total memory usage: 3.50MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:20:25 2004 Input: EulerPhi(100000) Output: Magma V2.11-6 Tue Oct 12 2004 10:20:25 on modular [Seed = 3286854361] ------------------------------------- 40000 Total time: 0.190 seconds, Total memory usage: 3.50MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:20:34 2004 Input: EulerPhi(1000000000) Output: Magma V2.11-6 Tue Oct 12 2004 10:20:33 on modular [Seed = 3337383876] ------------------------------------- 400000000 Total time: 0.200 seconds, Total memory usage: 3.50MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:23:39 2004 Input: EulerPhi(1052345342553245234523452000000000000000000000000000002) Output: Magma V2.11-6 Tue Oct 12 2004 10:23:37 on modular [Seed = 322550472] ------------------------------------- 502607615045299715592807380256022539161011067493457920 Total time: 0.710 seconds, Total memory usage: 3.66MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:23:44 2004 Input: EulerPhi(1052345342553245234523452000000000000000000000000000002) Output: Magma V2.11-6 Tue Oct 12 2004 10:23:42 on modular [Seed = 439399366] ------------------------------------- 502607615045299715592807380256022539161011067493457920 Total time: 1.000 seconds, Total memory usage: 3.68MB '134.219' ************** MAGMA ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:23:47 2004 Input: EulerPhi(1052345342553245234523452000000000000000000000000000002) Output: Magma V2.11-6 Tue Oct 12 2004 10:23:46 on modular [Seed = 490190045] ------------------------------------- 502607615045299715592807380256022539161011067493457920 Total time: 0.550 seconds, Total memory usage: 3.59MB '129.137' ************** MAGMA ***************** Host 129.137.194.247 (129.137.194.247) Time: Tue Oct 12 15:12:09 2004 Input: GF81 := GF(3, 4); Output: Magma V2.11-6 Tue Oct 12 2004 15:12:08 on modular [Seed = 840916979] ------------------------------------- Total time: 0.220 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.194.247 (129.137.194.247) Time: Tue Oct 12 15:12:49 2004 Input: GF81 := GF(3, 4); GF81, PrimeField(GF81); Output: Magma V2.11-6 Tue Oct 12 2004 15:12:49 on modular [Seed = 3589847085] ------------------------------------- Finite field of size 3^4 Finite field of size 3 Total time: 0.190 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.194.247 (129.137.194.247) Time: Tue Oct 12 15:17:38 2004 Input: GF81 := GF(3, 4); GF81, PrimeField(GF81); Set(GF81); e := 2 * w^5; e; P := PolynomialRing(GF81); P; p := 2*x^6 - w*x^2 + 1; p; Evaluate(p, e); P![w^5, 1, 1, 0, w^31, 1]; P![ w^(5*i) : i in [1..8] ]; FF := FieldOfFractions(P); FF; V5 := VectorSpace(FF, 5); V5; Basis(V5); for i in [1..5] do V5.i; end for; V5sub := sub< V5 | $.1, x^2*$.3 - w^7*$.4, 2*$.1 - w*x^3*$.3 + w^8*x*$.4 >; V5sub; Q, f := quo< V5 | V5sub >; Q; f; Image(f); Kernel(f); V5sub eq Kernel(f); for n in [1..3] do Q.n, (Q.n)@@f, ""; // preimages end for; Output: Magma V2.11-6 Tue Oct 12 2004 15:17:37 on modular [Seed = 1885150442] ------------------------------------- Finite field of size 3^4 Finite field of size 3 { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10, w^11, w^12, w^13, w^14, w^15, w^16, w^17, w^18, w^19, w^20, w^21, w^22, w^23, w^24, w^25, w^26, w^27, w^28, w^29, w^30, w^31, w^32, w^33, w^34, w^35, w^36, w^37, w^38, w^39, 2, w^41, w^42, w^43, w^44, w^45, w^46, w^47, w^48, w^49, w^50, w^51, w^52, w^53, w^54, w^55, w^56, w^57, w^58, w^59, w^60, w^61, w^62, w^63, w^64, w^65, w^66, w^67, w^68, w^69, w^70, w^71, w^72, w^73, w^74, w^75, w^76, w^77, w^78, w^79, 0 } w^45 Univariate Polynomial Ring in x over GF(3^4) 2*x^6 + w^41*x^2 + 1 w^47 x^5 + w^31*x^4 + x^2 + x + w^5 2*x^7 + w^35*x^6 + w^30*x^5 + w^25*x^4 + w^20*x^3 + w^15*x^2 + w^10*x + w^5 Univariate rational function field over GF(3^4) Variables: $.1 Full Vector space of degree 5 over Univariate rational function field over GF(3^4) [ ( 1 0 0 0 0), ( 0 1 0 0 0), ( 0 0 1 0 0), ( 0 0 0 1 0), ( 0 0 0 0 1) ] ( 1 0 0 0 0) ( 0 1 0 0 0) ( 0 0 1 0 0) ( 0 0 0 1 0) ( 0 0 0 0 1) Vector space of degree 5, dimension 2 over Univariate rational function field over GF(3^4) Generators: ( 1 0 0 0 0) ( 0 0 $.1^2 w^47 0) ( 2 0 w^41*$.1^3 w^8*$.1 0) Echelonized basis: ( 1 0 0 0 0) ( 0 0 1 w^47/$.1^2 0) Full Vector space of degree 3 over Univariate rational function field over GF(3^4) Mapping from: ModTupFld: V5 to ModTupFld: Q Full Vector space of degree 3 over Univariate rational function field over GF(3^4) Vector space of degree 5, dimension 2 over Univariate rational function field over GF(3^4) Echelonized basis: ( 1 0 0 0 0) ( 0 0 1 w^47/$.1^2 0) true ( 1 0 0) ( 0 1 0 0 0) ( 0 1 0) ( 0 0 w^73*$.1^2 0 0) ( 0 0 1) ( 0 0 0 0 1) Total time: 0.200 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.194.247 (129.137.194.247) Time: Tue Oct 12 15:18:06 2004 Input: GF81 := GF(3, 4); GF81, PrimeField(GF81); Set(GF81); e := 2 * w^5; e; P := PolynomialRing(GF81); P; p := 2*x^6 - w*x^2 + 1; p; Evaluate(p, e); P![w^5, 1, 1, 0, w^31, 1]; P![ w^(5*i) : i in [1..8] ]; FF := FieldOfFractions(P); FF; V5 := VectorSpace(FF, 5); V5; Basis(V5); for i in [1..5] do V5.i; end for; V5sub := sub< V5 | $.1, x^2*$.3 - w^7*$.4, 2*$.1 - w*x^3*$.3 + w^8*x*$.4 >; V5sub; Q, f := quo< V5 | V5sub >; Q; f; Image(f); Kernel(f); V5sub eq Kernel(f); for n in [1..3] do Q.n, (Q.n)@@f, ""; end for; Output: Magma V2.11-6 Tue Oct 12 2004 15:18:06 on modular [Seed = 1968708051] ------------------------------------- Finite field of size 3^4 Finite field of size 3 { 1, w, w^2, w^3, w^4, w^5, w^6, w^7, w^8, w^9, w^10, w^11, w^12, w^13, w^14, w^15, w^16, w^17, w^18, w^19, w^20, w^21, w^22, w^23, w^24, w^25, w^26, w^27, w^28, w^29, w^30, w^31, w^32, w^33, w^34, w^35, w^36, w^37, w^38, w^39, 2, w^41, w^42, w^43, w^44, w^45, w^46, w^47, w^48, w^49, w^50, w^51, w^52, w^53, w^54, w^55, w^56, w^57, w^58, w^59, w^60, w^61, w^62, w^63, w^64, w^65, w^66, w^67, w^68, w^69, w^70, w^71, w^72, w^73, w^74, w^75, w^76, w^77, w^78, w^79, 0 } w^45 Univariate Polynomial Ring in x over GF(3^4) 2*x^6 + w^41*x^2 + 1 w^47 x^5 + w^31*x^4 + x^2 + x + w^5 2*x^7 + w^35*x^6 + w^30*x^5 + w^25*x^4 + w^20*x^3 + w^15*x^2 + w^10*x + w^5 Univariate rational function field over GF(3^4) Variables: $.1 Full Vector space of degree 5 over Univariate rational function field over GF(3^4) [ ( 1 0 0 0 0), ( 0 1 0 0 0), ( 0 0 1 0 0), ( 0 0 0 1 0), ( 0 0 0 0 1) ] ( 1 0 0 0 0) ( 0 1 0 0 0) ( 0 0 1 0 0) ( 0 0 0 1 0) ( 0 0 0 0 1) Vector space of degree 5, dimension 2 over Univariate rational function field over GF(3^4) Generators: ( 1 0 0 0 0) ( 0 0 $.1^2 w^47 0) ( 2 0 w^41*$.1^3 w^8*$.1 0) Echelonized basis: ( 1 0 0 0 0) ( 0 0 1 w^47/$.1^2 0) Full Vector space of degree 3 over Univariate rational function field over GF(3^4) Mapping from: ModTupFld: V5 to ModTupFld: Q Full Vector space of degree 3 over Univariate rational function field over GF(3^4) Vector space of degree 5, dimension 2 over Univariate rational function field over GF(3^4) Echelonized basis: ( 1 0 0 0 0) ( 0 0 1 w^47/$.1^2 0) true ( 1 0 0) ( 0 1 0 0 0) ( 0 1 0) ( 0 0 w^73*$.1^2 0 0) ( 0 0 1) ( 0 0 0 0 1) Total time: 0.190 seconds, Total memory usage: 3.56MB '143.239' ************** MAGMA ***************** Host 143.239.211.125 (143.239.211.125) Time: Wed Oct 13 06:27:09 2004 Input: R:=PolynomialRing(GF(2)); g:=x^3+x+1; Factorization(x^7-1); C:=CyclicCode(7,g); C; G:=GeneratorMatrix(C); G; H:=ParityCheckMatrix(C); H; Output: Magma V2.11-6 Wed Oct 13 2004 06:27:05 on modular [Seed = 2628837227] ------------------------------------- [ , , ] [7, 4, 3] Cyclic Linear Code over GF(2) Generator matrix: [1 0 0 0 1 1 0] [0 1 0 0 0 1 1] [0 0 1 0 1 1 1] [0 0 0 1 1 0 1] [1 0 0 0 1 1 0] [0 1 0 0 0 1 1] [0 0 1 0 1 1 1] [0 0 0 1 1 0 1] [1 0 0 1 0 1 1] [0 1 0 1 1 1 0] [0 0 1 0 1 1 1] Total time: 0.200 seconds, Total memory usage: 3.50MB '143.239' ************** MAGMA ***************** Host 143.239.211.125 (143.239.211.125) Time: Wed Oct 13 06:27:56 2004 Input: R:=PolynomialRing(GF(2)); g:=x^3+x+1; Factorization(x^7-1); C:=CyclicCode(7,g); C; G:=GeneratorMatrix(C); G; print ".."; H:=ParityCheckMatrix(C); H; Output: Magma V2.11-6 Wed Oct 13 2004 06:27:55 on modular [Seed = 2578832316] ------------------------------------- [ , , ] [7, 4, 3] Cyclic Linear Code over GF(2) Generator matrix: [1 0 0 0 1 1 0] [0 1 0 0 0 1 1] [0 0 1 0 1 1 1] [0 0 0 1 1 0 1] [1 0 0 0 1 1 0] [0 1 0 0 0 1 1] [0 0 1 0 1 1 1] [0 0 0 1 1 0 1] .. [1 0 0 1 0 1 1] [0 1 0 1 1 1 0] [0 0 1 0 1 1 1] Total time: 0.190 seconds, Total memory usage: 3.50MB '69.86.4' ************** MAGMA ***************** Host 69.86.47.89 (69.86.47.89) Time: Wed Oct 13 12:34:50 2004 Input: a*0 Output: Magma V2.11-6 Wed Oct 13 2004 12:34:49 on modular [Seed = 1315067515] ------------------------------------- >> a*0; ^ User error: Identifier 'a' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '69.86.4' ************** MAGMA ***************** Host 69.86.47.89 (69.86.47.89) Time: Wed Oct 13 12:34:56 2004 Input: 4636*0 Output: Magma V2.11-6 Wed Oct 13 2004 12:34:56 on modular [Seed = 1097685357] ------------------------------------- 0 Total time: 0.190 seconds, Total memory usage: 3.50MB '69.86.4' ************** MAGMA ***************** Host 69.86.47.89 (69.86.47.89) Time: Wed Oct 13 12:35:14 2004 Input: (2+535324+352354345^23343 Output: Magma V2.11-6 Wed Oct 13 2004 12:35:13 on modular [Seed = 1951951913] ------------------------------------- >> (2+535324+352354345^23343; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.50MB '69.86.4' ************** MAGMA ***************** Host 69.86.47.89 (69.86.47.89) Time: Wed Oct 13 12:35:41 2004 Input: (2+535324+352354345)^23343 Output: Magma V2.11-6 Wed Oct 13 2004 12:35:21 on modular [Seed = 1766158652] ------------------------------------- 3435074981486331310655138341083532339076632810801018810000749059972616725269265\ 5228394170886952731075031749576782404000712328176017293219110080146874468843934\ 9654627113189136560662231793750409591620589446500880261165954880887649391423170\ 3056775080282750488016313983583962384887945506311017405065037994414647583482323\ 2420172478666536464571316707305175350475473911391490317346544370777138520647830\ 8644159616839963240294173487285779342750787358433393650428344957932344349887368\ 0621386078778134909312314467369078497854419241815844389597110791871019420315818\ 5092749479005631335903256503150869239077707152816052381005918605672211648517763\ 1317371006695355513405439017644083058171584700771802592548548549627799186401862\ 5730515066484062532067162179360228912184388135697801937293322815057902828709081\ 4405641776528901207729690775512116580159630995629521749244022985106986987945436\ 6724923511709467555212962028506460522669863036121118146011163571530790784381051\ 3894567759049149673885107611331574061276754833312088135994015689150548916335461\ 9135041461944873113550608565936667946698387544806585843582688158268147168812353\ 1998963915378275955004030544894445635901678461808019860601237585190851380332353\ 1950211759987594309148446330397478006004439895953044697112136113195025596054719\ 2909323097249451561108505396100956951331672232259121153334578951588898636332363\ 5627219791795442760575478441800343846690558795889391446926738361275551884559707\ 9913591570087319273983710877676233092338178747258353890556814213864972279554871\ 7238463156044158560742904352492580595967553143731178471435322141590249933635606\ 5572520726908227643899530185497391309339601742587289991576483229327227757758712\ 4725154288692952743059110725137391284103566930014443101985255802822990127260413\ 7342711988708038329603484749473624543500316775243639105128053119125741323153861\ 1776854532975169915667397391246095579240341927579293627021899460052896364332695\ 3042451020656468150698484141345362733857358632760868684329727916766504410561029\ 7504576690779992754527274240650584743294115520517266525267972446896397391659719\ 7822534399597807779183148921090528971988885823750884742752498293044929781252079\ 6195455309836895567557649028260278593587006448027918833416576939912520829237749\ 5626118231563197779238603288874513294087109825670492340715939957339615102996999\ 8120335249071251238146721921473662957484267124346100356795944695976625313658889\ 3634054325643261514162277064552903592813950729984594007064857816031289097867894\ 0023853930815014447142196360888335963146619937784008236495140673140989398275447\ 3285294030917071704414721695007548598460372476360766792872048026277165242131560\ 6856388955460921010343374694660172792306789815828370617352990862166562361149844\ 4518873792788391039073930003977264938576118427622276715268386904664549829419925\ 7078220822897547925348048976764368914782745456288092411377475797732028881997699\ 3614828740308632615250987871127787244728605972913747174951297804574979134282839\ 2893815507530622855067966894718033985484048858076411295434518032902100419213494\ 9936259144865945027458430711934941501392741854822870327617481170122450546115957\ 6487664042204183715343445234725508308536493852469804611040655217002768210772157\ 4761618026743401068196179009026366991809671318971608583257270311509843927078752\ 1230937162099727730398875691265131983374169039314251172887474706107205236341718\ 3317708467811194570034148084342900799597575614381815689000882448086321153143567\ 4950354128310069629319777918630263959054376517111904128312157245426330615323034\ 2569696630530393191327819002260189768037452252144750182614382308986975041621360\ 4987032099160399922858609092157586621963253585755274580822207963235405719655650\ 4209932336102683834830969288091053123005002292528473238170813835583063210547614\ 2122185536884450912065665766145972792756443037388879438826340716274982084227704\ 7426381999036877075658284234536518002289945327560360735418244466101732157929584\ 5957411702280717913159279579074359025976232333425553609511483259541547307085082\ 4517144901283039097020162816354883413400323251496685404991815109694838676240308\ 5973114206242894527462494828142009246174395467211759260374149428951304921652282\ 0483012201864834127045131149267333318688596257887149603586556434211041894518215\ 6019438968426929647434502394243298053889764060293607829639936606348079387736207\ 6099869729046068132797016893431641955957935910767611955528959588803183549382593\ 7577313897710683466162940189897015284659191494273470624715894803823730281909866\ 2404505342013157020435255237282360489684967387358932422060909989227517104737687\ 5659028027291454269683310627997519133960494885307087751611152225254958240211915\ 7310558447128330165577119635319421583720395748931485183909190621544385598722303\ 0787264607950518316294299580523360342355776261485570353277181089338807517752074\ 3950596676440689291924533192678825478224708650565585346271121778954985609361903\ 0124068249672469796872232572240255045689433840318296774673761685546511744270719\ 9778627743027672377540104687909654799340024132895726911471857717476965412615607\ 1428131242389740291740459348391112430701401482398201801187471567959287811178036\ 6026253075984281025571021294134083799069949181265246484531882009523406444342968\ 7073989320001953115852829313797822936170274647160197280141863382985872803942794\ 8916590189636674023014104204611169445467394482948061324324937425074861418934776\ 9142282198025255682069907417679047793256655426305299203510281693275196382104331\ 0981876514723440658977539787523511484839867155371449021590415762705559335349981\ 1068502953691801270022186818085552007411956809082319365042719553758805002051805\ 4819757911787073272597095057854089389834499344222900095491754048252215458777259\ 4106609839740044562389983477056451879450827459546685889912016522678986000958908\ 8960721286265388535355398475645916370268950850544497314858043679119504801898122\ 8383305647781870101184459012335039321423837411698106404474866970307286694720293\ 2154147501993159428533460952735512852176869980589763554221278488394702510092455\ 3620195666264541738873458223107692176575710872461149613914504973269079884777815\ 9258829658390388704018379793140723909855126052329483501641054547205726899357108\ 2179869346487347453924945521956397119604621478500726764587513220272961389686693\ 9170438073464033961442589358318780186943504891269275919671585916146177367184736\ 2923695834879945909846154122492792107302016157169582235336342992620850992556067\ 2796409580090570627453582677477082774803238529926853931948362514717352249351946\ 3210969964571103859948271292537868030353090352872400824817155051634073762954021\ 5746304939234628513752469870229536978526924131434464453379646769421348951769130\ 6251695033260767370219212664438667478130024627265366567287689448186227760485423\ 1828354231404224267691998637891008492235615995811335087828460208816151984486881\ 1616763720307793616670018357823514231675226103269860387016311656643812435127645\ 9222198130261559989711924323983583417754832990206894480923989567461930290881500\ 0929139521737183028298056376096847173047424428049334813841497903060470837886405\ 8520397924727469167797200723871356287662987170004759988522890351215989826230822\ 5365731583410524875858043078506070820105851340558236197329895726107628736966322\ 2690881741369046847548959381855118535028526084053528127908027062386428766161958\ 0646113633435868020423580069603776250027476642002638911683784419759058199274875\ 5906910824290074247784017944538501634063782205900279260174040865057780549561397\ 2755701970155139942359498674658766111185895452381468341467657363204969134137972\ 1549939982137042970363140397442270414191557425828486136137791461300985913201957\ 0642674097651398645892119098420795483335088147940906036304071878968915258124745\ 0239207563372082566445046403338598861073474879847443624433145438711909029072468\ 8325541541321470379171771211329178078429897838399646720232880842789024352682335\ 2822011870301452295936300962457776794388890432110285074176870360649991265726307\ 6990579631720702299688329890490855618704421982191720044095324300956568133139028\ 5742669603313001222627505305416281897172984825959413013812068185210783601711248\ 4494105614392754835352942026815433649820883350995410128496205290734766662535209\ 0946634028309347270215772622388818127789025083034899656002232835345135351054925\ 9621186912539931569607191485772063407155294431015355800624549524924521475532594\ 2410390421163453063340302178654822593142310757358713214788223096001644349154326\ 5540116592226256782788368011203153081559197850706598242882700293980242673475924\ 0224655591962253759082165708185845842099148903293073981757861134911999414890746\ 9216589572236571039598812979445791328643047494797982227189261130252378982395728\ 9563720310484771665515975665753326937277012643682645312430437709555875356269241\ 1991611940943203217247178351029329434035514677858700224700199266022867433312405\ 1776428694931919495363363916395702851525251307282024836415894842626573408838256\ 0754778529546001696551581528810241574110903094597260731871994479880747029981657\ 1849796081641633719591458138465894828052630494311836757520943224627639329045297\ 7508698529931159354942174449204563516698574963837911027106229898921550604255987\ 8885267431388966626272870085841190912030531466001823480274750650217686697942552\ 8909414104257809137160670758270380107055147512376146085358746744081772118241531\ 0335761847384500811290203209645862031398933707603308025882138727761039912746839\ 9824349409388814797248818745037080269953061485213793929323651119033641128775657\ 1722714378696554454511695018711864764793352358545471390771002543274363735447553\ 7605066985418578071658554035787835085925881202098941420358667077660082769835321\ 8568938593381902685191324739688470182204704717429905427529246576018831494223691\ 8448888559435565209819456203041124248735244058473353665294861314172275955434998\ 4 ** WARNING: Output too long, hence truncated. '146.6.1' ************** MAGMA ***************** Host 146.6.101.9 (146.6.101.9) Time: Wed Oct 13 12:46:13 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Wed Oct 13 2004 12:46:13 on modular [Seed = 3253590792] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.200 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Wed Oct 13 16:26:57 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(X^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Wed Oct 13 2004 16:26:56 on modular [Seed = 2662486067] ------------------------------------- >> K := NumberField(X^5 + 7*x^4 + 3*x^2 - x + 1); ^ User error: Identifier 'X' has not been declared or assigned >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I := 2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Wed Oct 13 16:27:18 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Wed Oct 13 2004 16:27:17 on modular [Seed = 2359312916] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Wed Oct 13 16:27:41 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); I := 5*OK; Factorization(I); Output: Magma V2.11-6 Wed Oct 13 2004 16:27:41 on modular [Seed = 2259306502] ------------------------------------- [ , , ] Total time: 0.190 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.26.72 (129.137.26.72) Time: Thu Oct 14 05:43:14 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Thu Oct 14 2004 05:43:11 on modular [Seed = 1147883391] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.270 seconds, Total memory usage: 3.50MB '200.18.' ************** MAGMA ***************** Host 200.18.153.143 (200.18.153.143) Time: Thu Oct 14 13:45:33 2004 Input: L:=SimpleLieAlgebra("A", 3, Rationals); Output: Magma V2.11-6 Thu Oct 14 2004 13:45:32 on modular [Seed = 3080211931] ------------------------------------- >> L:=SimpleLieAlgebra("A", 3, Rationals);; ^ Runtime error in 'SimpleLieAlgebra': Bad argument types Argument types given: MonStgElt, RngIntElt, Intrinsic Total time: 0.190 seconds, Total memory usage: 3.50MB '200.18.' ************** MAGMA ***************** Host 200.18.153.143 (200.18.153.143) Time: Thu Oct 14 13:46:10 2004 Input: L:=SimpleLieAlgebra(A, 3, Rationals); Output: Magma V2.11-6 Thu Oct 14 2004 13:46:09 on modular [Seed = 1517658216] ------------------------------------- >> L:=SimpleLieAlgebra(A, 3, Rationals);; ^ User error: Identifier 'A' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '200.18.' ************** MAGMA ***************** Host 200.18.153.143 (200.18.153.143) Time: Thu Oct 14 13:46:27 2004 Input: L:=SimpleLieAlgebra("D", 3); Output: Magma V2.11-6 Thu Oct 14 2004 13:46:27 on modular [Seed = 1264890219] ------------------------------------- >> L:=SimpleLieAlgebra("D", 3);; ^ Runtime error in 'SimpleLieAlgebra': Bad argument types Argument types given: MonStgElt, RngIntElt Total time: 0.190 seconds, Total memory usage: 3.50MB '200.18.' ************** MAGMA ***************** Host 200.18.153.143 (200.18.153.143) Time: Thu Oct 14 13:46:52 2004 Input: L:=SimpleLieAlgebra["D", 3]; Output: Magma V2.11-6 Thu Oct 14 2004 13:46:52 on modular [Seed = 2085848739] ------------------------------------- >> L:=SimpleLieAlgebra["D", 3];; ^ Runtime error in '[]': Bad argument types Total time: 0.200 seconds, Total memory usage: 3.50MB '200.18.' ************** MAGMA ***************** Host 200.18.153.143 (200.18.153.143) Time: Thu Oct 14 13:55:34 2004 Input: L:=SimpleLieAlgebra Output: Magma V2.11-6 Thu Oct 14 2004 13:55:34 on modular [Seed = 3303749632] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 3.50MB '192.219' ************** MAGMA ***************** Host 192.219.240.44 (192.219.240.44) Time: Thu Oct 14 14:43:48 2004 Input: Factorization(256234564356433); Output: Magma V2.11-6 Thu Oct 14 2004 14:43:47 on modular [Seed = 3656798307] ------------------------------------- [ <13, 1>, <19710351104341, 1> ] Total time: 0.190 seconds, Total memory usage: 3.50MB '192.219' ************** MAGMA ***************** Host 192.219.240.44 (192.219.240.44) Time: Thu Oct 14 14:48:04 2004 Input: Factorization(43764674364367346743674374437843734674436743764376); Output: Magma V2.11-6 Thu Oct 14 2004 14:48:04 on modular [Seed = 3506395245] ------------------------------------- [ <2, 3>, <83, 1>, <1447, 1>, <10477, 1>, <14645863, 1>, <8830517774583091, 1>, <33616230319215767, 1> ] Total time: 0.430 seconds, Total memory usage: 3.66MB '68.75.1' ************** MAGMA ***************** Host 68.75.175.128 (68.75.175.128) Time: Thu Oct 14 23:21:25 2004 Input: Factorization(193487219); Output: Magma V2.11-6 Thu Oct 14 2004 23:21:24 on modular [Seed = 991246346] ------------------------------------- [ <193487219, 1> ] Total time: 0.190 seconds, Total memory usage: 3.50MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.13 (66.63.132.13) Time: Thu Oct 14 23:32:23 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(f); m(pts[1]); Height($1); Output: Magma V2.11-6 Thu Oct 14 2004 23:32:15 on modular [Seed = 2018934208] ------------------------------------- 0 >> F := S[1]; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,1000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.580 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.13 (66.63.132.13) Time: Thu Oct 14 23:32:58 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(f); m(pts[1]); Height($1); Output: Magma V2.11-6 Thu Oct 14 2004 23:32:56 on modular [Seed = 2710545486] ------------------------------------- 0 >> F := S[1]; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,1000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.880 seconds, Total memory usage: 4.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.13 (66.63.132.13) Time: Thu Oct 14 23:36:02 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); #S; f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); #S; Output: Magma V2.11-6 Thu Oct 14 2004 23:35:54 on modular [Seed = 4191681892] ------------------------------------- 0 0 Total time: 4.099 seconds, Total memory usage: 5.62MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:31:00 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:30:55 on modular [Seed = 1041276997] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:31:11 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5 + 7*x^4 + 3*x^2 - x + 1); OK := MaximalOrder(K); I := 5*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:31:09 on modular [Seed = 3656861615] ------------------------------------- [ , , ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:36:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 - 10*x^2 + 1); OK := MaximalOrder(K); I := 5*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:36:00 on modular [Seed = 2760508846] ------------------------------------- [ , ] Total time: 0.210 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:40:27 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 - 10*x^2 + 1); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:40:24 on modular [Seed = 3757146075] ------------------------------------- 147456 Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:40:44 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:40:41 on modular [Seed = 3387386364] ------------------------------------- 8 Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:40:54 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 4); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:40:52 on modular [Seed = 4225063891] ------------------------------------- >> K := NumberField(x^2 - 4); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> Discriminant(K);; ^ User error: Identifier 'K' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:41:03 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 5); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:41:01 on modular [Seed = 4158216150] ------------------------------------- 20 Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:41:13 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 7); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:41:10 on modular [Seed = 3922151731] ------------------------------------- 28 Total time: 0.200 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:41:23 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 11); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:41:22 on modular [Seed = 3821880109] ------------------------------------- 44 Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:42:10 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 - 10*x^2 + 1); OK := MaximalOrder(K); Discriminant(K); Output: Magma V2.11-6 Fri Oct 15 2004 10:42:10 on modular [Seed = 2927627824] ------------------------------------- 147456 Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:42:47 2004 Input: Factor(147456); Output: Magma V2.11-6 Fri Oct 15 2004 10:42:46 on modular [Seed = 1367339496] ------------------------------------- >> Factor(147456);; ^ Runtime error in 'Factor': Bad argument types Argument types given: RngIntElt Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:42:55 2004 Input: Factorization(147456); Output: Magma V2.11-6 Fri Oct 15 2004 10:42:55 on modular [Seed = 1198122999] ------------------------------------- [ <2, 14>, <3, 2> ] Total time: 0.180 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:43:23 2004 Input: 2^14*9 Output: Magma V2.11-6 Fri Oct 15 2004 10:43:21 on modular [Seed = 2035800623] ------------------------------------- 147456 Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:43:39 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 - 10*x^2 + 1); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:43:39 on modular [Seed = 1716045090] ------------------------------------- [ ] Total time: 0.220 seconds, Total memory usage: 3.59MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:45:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^4 - 10*x^2 + 1); OK := MaximalOrder(K); I := 3*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:45:47 on modular [Seed = 3656874525] ------------------------------------- [ ] Total time: 0.210 seconds, Total memory usage: 3.59MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:46:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^ - 2); OK := MaximalOrder(K); I := 3*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:46:21 on modular [Seed = 4225062937] ------------------------------------- >> K := NumberField(x^ - 2); ^ Runtime error in '^': Argument 2 (-2) should be >= 0 >> OK := MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I := 3*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:46:35 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 3*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:46:35 on modular [Seed = 4057944677] ------------------------------------- [ ] Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:46:48 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:46:47 on modular [Seed = 3871884654] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:52:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 3*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:52:50 on modular [Seed = 3303694808] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 10:54:19 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 10:54:18 on modular [Seed = 2309434445] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:01:23 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; I^2; Output: Magma V2.11-6 Fri Oct 15 2004 11:01:22 on modular [Seed = 2002374741] ------------------------------------- Principal Ideal of OK Generator: [4, 0] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:02:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 4*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:02:21 on modular [Seed = 1058117666] ------------------------------------- [ ] Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:03:20 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; I^2; Output: Magma V2.11-6 Fri Oct 15 2004 11:03:18 on modular [Seed = 3506337542] ------------------------------------- Principal Ideal of OK Generator: [4, 0] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:03:28 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:03:28 on modular [Seed = 2743927811] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:03:29 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:03:28 on modular [Seed = 2844200457] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:03:49 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := (2,a)*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:03:46 on modular [Seed = 3197114636] ------------------------------------- >> I := (2,a)*OK; ^ Runtime error in elt< ... >: Bad arguments >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:04:25 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := [2,a]*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:04:23 on modular [Seed = 1985532386] ------------------------------------- >> I := [2,a]*OK; ^ Runtime error in '*': Bad argument types Argument types given: SeqEnum[FldNumElt], RngOrd >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:04:33 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := [2,a]; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:04:30 on modular [Seed = 1231548117] ------------------------------------- >> Factorization(I);; ^ Runtime error in 'Factorization': Bad argument types Argument types given: SeqEnum[FldNumElt] Total time: 0.180 seconds, Total memory usage: 3.50MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:04:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:04:51 on modular [Seed = 771786846] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.58MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:05:11 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; I^2; Output: Magma V2.11-6 Fri Oct 15 2004 11:05:09 on modular [Seed = 170175564] ------------------------------------- Ideal of OK Two element generators: [4, 0] [2, 0] Total time: 0.180 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:09:42 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; I^3; Output: Magma V2.11-6 Fri Oct 15 2004 11:09:41 on modular [Seed = 439661389] ------------------------------------- Ideal of OK Two element generators: [8, 0] [0, 2] Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:09:47 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; I^4; Output: Magma V2.11-6 Fri Oct 15 2004 11:09:47 on modular [Seed = 3855305916] ------------------------------------- Ideal of OK Two element generators: [16, 0] [4, 0] Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:09:53 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; I^5; Output: Magma V2.11-6 Fri Oct 15 2004 11:09:52 on modular [Seed = 3922149579] ------------------------------------- Ideal of OK Two element generators: [32, 0] [0, 4] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:09:58 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; I^2; Output: Magma V2.11-6 Fri Oct 15 2004 11:09:58 on modular [Seed = 3988997321] ------------------------------------- Ideal of OK Two element generators: [4, 0] [2, 0] Total time: 0.190 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:12:38 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK + a*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:12:37 on modular [Seed = 2069222139] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.58MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:18:43 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 3*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:18:43 on modular [Seed = 439660845] ------------------------------------- [ ] Total time: 0.200 seconds, Total memory usage: 3.56MB '130.113' ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Fri Oct 15 11:20:08 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2 - 2); OK := MaximalOrder(K); I := 2*OK; Factorization(I); Output: Magma V2.11-6 Fri Oct 15 2004 11:20:06 on modular [Seed = 2309431877] ------------------------------------- [ ] Total time: 0.190 seconds, Total memory usage: 3.56MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:33:43 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-15280281,0]); TwoDescent(E); Output: Magma V2.11-6 Fri Oct 15 2004 13:33:40 on modular [Seed = 3689583455] ------------------------------------- [ 4036*x^4 - 19496*x^3 + 5028*x^2 + 16144*x - 4874, x^4 + 61121124, 9121*x^4 + 10424*x^3 + 7818*x^2 + 10424*x + 9121, x^4 - 23454*x^2 + 15280281, -931*x^4 - 6352*x^3 + 18144*x^2 + 15616*x - 9548, 4*x^4 + 8*x^3 + 23460*x^2 + 23456*x + 3825934, 796*x^4 + 1326*x^3 + 4563*x^2 - 1989*x + 1791 ] Total time: 0.960 seconds, Total memory usage: 5.93MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:36:17 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-15280281,0]); g := TwoDescent(E); S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(f); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:35:42 on modular [Seed = 2476923021] ------------------------------------- 4 Point [ 1, 128, 719, 15 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 128, 510, 735 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 279, 319, 894 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 598, 232, 1000 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 741, 492, 525 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 893, 135, 890 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field >> AssociatedEC(f); ^ User error: Identifier 'f' has not been declared or assigned (683122402795411487903634390243/147960732583848157843074241 : -300439766538110800080999955254570446305293228/17997811933971834271179365125305\ 99167711 : 1) 60.38251237547301286667 Total time: 17.440 seconds, Total memory usage: 20.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:39:35 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-29822521,0]); g := TwoDescent(E); S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:39:18 on modular [Seed = 1057912074] ------------------------------------- 4 Point [ 1, 129, 362, 979 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 524, 503, 766 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 558, 739, 47 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 623, 1002, 98 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 982, 8, 729 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 29822521*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 29822521*x over Rational Field function(p) ... end function (219836805842156751818841232515787/974857411744724062308148201 : 3258541272274600289877540372970155745332954925476/30437687011104535504379607498\ 696175437301 : 1) 65.52944669907576269451 Total time: 8.500 seconds, Total memory usage: 10.30MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:40:24 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-57335184,0]); g := TwoDescent(E); S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:40:09 on modular [Seed = 489445143] ------------------------------------- 4 Point [ 1, 327, 376, 776 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 57335184*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 3583449*x over Rational Field function(p) ... end function (104215459691502827700382779446307/30269646419561748862746222049 : 888647787568665906231710421126995045443216028820/526636580250862594168563735795\ 7449310168657 : 1) 66.043645339308426400748 Total time: 7.490 seconds, Total memory usage: 12.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:42:40 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-67732900,0]); g := TwoDescent(E); S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:41:14 on modular [Seed = 3771836969] ------------------------------------- 4 Point [ 1, 0, 0, 0 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 500, 587, 119 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 500, 422, 890 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 509, 154, 316 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 509, 855, 693 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 10.939 seconds, Total memory usage: 10.12MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:43:35 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-67732900,0]); g := TwoDescent(E); S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:43:09 on modular [Seed = 3146446565] ------------------------------------- FourDescent( f: x^4 + 49380*x^2 + 67732900 ) ReduceFD( fd: [ [ -5 6 0 0] [ 6 -7 0 0] [ 0... ) StollReduce( desc: [ [ 0 0 5810 24690] [ 0 0 -6778 -28805... ) Covariant( mat1: [ 0 0 5810 24690] [ 0 0 -6778 -28805] ..., mat2: [ 5 -6 0 0] [ -6 7 0 0] ... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 303, column 29: >> trans2 := trans1^-1; ^ Runtime error in '^': Division by zero in (possibly) real or complex division. Maybe loss of precision? >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S[1]; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,1000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field >> AssociatedEC(F); ^ User error: Identifier 'F' has not been declared or assigned >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 4.950 seconds, Total memory usage: 7.75MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:44:12 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-67732900,0]); g := TwoDescent(E); #g S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:44:10 on modular [Seed = 2912739508] ------------------------------------- >> S := FourDescent(g[3]); ^ User error: bad syntax >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S[1]; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,1000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field >> AssociatedEC(F); ^ User error: Identifier 'F' has not been declared or assigned >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.980 seconds, Total memory usage: 5.93MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:45:18 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-67732900,0]); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 13:44:35 on modular [Seed = 2594953069] ------------------------------------- 7 Errors: /bin/sh: line 1: 13033 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:45:47 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-67732900,0]); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:45:30 on modular [Seed = 2361246021] ------------------------------------- 7 4 Point [ 1, 262, 270, 921 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 996, 443, 104 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field function(p) ... end function (253925231010532663432964331594005/6391445081649616066085319841 : -3958535606004859444939964064509149215792204823275/5109737529367398385721536668\ 31705027275889 : 1) 66.38042152398087125675 Total time: 8.339 seconds, Total memory usage: 15.80MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:46:59 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-63059481,0]); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:46:18 on modular [Seed = 1700014333] ------------------------------------- 7 4 Point [ 1, 598, 20, 235 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 63059481*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 63059481*x over Rational Field function(p) ... end function (3464571045146487971180651019126867/179826891841656233510952918481 : 185798736247955242185318846831785254050275892974796/762573935018511736405678014\ 71514991561307879 : 1) 68.066624243197622945444 Total time: 20.269 seconds, Total memory usage: 13.44MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:48:38 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-10169721,0]); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:48:06 on modular [Seed = 990541599] ------------------------------------- 7 4 Point [ 1, 253, 943, 266 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 400, 420, 6 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10169721*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10169721*x over Rational Field function(p) ... end function (1965575537930259018265536242704083/599819728649740796780399346721 : 20053222811245828075935743202324394783861138563732/4645485608973825560766274641\ 61950607294013519 : 1) 68.58630544864885791866 Total time: 16.000 seconds, Total memory usage: 12.78MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:57:04 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-97555129,0]); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 13:56:21 on modular [Seed = 1984378950] ------------------------------------- 7 Errors: /bin/sh: line 1: 13315 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:57:48 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-97555129,0]); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 13:57:15 on modular [Seed = 1818042978] ------------------------------------- 7 FourDescent( f: x^4 + 390220516 ) ReduceFD( fd: [ [ 0 -194405 0 -3952] [-194405 -388810 -211868... ) StollReduce( desc: [ [0 0 0 1] [0 0 1 1] [0 1 0 0] [1 1 0 0], [ 11841381545 ... ) Covariant( mat1: [0 0 0 1] [0 0 1 1] [0 1 0 0] [1 1 0 0], mat2: [ 11841381545 65517545667 42 -87... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 350, column 33: >> covmat *:= 1/Sqrt(&+[Norm(c) : c in Eltseq(covmat)]); ^ Runtime error in '/': Division by zero >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S[1]; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,1000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 97555129*x over Rational Field >> AssociatedEC(F); ^ User error: Identifier 'F' has not been declared or assigned >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.880 seconds, Total memory usage: 28.90MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 13:57:59 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-97555129,0]); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 13:54:03 on modular [Seed = 2811684974] ------------------------------------- 7 Errors: /bin/sh: line 1: 13269 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:01:46 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-97555129,0]); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:00:14 on modular [Seed = 4224363168] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 97555129*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 97555129*x over Rational Field function(p) ... end function (54104825871641124706206387105790236/275529335853229300926930625 : 12585022749576367850741973761111953571197136889020766/4573532483987292207147016\ 173056817390625 : 1) 75.19713094377354423158 Total time: 8.119 seconds, Total memory usage: 25.08MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:06:55 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); g := TwoDescent(E); g; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 14:06:13 on modular [Seed = 1615933569] ------------------------------------- Errors: /bin/sh: line 1: 13588 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:07:02 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); g := TwoDescent(E); #g; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 14:03:06 on modular [Seed = 3197103889] ------------------------------------- Errors: /bin/sh: line 1: 13515 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:08:52 2004 Input: E := EllipticCurve( [0,0,0,-56385081,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 14:08:10 on modular [Seed = 588410973] ------------------------------------- 7 Errors: /bin/sh: line 1: 13655 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:10:10 2004 Input: E := EllipticCurve( [0,0,0,-56385081,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:09:27 on modular [Seed = 506416445] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 191, 47, 104 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 191, 962, 905 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 818, 155, 344 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 818, 854, 665 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 56385081*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 56385081*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.640 seconds, Total memory usage: 12.95MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:11:02 2004 Input: P := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); g := TwoDescent(E); g; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Fri Oct 15 2004 14:07:06 on modular [Seed = 1081151742] ------------------------------------- Errors: /bin/sh: line 1: 13620 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:12:21 2004 Input: E := EllipticCurve( [0,0,0,-56385081,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:11:10 on modular [Seed = 3771839274] ------------------------------------- 7 4 Point [ 1, 129, 600, 586 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 56385081*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 56385081*x over Rational Field function(p) ... end function (-7844996904618812306881929059284707/10297227098672094717357345373921 : 6813212002164434109838166961540542941324456643558652/33043073499034311589622301\ 192163903847508565969 : 1) 78.93283437148434700247 Total time: 6.360 seconds, Total memory usage: 13.49MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:15:08 2004 Input: E := EllipticCurve( [0,0,0,-48177481,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:13:41 on modular [Seed = 3213815198] ------------------------------------- 7 4 Point [ 1, 102, 154, 214 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 467, 877, 139 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 601, 827, 302 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 956, 663, 638 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 48177481*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 48177481*x over Rational Field function(p) ... end function (212555108015339509897232195377729168619/6784419343339427159073667553435041 : 3021890666158908445828276190652152526552796323075227773980/55881624865935877688\ 0593633349638929481731403152911 : 1) 79.15441387973852727100 Total time: 7.809 seconds, Total memory usage: 14.22MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:20:39 2004 Input: E := EllipticCurve( [0,0,0,-41332041,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:17:24 on modular [Seed = 1415905559] ------------------------------------- 7 4 Point [ 1, 107, 258, 195 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 438, 464, 574 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 744, 332, 765 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 41332041*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 41332041*x over Rational Field function(p) ... end function (302145718808297001518152133535621264668547/17652467155695133516404957189495812\ 329 : -153922135402658586109750945737438775144313685822414062558690196/74166556\ 956921081880460621563203426363583356187458630517 : 1) 86.54860520542656843190 Total time: 17.399 seconds, Total memory usage: 14.47MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:25:31 2004 Input: E := EllipticCurve( [0,0,0,-24970009,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:24:00 on modular [Seed = 3538126437] ------------------------------------- 7 4 Point [ 1, 788, 874, 649 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 998, 195, 219 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 24970009*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 24970009*x over Rational Field function(p) ... end function (116667007906201297800863929926005341562780179/66538218470059510969692163395810\ 37475025 : -1207891071184016366607227370906321400821749535025774097552008365092\ /542758649257154530432617627832755006498838987960748452937625 : 1) 92.72320914078325415630 Total time: 8.109 seconds, Total memory usage: 14.62MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:27:29 2004 Input: E := EllipticCurve( [0,0,0,-19616041,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:26:10 on modular [Seed = 2744317079] ------------------------------------- 7 4 Point [ 1, 518, 776, 867 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 851, 881, 613 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 19616041*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 19616041*x over Rational Field function(p) ... end function (35147940166332759955384638553322602845862539547/675903191864256923687585644298\ 6940073664449 : 345299587231182967670878795901029380607693868702897265805714270\ 2787236/17572224617879657189046238764846369578239447179714165751967656543 : 1) 98.73849691281249363328 Total time: 6.980 seconds, Total memory usage: 8.93MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:29:01 2004 Input: E := EllipticCurve( [0,0,0,-55413136,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:28:20 on modular [Seed = 2276905012] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 55413136*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 3463321*x over Rational Field function(p) ... end function (-13253573926357265391988337602939745453384100/95653266474015151920048956832233\ 58854881 : 43262947450183507799087329987890387341113359979681620580807250610/93\ 5512744081868556297605527822955158599073959805351695000529 : 1) 99.86135021028670166742 Total time: 3.669 seconds, Total memory usage: 6.37MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:31:27 2004 Input: E := EllipticCurve( [0,0,0,-72403081,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:29:55 on modular [Seed = 1933714726] ------------------------------------- 7 4 Point [ 1, 29, 52, 449 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 557, 134, 813 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 735, 752, 588 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 823, 604, 521 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 995, 840, 449 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 72403081*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 72403081*x over Rational Field function(p) ... end function (-153293591980201190438053026914594568907222057167/2094642465983214560883916251\ 6896174351676484 : 356012665119414745550891349193592727768694733248664703433497\ 02193620607/95866054999438583284683228771152931532756946172615478618085431352 : 1) 100.058052636127641221719 Total time: 8.179 seconds, Total memory usage: 11.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:33:37 2004 Input: E := EllipticCurve( [0,0,0,-6620329,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:32:30 on modular [Seed = 1114838154] ------------------------------------- 7 4 Point [ 1, 378, 445, 156 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 525, 551, 678 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 540, 794, 496 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6620329*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6620329*x over Rational Field function(p) ... end function (-59518455217887800639461164126771110277907673775/23777864448661118143069669786\ 291113658816036 : -345534715113125327318907336730422064955498537378322360210540\ 5966105265/115946934365738093020581118050199362464437923051372878214545344216 : 1) 100.21648746229523396777 Total time: 5.990 seconds, Total memory usage: 25.71MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:37:39 2004 Input: E := EllipticCurve( [0,0,0,-31775769,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:34:01 on modular [Seed = 689467462] ------------------------------------- 7 4 Point [ 1, 56, 984, 408 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 619, 72, 427 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 883, 628, 914 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 31775769*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 31775769*x over Rational Field function(p) ... end function (749880702747372491200510621846726950270537096222157683/11586695304268960915475\ 4098952331063978494410938609 : -31902780650338416386358810719639477085382334504\ 7943727560938624989837554704493500/12472094123248413102900773317039024897150078\ 20647563329443072433501880500023 : 1) 115.37871242136358773677 Total time: 19.449 seconds, Total memory usage: 16.16MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:40:58 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:39:13 on modular [Seed = 3771840711] ------------------------------------- 7 4 Point [ 1, 160, 882, 599 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 737, 468, 4 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 882, 160, 410 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 9.320 seconds, Total memory usage: 13.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:45:19 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:42:30 on modular [Seed = 3990664845] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 1000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.060 seconds, Total memory usage: 7.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:48:33 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,600); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:45:44 on modular [Seed = 2510605883] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 600 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.050 seconds, Total memory usage: 7.53MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:51:40 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:48:50 on modular [Seed = 1415909055] ------------------------------------- 7 4 >> pts := Points(F); ^ Runtime error in 'Points': Bad argument types Argument types given: SeqEnum[AlgMatElt] Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.130 seconds, Total memory usage: 7.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 14:54:57 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 14:51:55 on modular [Seed = 222056511] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function (3167 : 0 : 1) 0.E-92 Total time: 16.219 seconds, Total memory usage: 7.48MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 15:07:04 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 15:06:17 on modular [Seed = 489440204] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 503 and ignored at the #3 lift Point [ 1, 389, 49, 53 ] was singular mod 503 and ignored at the #1 lift Point [ 1, 389, 454, 450 ] was singular mod 503 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 9.099 seconds, Total memory usage: 7.42MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 15:13:30 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 15:13:20 on modular [Seed = 1348546683] ------------------------------------- 7 4 Point [ 1, 55, 96, 472 ] was singular mod 503 and ignored at the #1 lift Point [ 1, 155, 252, 477 ] was singular mod 503 and ignored at the #1 lift Point [ 1, 329, 205, 400 ] was singular mod 503 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 4.809 seconds, Total memory usage: 6.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 15:14:56 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 15:13:51 on modular [Seed = 1081155668] ------------------------------------- 7 4 Point [ 1, 239, 477, 59 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 648, 54, 316 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 910, 674, 32 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 5.860 seconds, Total memory usage: 6.31MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 15:15:32 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 15:15:12 on modular [Seed = 287338922] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 9.839 seconds, Total memory usage: 7.39MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.152 (66.63.132.152) Time: Fri Oct 15 15:16:16 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Fri Oct 15 2004 15:15:47 on modular [Seed = 4224359267] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 1000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.769 seconds, Total memory usage: 7.36MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:05:50 2004 Input: modpow(2,3,5) Output: Magma V2.11-6 Fri Oct 15 2004 16:05:48 on modular [Seed = 3622222666] ------------------------------------- >> modpow(2,3,5); ^ User error: Identifier 'modpow' has not been declared or assigned Total time: 0.230 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:06:05 2004 Input: ModPow(2,3,5) Output: Magma V2.11-6 Fri Oct 15 2004 16:06:05 on modular [Seed = 3855911241] ------------------------------------- >> ModPow(2,3,5); ^ User error: Identifier 'ModPow' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:09:08 2004 Input: ModExp(2,3,5) Output: Magma V2.11-6 Fri Oct 15 2004 16:09:08 on modular [Seed = 1818034952] ------------------------------------- >> ModExp(2,3,5); ^ User error: Identifier 'ModExp' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:09:37 2004 Input: Modexp(2,3,5) Output: Magma V2.11-6 Fri Oct 15 2004 16:09:36 on modular [Seed = 2243226117] ------------------------------------- 3 Total time: 0.190 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:09:56 2004 Input: Modexp(2,3,5) Output: Magma V2.11-6 Fri Oct 15 2004 16:09:56 on modular [Seed = 2577987085] ------------------------------------- 3 Total time: 0.190 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:10:10 2004 Input: D(x^2,x) Output: Magma V2.11-6 Fri Oct 15 2004 16:10:10 on modular [Seed = 2761280262] ------------------------------------- >> D(x^2,x); ^ User error: Identifier 'x' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:12:46 2004 Input: Modexp(2,3,5) Output: Magma V2.11-6 Fri Oct 15 2004 16:12:44 on modular [Seed = 1432632170] ------------------------------------- 3 Total time: 0.190 seconds, Total memory usage: 3.50MB '84.80.2' ************** MAGMA ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:13:20 2004 Input: Modexp(2,97725217,97725217) Output: Magma V2.11-6 Fri Oct 15 2004 16:13:20 on modular [Seed = 1933712656] ------------------------------------- 2 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:51:38 2004 Input: P := PolynomialRing(GF(2)); f := x^136 + x^11 + x^2 + x + 1; F := ext; F; Output: Magma V2.11-6 Fri Oct 15 2004 16:51:37 on modular [Seed = 1933707820] ------------------------------------- Finite field of size 2^136 Total time: 0.210 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:52:10 2004 Input: P := PolynomialRing(GF(2)); f := x^136 + x^11 + x^2 + x + 1; F := ext; F; DefiningPolynomial(F); Output: Magma V2.11-6 Fri Oct 15 2004 16:52:10 on modular [Seed = 2192833533] ------------------------------------- Finite field of size 2^136 x^136 + x^11 + x^2 + x + 1 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:52:24 2004 Input: P := PolynomialRing(GF(2)); f := x^136 + x^11 + x^2 + x + 1; f; F := ext; F; DefiningPolynomial(F); Output: Magma V2.11-6 Fri Oct 15 2004 16:52:24 on modular [Seed = 2310598660] ------------------------------------- x^136 + x^11 + x^2 + x + 1 Finite field of size 2^136 x^136 + x^11 + x^2 + x + 1 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:52:30 2004 Input: P := PolynomialRing(GF(2)); f := x^136 + x^11 + x^2 + x + 1; f; F := ext; F; DefiningPolynomial(F); Output: Magma V2.11-6 Fri Oct 15 2004 16:52:29 on modular [Seed = 2493902108] ------------------------------------- x^136 + x^11 + x^2 + x + 1 Finite field of size 2^136 x^136 + x^11 + x^2 + x + 1 Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:53:10 2004 Input: P := PolynomialRing(GF(2)); P; Output: Magma V2.11-6 Fri Oct 15 2004 16:53:09 on modular [Seed = 2710624273] ------------------------------------- >> P := PolynomialRing(GF(2)); ^ Runtime error in 'AssignNames': Argument 2 must have length 1 Univariate Polynomial Ring over GF(2) Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:53:21 2004 Input: P := PolynomialRing(GF(2), 3); P; Output: Magma V2.11-6 Fri Oct 15 2004 16:53:21 on modular [Seed = 2896024936] ------------------------------------- Polynomial ring of rank 3 over GF(2) Lexicographical Order Variables: x, y, z Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:53:59 2004 Input: P := PolynomialRing(GF(2), 136); P; Output: Magma V2.11-6 Fri Oct 15 2004 16:53:59 on modular [Seed = 2994981712] ------------------------------------- >> P := PolynomialRing(GF(2), 136); ^ User error: bad syntax >> P;; ^ User error: Identifier 'P' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:54:05 2004 Input: P := PolynomialRing(GF(2), 136); P; Output: Magma V2.11-6 Fri Oct 15 2004 16:54:05 on modular [Seed = 3354836527] ------------------------------------- >> P := PolynomialRing(GF(2), 136); ^ User error: bad syntax >> P;; ^ User error: Identifier 'P' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:54:58 2004 Input: sx := ; sx; Output: Magma V2.11-6 Fri Oct 15 2004 16:54:58 on modular [Seed = 3605507825] ------------------------------------- >> sx := ; ^ User error: Identifier 'x' has not been declared or assigned >> sx;; ^ User error: Identifier 'sx' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:57:06 2004 Input: [1 .. 136]; Output: Magma V2.11-6 Fri Oct 15 2004 16:57:06 on modular [Seed = 4173955167] ------------------------------------- [ 1 .. 136 ] Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:57:22 2004 Input: X := [1 .. 136]; Output: Magma V2.11-6 Fri Oct 15 2004 16:57:22 on modular [Seed = 104300208] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:57:27 2004 Input: X := [1 .. 136]; X; Output: Magma V2.11-6 Fri Oct 15 2004 16:57:27 on modular [Seed = 53640112] ------------------------------------- [ 1 .. 136 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:57:40 2004 Input: X := [1 .. 136]; X; X[5]; Output: Magma V2.11-6 Fri Oct 15 2004 16:57:40 on modular [Seed = 472736988] ------------------------------------- [ 1 .. 136 ] 5 Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 16:58:51 2004 Input: F := GF(2^136); F; Output: Magma V2.11-6 Fri Oct 15 2004 16:58:50 on modular [Seed = 773805344] ------------------------------------- Finite field of size 2^136 Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:01:24 2004 Input: n := 136; for i in [1 .. n] do print(x); print(i); print(", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:01:24 on modular [Seed = 1449602550] ------------------------------------- >> print(x); ^ User error: Identifier 'x' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:01:36 2004 Input: n := 136; for i in [1 .. n] do print('x'); print(i); print(", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:01:36 on modular [Seed = 1398941927] ------------------------------------- >> print('x'); ^ User error: Identifier 'x' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:01:43 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(i); print(", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:01:43 on modular [Seed = 1483285483] ------------------------------------- x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 , x 9 , x 10 , x 11 , x 12 , x 13 , x 14 , x 15 , x 16 , x 17 , x 18 , x 19 , x 20 , x 21 , x 22 , x 23 , x 24 , x 25 , x 26 , x 27 , x 28 , x 29 , x 30 , x 31 , x 32 , x 33 , x 34 , x 35 , x 36 , x 37 , x 38 , x 39 , x 40 , x 41 , x 42 , x 43 , x 44 , x 45 , x 46 , x 47 , x 48 , x 49 , x 50 , x 51 , x 52 , x 53 , x 54 , x 55 , x 56 , x 57 , x 58 , x 59 , x 60 , x 61 , x 62 , x 63 , x 64 , x 65 , x 66 , x 67 , x 68 , x 69 , x 70 , x 71 , x 72 , x 73 , x 74 , x 75 , x 76 , x 77 , x 78 , x 79 , x 80 , x 81 , x 82 , x 83 , x 84 , x 85 , x 86 , x 87 , x 88 , x 89 , x 90 , x 91 , x 92 , x 93 , x 94 , x 95 , x 96 , x 97 , x 98 , x 99 , x 100 , x 101 , x 102 , x 103 , x 104 , x 105 , x 106 , x 107 , x 108 , x 109 , x 110 , x 111 , x 112 , x 113 , x 114 , x 115 , x 116 , x 117 , x 118 , x 119 , x 120 , x 121 , x 122 , x 123 , x 124 , x 125 , x 126 , x 127 , x 128 , x 129 , x 130 , x 131 , x 132 , x 133 , x 134 , x 135 , x 136 , Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:02:07 2004 Input: n := 136; for i in [1 .. n] do print("x",i,", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:02:07 on modular [Seed = 1818040231] ------------------------------------- >> print("x",i,", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:02:15 2004 Input: n := 136; for i in [1 .. n] do print("x", i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:02:15 on modular [Seed = 1767379642] ------------------------------------- >> print("x", i, ", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:02:37 2004 Input: sx := ; sx; Output: Magma V2.11-6 Fri Oct 15 2004 17:02:37 on modular [Seed = 2102134420] ------------------------------------- >> sx := ; ^ User error: Identifier 'x' has not been declared or assigned >> sx;; ^ User error: Identifier 'sx' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:03:02 2004 Input: ? print; Output: Magma V2.11-6 Fri Oct 15 2004 17:03:01 on modular [Seed = 2175859584] ------------------------------------- 35 matches: 1 O /language/statement/print 2 S /language/IO/print 3 S /language/IO/print/auto-print 4 S /language/IO/print/print 5 S /magma/combinatorial-geometrical-incidence/MultiGraph/\ multig-constr/multi-print 6 S /magma/combinatorial-geometrical-incidence/network/\ network-constr/network-print 7 S /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access 8 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/print 9 S /magma/ring-field-algebra/finitely-presented/algebras/print 10 I /language/IO/print/print/print 11 I /language/IO/print/printing-file/PrintFile 12 I /language/IO/print/printing-file/PrintFile 13 I /language/IO/print/printing-file/PrintFileMagma 14 I /magma/group/braid/braid-groups-construction/GetElementPrintFormat 15 I /magma/group/braid/braid-groups-construction/SetElementPrintFormat 16 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintCollector 17 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 18 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 19 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 20 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 21 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintPrimes 22 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 23 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 24 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintQuotient 25 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintRelat 26 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintSeries 27 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree 28 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision 29 I /system/environment-options/Set-Get/SetPrintLevel 30 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalCount 31 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalTime 32 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 33 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 34 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime 35 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime To view an entry, type ? followed by the number next to it Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:03:22 2004 Input: ? 1; Output: Magma V2.11-6 Fri Oct 15 2004 17:03:22 on modular [Seed = 2493902474] ------------------------------------- No references for word "1;" Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:03:36 2004 Input: ? print; ? 1; Output: Magma V2.11-6 Fri Oct 15 2004 17:03:36 on modular [Seed = 2443242429] ------------------------------------- 35 matches: 1 O /language/statement/print 2 S /language/IO/print 3 S /language/IO/print/auto-print 4 S /language/IO/print/print 5 S /magma/combinatorial-geometrical-incidence/MultiGraph/\ multig-constr/multi-print 6 S /magma/combinatorial-geometrical-incidence/network/\ network-constr/network-print 7 S /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access 8 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/print 9 S /magma/ring-field-algebra/finitely-presented/algebras/print 10 I /language/IO/print/print/print 11 I /language/IO/print/printing-file/PrintFile 12 I /language/IO/print/printing-file/PrintFile 13 I /language/IO/print/printing-file/PrintFileMagma 14 I /magma/group/braid/braid-groups-construction/GetElementPrintFormat 15 I /magma/group/braid/braid-groups-construction/SetElementPrintFormat 16 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintCollector 17 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 18 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 19 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 20 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 21 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintPrimes 22 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 23 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 24 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintQuotient 25 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintRelat 26 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintSeries 27 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree 28 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision 29 I /system/environment-options/Set-Get/SetPrintLevel 30 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalCount 31 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalTime 32 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 33 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 34 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime 35 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime To view an entry, type ? followed by the number next to it No references for word "1;" Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:03:45 2004 Input: ? print; ? 1 Output: Magma V2.11-6 Fri Oct 15 2004 17:03:45 on modular [Seed = 2662327467] ------------------------------------- 35 matches: 1 O /language/statement/print 2 S /language/IO/print 3 S /language/IO/print/auto-print 4 S /language/IO/print/print 5 S /magma/combinatorial-geometrical-incidence/MultiGraph/\ multig-constr/multi-print 6 S /magma/combinatorial-geometrical-incidence/network/\ network-constr/network-print 7 S /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access 8 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/print 9 S /magma/ring-field-algebra/finitely-presented/algebras/print 10 I /language/IO/print/print/print 11 I /language/IO/print/printing-file/PrintFile 12 I /language/IO/print/printing-file/PrintFile 13 I /language/IO/print/printing-file/PrintFileMagma 14 I /magma/group/braid/braid-groups-construction/GetElementPrintFormat 15 I /magma/group/braid/braid-groups-construction/SetElementPrintFormat 16 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintCollector 17 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 18 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 19 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 20 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 21 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintPrimes 22 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 23 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 24 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintQuotient 25 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintRelat 26 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintSeries 27 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree 28 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision 29 I /system/environment-options/Set-Get/SetPrintLevel 30 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalCount 31 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalTime 32 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 33 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 34 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime 35 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/statement/print KIND: Overview =============================================================================== The print-statement allows you to evaluate an expression and see the result as output. It has the syntax > print EXPRESSION; If the values of several expressions are required, they may be placed in the one print-statement, separated by commas: > print EXPRESSION, EXPRESSION, ..., EXPRESSION; Like all statements, a print-statement must end with a semicolon ( ; ). EXAMPLE: > print 60 * 24; 1440 > x := 7; > print x, 5 * x, x ^ 2; 7 35 49 > print Centre(DihedralGroup(GrpPerm, 8)); Permutation group acting on a set of cardinality 8 Order = 2 (1, 5)(2, 6)(3, 7)(4, 8) SEE ALSO: +1 /language/IO/print/printing-file/PrintFile =============================================================================== Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:04:03 2004 Input: ? print; ? 5 Output: Magma V2.11-6 Fri Oct 15 2004 17:04:02 on modular [Seed = 2710625255] ------------------------------------- 35 matches: 1 O /language/statement/print 2 S /language/IO/print 3 S /language/IO/print/auto-print 4 S /language/IO/print/print 5 S /magma/combinatorial-geometrical-incidence/MultiGraph/\ multig-constr/multi-print 6 S /magma/combinatorial-geometrical-incidence/network/\ network-constr/network-print 7 S /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access 8 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/print 9 S /magma/ring-field-algebra/finitely-presented/algebras/print 10 I /language/IO/print/print/print 11 I /language/IO/print/printing-file/PrintFile 12 I /language/IO/print/printing-file/PrintFile 13 I /language/IO/print/printing-file/PrintFileMagma 14 I /magma/group/braid/braid-groups-construction/GetElementPrintFormat 15 I /magma/group/braid/braid-groups-construction/SetElementPrintFormat 16 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintCollector 17 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 18 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 19 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 20 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 21 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintPrimes 22 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 23 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 24 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintQuotient 25 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintRelat 26 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintSeries 27 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree 28 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision 29 I /system/environment-options/Set-Get/SetPrintLevel 30 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalCount 31 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalTime 32 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 33 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 34 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime 35 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/MultiGraph/multig-constr/\ multi-print KIND: Section =============================================================================== Printing of a Multi(di)graph. A multi(di)graph is displayed by listing, for each vertex, all of its adjacent vertices. If the multigraph has multiple edges from u to v, then the adjacency list of u contains as many copies of the vertex v as there are edges from u to v. The vertices in the adjacency list are not ordered, they appear in the order in which they were created. See the previous examples H109E1 and H109E2. =============================================================================== Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:04:53 2004 Input: ? print; ? 26 Output: Magma V2.11-6 Fri Oct 15 2004 17:04:52 on modular [Seed = 3011692995] ------------------------------------- 35 matches: 1 O /language/statement/print 2 S /language/IO/print 3 S /language/IO/print/auto-print 4 S /language/IO/print/print 5 S /magma/combinatorial-geometrical-incidence/MultiGraph/\ multig-constr/multi-print 6 S /magma/combinatorial-geometrical-incidence/network/\ network-constr/network-print 7 S /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access 8 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/print 9 S /magma/ring-field-algebra/finitely-presented/algebras/print 10 I /language/IO/print/print/print 11 I /language/IO/print/printing-file/PrintFile 12 I /language/IO/print/printing-file/PrintFile 13 I /language/IO/print/printing-file/PrintFileMagma 14 I /magma/group/braid/braid-groups-construction/GetElementPrintFormat 15 I /magma/group/braid/braid-groups-construction/SetElementPrintFormat 16 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintCollector 17 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 18 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintExtensions 19 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 20 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintModules 21 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintPrimes 22 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 23 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintProcess 24 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintQuotient 25 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintRelat 26 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/print-access/PrintSeries 27 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintTermsOfDegree 28 I /magma/ring-field-algebra/lazy/elements/coeffs/PrintToPrecision 29 I /system/environment-options/Set-Get/SetPrintLevel 30 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalCount 31 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintByTotalTime 32 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 33 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByCount 34 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime 35 I /system/Profiler/call-graph/internal-reports/\ ProfilePrintChildrenByTime To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/group/finitely-presented-groups-advanced/soluble-quotients/\ print-access/PrintSeries KIND: Intrinsic =============================================================================== PrintSeries(SQP) : SQProc -> Print: RngIntElt Default: 1 Prints information about the weight series, if calculated. Optionally, the list of modules and tails used for the construction of the soluble quotient is printed. The different print functions are sampled in the following functions. The optional argument Print is replaced by a set of optional arguments, specifying the amount of printing for each corresponding topic. =============================================================================== Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:05:58 2004 Input: n := 136; for i in [1 .. n] do print("x", i); print(", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:05:58 on modular [Seed = 3388519291] ------------------------------------- >> print("x", i); ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:06:17 2004 Input: n := 136; for i in [1 .. n] do print("x") print(i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:06:17 on modular [Seed = 3706562065] ------------------------------------- >> print(i, ", "); ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:06:23 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:06:23 on modular [Seed = 3655901970] ------------------------------------- x >> print(i, ", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:06:35 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(i + ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:06:35 on modular [Seed = 3788544830] ------------------------------------- x >> print(i + ", "); ^ Runtime error in '+': Bad argument types Argument types given: RngIntElt, MonStgElt Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:06:41 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:06:41 on modular [Seed = 4007629835] ------------------------------------- x >> print(i, ", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:07:01 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(%i%c, i, ", "); end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:07:12 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(i c, i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:07:11 on modular [Seed = 4241327623] ------------------------------------- >> print(i c, i, ", "); ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:07:27 2004 Input: n := 136; for i in [1 .. n] do print("x"); print(i); print(", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:07:26 on modular [Seed = 4190668019] ------------------------------------- x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 , x 9 , x 10 , x 11 , x 12 , x 13 , x 14 , x 15 , x 16 , x 17 , x 18 , x 19 , x 20 , x 21 , x 22 , x 23 , x 24 , x 25 , x 26 , x 27 , x 28 , x 29 , x 30 , x 31 , x 32 , x 33 , x 34 , x 35 , x 36 , x 37 , x 38 , x 39 , x 40 , x 41 , x 42 , x 43 , x 44 , x 45 , x 46 , x 47 , x 48 , x 49 , x 50 , x 51 , x 52 , x 53 , x 54 , x 55 , x 56 , x 57 , x 58 , x 59 , x 60 , x 61 , x 62 , x 63 , x 64 , x 65 , x 66 , x 67 , x 68 , x 69 , x 70 , x 71 , x 72 , x 73 , x 74 , x 75 , x 76 , x 77 , x 78 , x 79 , x 80 , x 81 , x 82 , x 83 , x 84 , x 85 , x 86 , x 87 , x 88 , x 89 , x 90 , x 91 , x 92 , x 93 , x 94 , x 95 , x 96 , x 97 , x 98 , x 99 , x 100 , x 101 , x 102 , x 103 , x 104 , x 105 , x 106 , x 107 , x 108 , x 109 , x 110 , x 111 , x 112 , x 113 , x 114 , x 115 , x 116 , x 117 , x 118 , x 119 , x 120 , x 121 , x 122 , x 123 , x 124 , x 125 , x 126 , x 127 , x 128 , x 129 , x 130 , x 131 , x 132 , x 133 , x 134 , x 135 , x 136 , Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:09:54 2004 Input: n := 136; for i in [1 .. n] do print("x" cat i cat ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:09:54 on modular [Seed = 3243429] ------------------------------------- >> print("x" cat i cat ", "); ^ Runtime error in 'cat': Bad argument types Argument types given: MonStgElt, RngIntElt Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:10:10 2004 Input: n := 136; for i in [1 .. n] do print(("x" cat i cat ", ")); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:10:10 on modular [Seed = 188380862] ------------------------------------- >> print(("x" cat i cat ", ")); ^ Runtime error in 'cat': Bad argument types Argument types given: MonStgElt, RngIntElt Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:10:17 2004 Input: n := 136; for i in [1 .. n] do print(["x" cat i cat ", "]); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:10:17 on modular [Seed = 371682216] ------------------------------------- >> print(["x" cat i cat ", "]); ^ Runtime error in 'cat': Bad argument types Argument types given: MonStgElt, RngIntElt Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:10:26 2004 Input: n := 136; for i in [1 .. n] do print(<"x" cat i cat ", ">); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:10:26 on modular [Seed = 287337684] ------------------------------------- >> print(<"x" cat i cat ", ">); ^ Runtime error in 'cat': Bad argument types Argument types given: MonStgElt, RngIntElt Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:10:45 2004 Input: n := 136; for i in [1 .. n] do print("x" &cat i cat ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:10:44 on modular [Seed = 455763656] ------------------------------------- >> print("x" &cat i cat ", "); ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:10:50 2004 Input: n := 136; for i in [1 .. n] do print("x" & i cat ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:10:50 on modular [Seed = 639065083] ------------------------------------- >> print("x" & i cat ", "); ^ User error: Bad reduction operator >> end for; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:11:17 2004 Input: n := 136; for i in [1 .. n] do print("xi, "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:11:17 on modular [Seed = 554720467] ------------------------------------- xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, xi, Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:13:08 2004 Input: n := 136; for i in [1 .. n] do print(x); print("xi, "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:13:07 on modular [Seed = 906447442] ------------------------------------- >> print(x); ^ User error: Identifier 'x' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:13:13 2004 Input: n := 136; for i in [1 .. n] do print('x'); print("xi, "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:13:13 on modular [Seed = 822103391] ------------------------------------- >> print('x'); ^ User error: Identifier 'x' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:13:20 2004 Input: n := 136; for i in [1 .. n] do print("x"); print("xi, "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:13:19 on modular [Seed = 1007501396] ------------------------------------- x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, x xi, Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:13:29 2004 Input: n := 136; for i in [1 .. n] do print("x",i); print("xi, "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:13:29 on modular [Seed = 1198930745] ------------------------------------- >> print("x",i); ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:13:31 2004 Input: n := 136; for i in [1 .. n] do print("x",i); print("xi, "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:13:31 on modular [Seed = 1114848830] ------------------------------------- >> print("x",i); ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:14:53 2004 Input: n := 136; Q := [Sprint("x", i, ", "): i in [1 .. 136]]; Q; Output: Magma V2.11-6 Fri Oct 15 2004 17:14:52 on modular [Seed = 1299984774] ------------------------------------- >> Q := [Sprint("x", i, ", "): i in [1 .. 136]]; ^ Runtime error in 'Sprint': Bad argument types Argument types given: MonStgElt, RngIntElt, MonStgElt >> Q;; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:14:58 2004 Input: n := 136; Q := [Sprintf("x", i, ", "): i in [1 .. 136]]; Q; Output: Magma V2.11-6 Fri Oct 15 2004 17:14:57 on modular [Seed = 1215902878] ------------------------------------- [ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x ] Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:16:00 2004 Input: n := 136; for i in [1 .. 136] do printf("x",i,", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:16:00 on modular [Seed = 1550656331] ------------------------------------- >> printf("x",i,", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:16:06 2004 Input: n := 136; for i in [1 .. 136] do printf("x", i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:16:06 on modular [Seed = 1733695606] ------------------------------------- >> printf("x", i, ", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:16:10 2004 Input: n := 136; for i in [1 .. 136] do printf("x", i, ", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:16:09 on modular [Seed = 1649614204] ------------------------------------- >> printf("x", i, ", "); ^ Runtime error: No constructor provided for this type of object Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:17:45 2004 Input: n := 136; for i in [1 .. 136] do printf("x%3o, ", i); end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:18:05 2004 Input: n := 136; for i in [1 .. 136] do printf("x %3o, ", i); end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:19:04 2004 Input: n := 136; for i in [1 .. 136] do printf("x"); printf(i); printf(", "); end for; Output: Magma V2.11-6 Fri Oct 15 2004 17:19:04 on modular [Seed = 2135818416] ------------------------------------- >> printf(i); ^ Runtime error in printf: Argument 1 should be a format string Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:23:28 2004 Input: R := PolynomialRing(GF(2), 136); R; Output: Magma V2.11-6 Fri Oct 15 2004 17:23:27 on modular [Seed = 2276915535] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:24:01 2004 Input: R := PolynomialRing(GF(2), 136); R;R.1; Output: Magma V2.11-6 Fri Oct 15 2004 17:24:00 on modular [Seed = 2411655544] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 $.1 Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:24:23 2004 Input: R := PolynomialRing(GF(2), 136); R;R.1; $.2; Output: Magma V2.11-6 Fri Oct 15 2004 17:24:23 on modular [Seed = 2327546762] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 $.1 >> $.2;; ^ Runtime error: Bad dollar structure Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:24:44 2004 Input: R := PolynomialRing(GF(2), 136); R;R.1; x2; Output: Magma V2.11-6 Fri Oct 15 2004 17:24:44 on modular [Seed = 2510591118] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 $.1 >> x2;; ^ User error: Identifier 'x2' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:26:18 2004 Input: F := PolynomialRing(GF(2), 136); F;F.1; Output: Magma V2.11-6 Fri Oct 15 2004 17:26:17 on modular [Seed = 2679021281] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 $.1 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:28:51 2004 Input: F := PolynomialRing(GF(2), 136); F;F.1; i := 5; F.i; Output: Magma V2.11-6 Fri Oct 15 2004 17:28:50 on modular [Seed = 2946412474] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 $.1 $.5 Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:31:04 2004 Input: [F.i : i in [1 .. 136]]; Output: Magma V2.11-6 Fri Oct 15 2004 17:31:04 on modular [Seed = 3287466844] ------------------------------------- >> [F.i : i in [1 .. 136]]; ^ User error: Identifier 'F' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:31:57 2004 Input: F := PolynomialRing(GF(2), 136); F; [F.i : i in [1 .. 136]]; Output: Magma V2.11-6 Fri Oct 15 2004 17:31:57 on modular [Seed = 3472870916] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 [ $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:32:28 2004 Input: F := PolynomialRing(GF(2), 136); F; [F.i^2 + F.i = 0 : i in [1 .. 136]]; Output: Magma V2.11-6 Fri Oct 15 2004 17:32:27 on modular [Seed = 3388524837] ------------------------------------- Polynomial ring of rank 136 over GF(2) Lexicographical Order Variables: $.1, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136 [ $.1^2 + $.1 = 0, $.2^2 + $.2 = 0, $.3^2 + $.3 = 0, $.4^2 + $.4 = 0, $.5^2 + $.5 = 0, $.6^2 + $.6 = 0, $.7^2 + $.7 = 0, $.8^2 + $.8 = 0, $.9^2 + $.9 = 0, $.10^2 + $.10 = 0, $.11^2 + $.11 = 0, $.12^2 + $.12 = 0, $.13^2 + $.13 = 0, $.14^2 + $.14 = 0, $.15^2 + $.15 = 0, $.16^2 + $.16 = 0, $.17^2 + $.17 = 0, $.18^2 + $.18 = 0, $.19^2 + $.19 = 0, $.20^2 + $.20 = 0, $.21^2 + $.21 = 0, $.22^2 + $.22 = 0, $.23^2 + $.23 = 0, $.24^2 + $.24 = 0, $.25^2 + $.25 = 0, $.26^2 + $.26 = 0, $.27^2 + $.27 = 0, $.28^2 + $.28 = 0, $.29^2 + $.29 = 0, $.30^2 + $.30 = 0, $.31^2 + $.31 = 0, $.32^2 + $.32 = 0, $.33^2 + $.33 = 0, $.34^2 + $.34 = 0, $.35^2 + $.35 = 0, $.36^2 + $.36 = 0, $.37^2 + $.37 = 0, $.38^2 + $.38 = 0, $.39^2 + $.39 = 0, $.40^2 + $.40 = 0, $.41^2 + $.41 = 0, $.42^2 + $.42 = 0, $.43^2 + $.43 = 0, $.44^2 + $.44 = 0, $.45^2 + $.45 = 0, $.46^2 + $.46 = 0, $.47^2 + $.47 = 0, $.48^2 + $.48 = 0, $.49^2 + $.49 = 0, $.50^2 + $.50 = 0, $.51^2 + $.51 = 0, $.52^2 + $.52 = 0, $.53^2 + $.53 = 0, $.54^2 + $.54 = 0, $.55^2 + $.55 = 0, $.56^2 + $.56 = 0, $.57^2 + $.57 = 0, $.58^2 + $.58 = 0, $.59^2 + $.59 = 0, $.60^2 + $.60 = 0, $.61^2 + $.61 = 0, $.62^2 + $.62 = 0, $.63^2 + $.63 = 0, $.64^2 + $.64 = 0, $.65^2 + $.65 = 0, $.66^2 + $.66 = 0, $.67^2 + $.67 = 0, $.68^2 + $.68 = 0, $.69^2 + $.69 = 0, $.70^2 + $.70 = 0, $.71^2 + $.71 = 0, $.72^2 + $.72 = 0, $.73^2 + $.73 = 0, $.74^2 + $.74 = 0, $.75^2 + $.75 = 0, $.76^2 + $.76 = 0, $.77^2 + $.77 = 0, $.78^2 + $.78 = 0, $.79^2 + $.79 = 0, $.80^2 + $.80 = 0, $.81^2 + $.81 = 0, $.82^2 + $.82 = 0, $.83^2 + $.83 = 0, $.84^2 + $.84 = 0, $.85^2 + $.85 = 0, $.86^2 + $.86 = 0, $.87^2 + $.87 = 0, $.88^2 + $.88 = 0, $.89^2 + $.89 = 0, $.90^2 + $.90 = 0, $.91^2 + $.91 = 0, $.92^2 + $.92 = 0, $.93^2 + $.93 = 0, $.94^2 + $.94 = 0, $.95^2 + $.95 = 0, $.96^2 + $.96 = 0, $.97^2 + $.97 = 0, $.98^2 + $.98 = 0, $.99^2 + $.99 = 0, $.100^2 + $.100 = 0, $.101^2 + $.101 = 0, $.102^2 + $.102 = 0, $.103^2 + $.103 = 0, $.104^2 + $.104 = 0, $.105^2 + $.105 = 0, $.106^2 + $.106 = 0, $.107^2 + $.107 = 0, $.108^2 + $.108 = 0, $.109^2 + $.109 = 0, $.110^2 + $.110 = 0, $.111^2 + $.111 = 0, $.112^2 + $.112 = 0, $.113^2 + $.113 = 0, $.114^2 + $.114 = 0, $.115^2 + $.115 = 0, $.116^2 + $.116 = 0, $.117^2 + $.117 = 0, $.118^2 + $.118 = 0, $.119^2 + $.119 = 0, $.120^2 + $.120 = 0, $.121^2 + $.121 = 0, $.122^2 + $.122 = 0, $.123^2 + $.123 = 0, $.124^2 + $.124 = 0, $.125^2 + $.125 = 0, $.126^2 + $.126 = 0, $.127^2 + $.127 = 0, $.128^2 + $.128 = 0, $.129^2 + $.129 = 0, $.130^2 + $.130 = 0, $.131^2 + $.131 = 0, $.132^2 + $.132 = 0, $.133^2 + $.133 = 0, $.134^2 + $.134 = 0, $.135^2 + $.135 = 0, $.136^2 + $.136 = 0 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:47:40 2004 Input: F := PolynomialRing(GF(2), 136); F; write("c:tempoutput.txt", [F.i^2 + F.i = 0 : i in [1 .. 136]]); Output: WARNING: MAGMA command contains unsafe command 'write', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:48:02 2004 Input: F := PolynomialRing(GF(2), 136); F; Write("c:tempoutput.txt", [F.i^2 + F.i = 0 : i in [1 .. 136]]); Output: WARNING: MAGMA command contains unsafe command 'write', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 17:48:16 2004 Input: F := PolynomialRing(GF(2), 136); F; PrintFile("c:tempoutput.txt", [F.i^2 + F.i = 0 : i in [1 .. 136]]); Output: WARNING: MAGMA command contains unsafe command 'file', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:17:38 2004 Input: P1 := PolynomialRing(GF(2)); P := PolynomialRing(GF(2), 3); X := GF(2); B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); Output: Magma V2.11-6 Fri Oct 15 2004 18:16:17 on modular [Seed = 205324597] ------------------------------------- >> B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, ^ Runtime error in '*': Bad argument types Argument types given: FldFin, RngMPolElt >> BB := B cat L; ^ User error: Identifier 'B' has not been declared or assigned >> GroebnerBasis(BB);; ^ User error: Identifier 'BB' has not been declared or assigned Total time: 0.130 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:18:39 2004 Input: P1 := PolynomialRing(GF(2)); P := PolynomialRing(GF(2), 3); X := GF(2); B := [1 + x2 + X * x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); Output: Magma V2.11-6 Fri Oct 15 2004 18:18:39 on modular [Seed = 1182223346] ------------------------------------- >> B := [1 + x2 + X * x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 ^ Runtime error in '*': Bad argument types Argument types given: FldFin, RngMPolElt >> BB := B cat L; ^ User error: Identifier 'B' has not been declared or assigned >> GroebnerBasis(BB);; ^ User error: Identifier 'BB' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:18:53 2004 Input: P1 := PolynomialRing(GF(2)); P := PolynomialRing(GF(2), 3); X := 1; B := [1 + x2 + X * x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); Output: Magma V2.11-6 Fri Oct 15 2004 18:18:53 on modular [Seed = 1348558230] ------------------------------------- [ 1 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:19:09 2004 Input: P1 := PolynomialRing(GF(2)); P := PolynomialRing(GF(2), 3); X := GF(2).1; B := [1 + x2 + X * x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); Output: Magma V2.11-6 Fri Oct 15 2004 18:19:09 on modular [Seed = 1834770619] ------------------------------------- [ 1 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:19:11 2004 Input: P1 := PolynomialRing(GF(2)); P := PolynomialRing(GF(2), 3); X := GF(2).1; B := [1 + x2 + X * x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); Output: Magma V2.11-6 Fri Oct 15 2004 18:19:10 on modular [Seed = 1615949236] ------------------------------------- [ 1 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:20:37 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); I := ideal

; Variety(I); quit; Output: Magma V2.11-6 Fri Oct 15 2004 18:20:37 on modular [Seed = 2460196524] ------------------------------------- [ 1 ] [] Total time: 0.190 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:04 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); I := ideal

; Variety(I); quit; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:03 on modular [Seed = 2693901540] ------------------------------------- [ 1 ] [] Total time: 0.200 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:05 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); I := ideal

; Variety(I); quit; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:05 on modular [Seed = 3146430433] ------------------------------------- [ 1 ] [] Total time: 0.200 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:07 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); I := ideal

; Variety(I); quit; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:06 on modular [Seed = 3197088487] ------------------------------------- [ 1 ] [] Total time: 0.200 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:11 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; GroebnerBasis(BB); I := ideal

; Variety(I); quit; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:10 on modular [Seed = 3371811989] ------------------------------------- [ 1 ] [] Total time: 0.190 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:22 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; X; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:22 on modular [Seed = 3321153964] ------------------------------------- F1.1 Total time: 0.190 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:38 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; X; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^2 + x0, x1^2 + x1, x2^2 + x2]; BB := B cat L; BB; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:37 on modular [Seed = 3723284903] ------------------------------------- F1.1 [ F1.1*x0*x2 + F1.1^2*x1^2 + F1.1^2*x1*x2 + x2^2 + x2 + 1, x0^2 + x0*x1 + F1.1^2*x0*x2 + F1.1^2*x0 + x1^2 + F1.1*x1 + x2 + 1, x0^2 + F1.1^2*x1^2 + x1*x2 + F1.1^2*x2^2 + F1.1^2*x2 + 1, x0^2 + x0, x1^2 + x1, x2^2 + x2 ] Total time: 0.190 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:21:58 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; X; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^4 + x0, x1^4 + x1, x2^4 + x2]; BB := B cat L; BB; Output: Magma V2.11-6 Fri Oct 15 2004 18:21:58 on modular [Seed = 3990675808] ------------------------------------- F1.1 [ F1.1*x0*x2 + F1.1^2*x1^2 + F1.1^2*x1*x2 + x2^2 + x2 + 1, x0^2 + x0*x1 + F1.1^2*x0*x2 + F1.1^2*x0 + x1^2 + F1.1*x1 + x2 + 1, x0^2 + F1.1^2*x1^2 + x1*x2 + F1.1^2*x2^2 + F1.1^2*x2 + 1, x0^4 + x0, x1^4 + x1, x2^4 + x2 ] Total time: 0.200 seconds, Total memory usage: 3.56MB '129.137' ************** MAGMA ***************** Host 129.137.209.109 (129.137.209.109) Time: Fri Oct 15 18:22:07 2004 Input: P1 := PolynomialRing(GF(2)); f1 := x^2 + x + 1; F1 := ext; P := PolynomialRing(F1, 3); X := F1.1; X; B := [1 + x2 + X*x0*x2 + (1 + X)*x1^2 + (1 + X)*x1*x2 + x2^2 - 0, 1 + (1 + X)*x0 + X*x1 + x2 + x0^2 + x0*x1 + (1 + X)*x0*x2 + x1^2 -0, (1 + X)*x2 + x0^2 + (1 + X)*x1^2 + x1*x2 + (1 + X)*x2^2 - 1]; L := [x0^4 + x0, x1^4 + x1, x2^4 + x2]; BB := B cat L; BB; GroebnerBasis(BB); I := ideal

; Variety(I); quit; Output: Magma V2.11-6 Fri Oct 15 2004 18:22:06 on modular [Seed = 4207670911] ------------------------------------- F1.1 [ F1.1*x0*x2 + F1.1^2*x1^2 + F1.1^2*x1*x2 + x2^2 + x2 + 1, x0^2 + x0*x1 + F1.1^2*x0*x2 + F1.1^2*x0 + x1^2 + F1.1*x1 + x2 + 1, x0^2 + F1.1^2*x1^2 + x1*x2 + F1.1^2*x2^2 + F1.1^2*x2 + 1, x0^4 + x0, x1^4 + x1, x2^4 + x2 ] [ x0 + 1, x1 + F1.1, x2 + F1.1^2 ] [ <1, F1.1, F1.1^2> ] Total time: 0.190 seconds, Total memory usage: 3.56MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:34:16 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:31:57 on modular [Seed = 2929679828] ------------------------------------- 7 4 Point [ 1, 197, 146, 956 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 399, 862, 832 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 11.529 seconds, Total memory usage: 9.58MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:38:34 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 01:34:38 on modular [Seed = 3639159553] ------------------------------------- 7 Errors: /bin/sh: line 1: 30447 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:42:30 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:39:23 on modular [Seed = 3045343368] ------------------------------------- 7 4 Point [ 1, 56, 764, 876 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 342, 685, 715 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.809 seconds, Total memory usage: 14.85MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:43:46 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:43:17 on modular [Seed = 3554813456] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 421, 613, 231 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 421, 396, 778 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 588, 68, 376 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 588, 941, 633 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.800 seconds, Total memory usage: 10.93MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:45:13 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:44:57 on modular [Seed = 605409348] ------------------------------------- 7 4 Point [ 1, 411, 382, 916 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 937, 483, 564 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 6.269 seconds, Total memory usage: 13.49MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:47:50 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:46:21 on modular [Seed = 1851759354] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 1000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 7.870 seconds, Total memory usage: 7.94MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:51:57 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 01:48:02 on modular [Seed = 3146402960] ------------------------------------- 7 4 Point [ 1, 730, 360, 997 ] was singular mod 1009 and ignored at the #1 lift Errors: /bin/sh: line 1: 30850 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:55:18 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:53:48 on modular [Seed = 2411624922] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 421, 613, 231 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 421, 396, 778 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 588, 68, 376 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 588, 941, 633 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 8.000 seconds, Total memory usage: 7.63MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 01:57:23 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:57:10 on modular [Seed = 872795450] ------------------------------------- 7 4 Point [ 1, 268, 797, 330 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 6.440 seconds, Total memory usage: 13.49MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 02:00:05 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 01:58:45 on modular [Seed = 321055422] ------------------------------------- 7 4 Point [ 1, 1687, 1975, 1875 ] was singular mod 3001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 10.900 seconds, Total memory usage: 13.50MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 02:13:41 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 02:10:56 on modular [Seed = 2811649516] ------------------------------------- 7 4 Point [ 1, 2210, 415, 4935 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 2783, 4959, 167 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 3890, 2635, 2020 ] was singular mod 5003 and ignored at the #3 lift Point [ 1, 4596, 490, 2734 ] was singular mod 5003 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.789 seconds, Total memory usage: 13.49MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 02:40:10 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 02:39:49 on modular [Seed = 740142885] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 5000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 7.129 seconds, Total memory usage: 7.75MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 02:56:05 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 02:52:09 on modular [Seed = 790539017] ------------------------------------- 7 4 Errors: /bin/sh: line 1: 32272 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:00:18 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 02:57:02 on modular [Seed = 2761237413] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 -1 0] [ 0 -1 ..., bound: 5000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 17.370 seconds, Total memory usage: 11.22MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:04:13 2004 Input: E := EllipticCurve( [0,0,0,-21427641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[7]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 03:00:33 on modular [Seed = 1041217553] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field function(p) ... end function (-910440391628890938601099529802868632429873479844493775727/3857421619965038844\ 09393938683424026674935255294495044 : 46348186099042466735901061467563099250235\ 205386295163084372032573576328791801473415313/239577299579273657130198416025561\ 384088317389724050948915746896212077216966160072 : 1) 123.58582067448296015754 Total time: 20.670 seconds, Total memory usage: 18.72MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:06:08 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[7]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 03:05:33 on modular [Seed = 2794925989] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 -1 0] [ 0 -1 ..., bound: 5000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 17.359 seconds, Total memory usage: 7.76MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:07:06 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 03:06:24 on modular [Seed = 2209483469] ------------------------------------- 7 4 Errors: /bin/sh: line 1: 32701 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:07:51 2004 Input: E := EllipticCurve( [0,0,0,-10029889,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 03:07:24 on modular [Seed = 3771820402] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field function(p) ... end function (214984684892163287320059154580343445555227536454410937792/66037531249216383414\ 118728283862623787994547342768849 : 7299607688050397073205317059031863777288961\ 12432150834175650330524850423538645967640/1697017198850295179138407510316697336\ 6724677595488743087814534135224839779676007 : 1) 121.98877554061174066646 Total time: 13.539 seconds, Total memory usage: 13.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:09:36 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 03:08:54 on modular [Seed = 2051797564] ------------------------------------- 7 4 Point [ 1, 1204, 1472, 51 ] was singular mod 3001 and ignored at the #3 lift Point [ 1, 1439, 1470, 240 ] was singular mod 3001 and ignored at the #3 lift Point [ 1, 1905, 648, 343 ] was singular mod 3001 and ignored at the #1 lift Point [ 1, 2318, 924, 1160 ] was singular mod 3001 and ignored at the #3 lift Errors: /bin/sh: line 1: 314 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:10:21 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 03:10:01 on modular [Seed = 554740008] ------------------------------------- 7 4 Point [ 1, 233, 2668, 1679 ] was singular mod 3001 and ignored at the #3 lift Point [ 1, 329, 1748, 1948 ] was singular mod 3001 and ignored at the #1 lift Point [ 1, 813, 2613, 1766 ] was singular mod 3001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 9.980 seconds, Total memory usage: 6.33MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.72 (66.63.133.72) Time: Sat Oct 16 03:23:31 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,8000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 03:20:12 on modular [Seed = 3923272454] ------------------------------------- 7 4 Errors: /bin/sh: line 1: 682 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:11:43 2004 Input: Factorization(15); Output: Magma V2.11-6 Sat Oct 16 2004 13:11:41 on modular [Seed = 3538077124] ------------------------------------- [ <3, 1>, <5, 1> ] Total time: 0.270 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:12:27 2004 Input: Factorization(2^64-1); Output: Magma V2.11-6 Sat Oct 16 2004 13:12:27 on modular [Seed = 3588604661] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1>, <257, 1>, <641, 1>, <65537, 1>, <6700417, 1> ] Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:12:32 2004 Input: Factorization(2^63-1); Output: Magma V2.11-6 Sat Oct 16 2004 13:12:32 on modular [Seed = 3371753235] ------------------------------------- [ <7, 2>, <73, 1>, <127, 1>, <337, 1>, <92737, 1>, <649657, 1> ] Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:12:38 2004 Input: Factorization(2^62-1); Output: Magma V2.11-6 Sat Oct 16 2004 13:12:38 on modular [Seed = 3287536670] ------------------------------------- [ <3, 1>, <715827883, 1>, <2147483647, 1> ] Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:12:45 2004 Input: Factorization(2^61-1); Output: Magma V2.11-6 Sat Oct 16 2004 13:12:44 on modular [Seed = 3338064145] ------------------------------------- [ <2305843009213693951, 1> ] Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:15:31 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^7+1; Factorization(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:15:31 on modular [Seed = 4274972822] ------------------------------------- [ , , , ] >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.180 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:15:41 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^7+1; Primitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:15:40 on modular [Seed = 4056016790] ------------------------------------- >> Primitive(Pb); ^ User error: Identifier 'Primitive' has not been declared or assigned >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:15:49 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^7+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:15:48 on modular [Seed = 4106543851] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:15:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^32+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:15:58 on modular [Seed = 4024433146] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:05 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^31+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:04 on modular [Seed = 3805476077] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:13 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^17+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:13 on modular [Seed = 3839161058] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:20 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^15+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:19 on modular [Seed = 2679081383] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:24 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^13+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:24 on modular [Seed = 2460124321] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.180 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:29 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^14+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:29 on modular [Seed = 2510652323] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:35 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^12+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:34 on modular [Seed = 2293800609] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.180 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:47 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^18+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:47 on modular [Seed = 2209584551] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:52 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^19+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:52 on modular [Seed = 2260111449] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:16:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^20+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:16:57 on modular [Seed = 3112808299] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:17:02 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^21+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:17:02 on modular [Seed = 2994906215] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:17:10 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^64+z^22+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:17:09 on modular [Seed = 3045434235] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:21:09 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 10 do Pb := z^64+z^k+1; IsPrimitive(Pb); end for Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:21:09 on modular [Seed = 2912793715] ------------------------------------- >> Fb := ext< F2 | Pb >; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:21:32 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 10 do Pb := z^64+z^k+1; IsPrimitive(Pb); end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:21:31 on modular [Seed = 2811739751] ------------------------------------- false false false false false false false false false false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:21:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 10 do Pb := z^64+z^k+1; k; IsPrimitive(Pb); end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:21:44 on modular [Seed = 1533756073] ------------------------------------- 1 false 2 false 3 false 4 false 5 false 6 false 7 false 8 false 9 false 10 false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:21:51 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 63 do Pb := z^64+z^k+1; k; IsPrimitive(Pb); end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:21:51 on modular [Seed = 1550599593] ------------------------------------- 1 false 2 false 3 false 4 false 5 false 6 false 7 false 8 false 9 false 10 false 11 false 12 false 13 false 14 false 15 false 16 false 17 false 18 false 19 false 20 false 21 false 22 false 23 false 24 false 25 false 26 false 27 false 28 false 29 false 30 false 31 false 32 false 33 false 34 false 35 false 36 false 37 false 38 false 39 false 40 false 41 false 42 false 43 false 44 false 45 false 46 false 47 false 48 false 49 false 50 false 51 false 52 false 53 false 54 false 55 false 56 false 57 false 58 false 59 false 60 false 61 false 62 false 63 false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:23:28 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 63 do for l:=1 to 63 do Pb := z^64+z^k+z^l+1; if IsPrimitive(Pb)=true then k; l; IsPrimitive(Pb); end if; end for; end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:23:27 on modular [Seed = 1466388226] ------------------------------------- >> if IsPrimitive(Pb)=true then ^ Runtime error in if: Logical expected >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:23:53 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 63 do for l:=1 to 63 do Pb := z^64+z^k+z^l+1; if IsPrimitive(Pb) then k; l; IsPrimitive(Pb); end if; end for; end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:23:52 on modular [Seed = 1215844410] ------------------------------------- >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.240 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:25:03 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 63 do for l:=1 to 63 do for m:=1 to 63 do Pb := z^64+z^k+z^l+z^m+1; if IsPrimitive(Pb) then k; l; m; IsPrimitive(Pb); end if; end for; end for; end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:24:42 on modular [Seed = 2034852217] ------------------------------------- 1 2 11 true 1 3 4 true 1 4 3 true 1 4 46 true 1 6 49 true 1 6 50 true 1 7 12 true 1 7 25 true 1 8 35 true 1 8 51 true 1 8 63 true 1 9 58 true 1 10 31 true 1 10 46 true 1 11 2 true 1 11 30 true 1 12 7 true 1 13 34 true 1 13 54 true 1 15 18 true 1 15 29 true 1 15 46 true 1 16 19 true 1 16 54 true 1 18 15 true 1 18 29 true 1 18 50 true 1 19 16 true 1 19 30 true 1 19 58 true 1 22 57 true 1 23 29 true 1 23 35 true 1 23 56 true 1 25 7 true 1 25 39 true 1 26 42 true 1 26 54 true 1 27 40 true 1 27 61 true 1 28 34 true 1 29 15 true 1 29 18 true 1 29 23 true 1 30 11 true 1 30 19 true 1 31 10 true 1 31 55 true 1 34 13 true 1 34 28 true 1 34 55 true 1 35 8 true 1 35 23 true 1 35 48 true 1 35 62 true 1 38 56 true 1 39 25 true 1 39 49 true 1 40 27 true 1 42 26 true 1 42 52 true 1 44 51 true 1 46 4 true 1 46 10 true 1 46 15 true 1 47 51 true 1 48 35 true 1 48 54 true 1 49 6 true 1 49 39 true 1 50 6 true 1 50 18 true 1 51 8 true 1 51 44 true 1 51 47 true 1 52 42 true 1 54 13 true 1 54 16 true 1 54 26 true 1 54 48 true 1 55 31 true 1 55 34 true 1 55 57 true 1 56 23 true 1 56 38 true 1 56 59 true 1 56 62 true 1 56 63 true 1 57 22 true 1 57 55 true 1 58 9 true 1 58 19 true 1 58 60 true 1 59 56 true 1 60 58 true 1 61 27 true 1 62 35 true 1 62 56 true 1 63 8 true 1 63 56 true 2 1 11 true 2 3 4 true 2 3 14 true 2 3 28 true 2 3 52 true 2 4 3 true 2 4 57 true 2 5 10 true 2 5 40 true 2 5 55 true 2 6 37 true 2 7 42 true 2 7 59 true 2 8 39 true 2 8 63 true 2 9 37 true 2 10 5 true 2 11 1 true 2 11 27 true 2 11 37 true 2 12 25 true 2 12 49 true 2 12 53 true 2 14 3 true 2 14 43 true 2 17 34 true 2 17 39 true 2 17 42 true 2 23 25 true 2 24 47 true 2 25 12 true 2 25 23 true 2 25 33 true 2 25 57 true 2 26 61 true 2 27 11 true 2 28 3 true 2 29 39 true 2 29 63 true 2 30 37 true 2 30 53 true 2 33 25 true 2 33 43 true 2 34 17 true 2 35 36 true 2 36 35 true 2 37 6 true 2 37 9 true 2 37 11 true 2 37 30 true 2 37 44 true 2 38 55 true 2 39 8 true 2 39 17 true 2 39 29 true 2 40 5 true 2 41 55 true 2 42 7 true 2 42 17 true 2 43 14 true 2 43 33 true 2 43 53 true 2 43 60 true 2 44 37 true 2 45 52 true 2 47 24 true 2 47 60 true 2 49 12 true 2 51 56 true 2 52 3 true 2 52 45 true 2 53 12 true 2 53 30 true 2 53 43 true 2 53 54 true 2 54 53 true 2 55 5 true 2 55 38 true 2 55 41 true 2 56 51 true 2 57 4 true 2 57 25 true 2 59 7 true 2 60 43 true 2 60 47 true 2 60 61 true 2 61 26 true 2 61 60 true 2 63 8 true 2 63 29 true 3 1 4 true 3 2 4 true 3 2 14 true 3 2 28 true 3 2 52 true 3 4 1 true 3 4 2 true 3 4 37 true 3 4 62 true 3 5 44 true 3 6 49 true 3 8 41 true 3 10 30 true 3 10 39 true 3 13 16 true 3 13 54 true 3 14 2 true 3 15 18 true 3 16 13 true 3 16 25 true 3 17 58 true 3 18 15 true 3 18 51 true 3 18 57 true 3 19 25 true 3 19 41 true 3 20 29 true 3 21 24 true 3 21 45 true 3 24 21 true 3 24 58 true 3 25 16 true 3 25 19 true 3 25 26 true 3 25 51 true 3 26 25 true 3 26 43 true 3 27 49 true 3 28 2 true 3 28 57 true 3 29 20 true 3 29 47 true 3 30 10 true 3 30 55 true 3 34 47 true 3 34 50 true 3 34 53 true 3 36 45 true 3 37 4 true 3 37 53 true 3 37 63 true 3 38 43 true 3 38 62 true 3 39 10 true 3 40 41 true 3 41 8 true 3 41 19 true 3 41 40 true 3 41 46 true 3 43 26 true 3 43 38 true 3 44 5 true 3 45 21 true 3 45 36 true 3 46 41 true 3 47 29 true 3 47 34 true 3 49 6 true 3 49 27 true 3 49 51 true 3 49 54 true 3 49 57 true 3 50 34 true 3 51 18 true 3 51 25 true 3 51 49 true 3 52 2 true 3 53 34 true 3 53 37 true 3 54 13 true 3 54 49 true 3 55 30 true 3 55 57 true 3 57 18 true 3 57 28 true 3 57 49 true 3 57 55 true 3 58 17 true 3 58 24 true 3 62 4 true 3 62 38 true 3 63 37 true 4 1 3 true 4 1 46 true 4 2 3 true 4 2 57 true 4 3 1 true 4 3 2 true 4 3 37 true 4 3 62 true 4 5 47 true 4 5 59 true 4 6 9 true 4 6 49 true 4 6 51 true 4 6 63 true 4 9 6 true 4 9 11 true 4 10 31 true 4 11 9 true 4 11 50 true 4 14 47 true 4 15 45 true 4 17 62 true 4 18 35 true 4 19 21 true 4 21 19 true 4 21 35 true 4 21 62 true 4 22 49 true 4 27 33 true 4 30 51 true 4 31 10 true 4 33 27 true 4 34 55 true 4 35 18 true 4 35 21 true 4 37 3 true 4 43 58 true 4 45 15 true 4 46 1 true 4 47 5 true 4 47 14 true 4 49 6 true 4 49 22 true 4 50 11 true 4 51 6 true 4 51 30 true 4 55 34 true 4 57 2 true 4 58 43 true 4 59 5 true 4 62 3 true 4 62 17 true 4 62 21 true 4 63 6 true 5 2 10 true 5 2 40 true 5 2 55 true 5 3 44 true 5 4 47 true 5 4 59 true 5 6 53 true 5 7 8 true 5 7 24 true 5 8 7 true 5 8 63 true 5 9 38 true 5 9 47 true 5 10 2 true 5 11 13 true 5 12 23 true 5 13 11 true 5 14 30 true 5 15 17 true 5 15 26 true 5 17 15 true 5 17 46 true 5 20 43 true 5 21 47 true 5 23 12 true 5 23 42 true 5 23 43 true 5 24 7 true 5 25 54 true 5 26 15 true 5 26 55 true 5 29 30 true 5 30 14 true 5 30 29 true 5 31 51 true 5 31 57 true 5 38 9 true 5 39 49 true 5 40 2 true 5 42 23 true 5 43 20 true 5 43 23 true 5 44 3 true 5 44 46 true 5 46 17 true 5 46 44 true 5 47 4 true 5 47 9 true 5 47 21 true 5 47 48 true 5 48 47 true 5 49 39 true 5 51 31 true 5 53 6 true 5 53 58 true 5 54 25 true 5 54 55 true 5 55 2 true 5 55 26 true 5 55 54 true 5 57 31 true 5 57 62 true 5 58 53 true 5 59 4 true 5 59 60 true 5 60 59 true 5 62 57 true 5 63 8 true 6 1 49 true 6 1 50 true 6 2 37 true 6 3 49 true 6 4 9 true 6 4 49 true 6 4 51 true 6 4 63 true 6 5 53 true 6 8 35 true 6 9 4 true 6 9 24 true 6 9 33 true 6 10 31 true 6 11 35 true 6 11 59 true 6 13 55 true 6 15 22 true 6 15 34 true 6 17 47 true 6 20 25 true 6 21 60 true 6 22 15 true 6 24 9 true 6 25 20 true 6 25 47 true 6 27 49 true 6 30 33 true 6 31 10 true 6 33 9 true 6 33 30 true 6 34 15 true 6 35 8 true 6 35 11 true 6 37 2 true 6 40 57 true 6 40 61 true 6 41 43 true 6 42 57 true 6 43 41 true 6 43 56 true 6 45 63 true 6 47 17 true 6 47 25 true 6 47 61 true 6 49 1 true 6 49 3 true 6 49 4 true 6 49 27 true 6 49 56 true 6 50 1 true 6 51 4 true 6 53 5 true 6 55 13 true 6 55 63 true 6 56 43 true 6 56 49 true 6 57 40 true 6 57 42 true 6 59 11 true 6 60 21 true 6 61 40 true 6 61 47 true 6 63 4 true 6 63 45 true 6 63 55 true 7 1 12 true 7 1 25 true 7 2 42 true 7 2 59 true 7 5 8 true 7 5 24 true 7 8 5 true 7 9 12 true 7 9 21 true 7 9 56 true 7 9 61 true 7 9 63 true 7 10 43 true 7 12 1 true 7 12 9 true 7 13 25 true 7 13 48 true 7 15 61 true 7 17 41 true 7 18 57 true 7 20 41 true 7 21 9 true 7 21 30 true 7 21 46 true 7 22 58 true 7 24 5 true 7 24 58 true 7 25 1 true 7 25 13 true 7 26 30 true 7 27 41 true 7 29 51 true 7 30 21 true 7 30 26 true 7 33 43 true 7 33 59 true 7 36 61 true 7 39 62 true 7 40 46 true 7 41 17 true 7 41 20 true 7 41 27 true 7 41 56 true 7 42 2 true 7 42 48 true 7 42 63 true 7 43 10 true 7 43 33 true 7 46 21 true 7 46 40 true 7 46 57 true 7 46 61 true 7 48 13 true 7 48 42 true 7 51 29 true 7 56 9 true 7 56 41 true 7 57 18 true 7 57 46 true 7 58 22 true 7 58 24 true 7 59 2 true 7 59 33 true 7 60 62 true 7 61 9 true 7 61 15 true 7 61 36 true 7 61 46 true 7 62 39 true 7 62 60 true 7 63 9 true 7 63 42 true 8 1 35 true 8 1 51 true 8 1 63 true 8 2 39 true 8 2 63 true 8 3 41 true 8 5 7 true 8 5 63 true 8 6 35 true 8 7 5 true 8 10 41 true 8 11 45 true 8 13 62 true 8 14 33 true 8 14 37 true 8 15 58 true 8 17 54 true 8 19 54 true 8 21 58 true 8 23 57 true 8 26 55 true 8 26 63 true 8 29 39 true 8 33 14 true 8 35 1 true 8 35 6 true 8 35 37 true 8 35 49 true 8 37 14 true 8 37 35 true 8 37 39 true 8 39 2 true 8 39 29 true 8 39 37 true 8 41 3 true 8 41 10 true 8 41 63 true 8 45 11 true 8 49 35 true 8 49 54 true 8 51 1 true 8 54 17 true 8 54 19 true 8 54 49 true 8 55 26 true 8 55 57 true 8 57 23 true 8 57 55 true 8 58 15 true 8 58 21 true 8 62 13 true 8 63 1 true 8 63 2 true 8 63 5 true 8 63 26 true 8 63 41 true 9 1 58 true 9 2 37 true 9 4 6 true 9 4 11 true 9 5 38 true 9 5 47 true 9 6 4 true 9 6 24 true 9 6 33 true 9 7 12 true 9 7 21 true 9 7 56 true 9 7 61 true 9 7 63 true 9 10 59 true 9 11 4 true 9 12 7 true 9 12 39 true 9 13 51 true 9 14 35 true 9 16 35 true 9 17 55 true 9 18 51 true 9 19 29 true 9 19 31 true 9 21 7 true 9 23 49 true 9 23 62 true 9 24 6 true 9 26 62 true 9 27 33 true 9 27 45 true 9 28 42 true 9 28 51 true 9 29 19 true 9 30 60 true 9 30 63 true 9 31 19 true 9 31 33 true 9 33 6 true 9 33 27 true 9 33 31 true 9 33 63 true 9 34 61 true 9 35 14 true 9 35 16 true 9 36 54 true 9 37 2 true 9 38 5 true 9 38 56 true 9 38 59 true 9 39 12 true 9 39 52 true 9 42 28 true 9 43 47 true 9 45 27 true 9 47 5 true 9 47 43 true 9 47 50 true 9 47 55 true 9 49 23 true 9 50 47 true 9 50 53 true 9 51 13 true 9 51 18 true 9 51 28 true 9 51 58 true 9 52 39 true 9 53 50 true 9 54 36 true 9 55 17 true 9 55 47 true 9 56 7 true 9 56 38 true 9 58 1 true 9 58 51 true 9 59 10 true 9 59 38 true 9 59 62 true 9 60 30 true 9 61 7 true 9 61 34 true 9 62 23 true 9 62 26 true 9 62 59 true 9 63 7 true 9 63 30 true 9 63 33 true 10 1 31 true 10 1 46 true 10 2 5 true 10 3 30 true 10 3 39 true 10 4 31 true 10 5 2 true 10 6 31 true 10 7 43 true 10 8 41 true 10 9 59 true 10 11 50 true 10 11 62 true 10 12 21 true 10 13 43 true 10 15 34 true 10 15 56 true 10 15 61 true 10 16 63 true 10 18 29 true 10 19 43 true 10 21 12 true 10 22 27 true 10 25 34 true 10 25 36 true 10 27 22 true 10 28 43 true 10 28 55 true 10 29 18 true 10 29 39 true 10 29 47 true 10 30 3 true 10 30 35 true 10 31 1 true 10 31 4 true 10 31 6 true 10 33 46 true 10 34 15 true 10 34 25 true 10 35 30 true 10 35 38 true 10 36 25 true 10 38 35 true 10 38 63 true 10 39 3 true 10 39 29 true 10 39 41 true 10 39 48 true 10 39 59 true 10 41 8 true 10 41 39 true 10 43 7 true 10 43 13 true 10 43 19 true 10 43 28 true 10 45 48 true 10 45 56 true 10 46 1 true 10 46 33 true 10 47 29 true 10 47 50 true 10 47 56 true 10 48 39 true 10 48 45 true 10 48 63 true 10 50 11 true 10 50 47 true 10 51 61 true 10 51 63 true 10 55 28 true 10 56 15 true 10 56 45 true 10 56 47 true 10 59 9 true 10 59 39 true 10 61 15 true 10 61 51 true 10 62 11 true 10 63 16 true 10 63 38 true 10 63 48 true 10 63 51 true 11 1 2 true 11 1 30 true 11 2 1 true 11 2 27 true 11 2 37 true 11 4 9 true ** WARNING: Output too long, hence truncated. '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:25:46 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); for k:=1 to 63 do for l:=k+1 to 63 do for m:=l+1 to 63 do Pb := z^64+z^k+z^l+z^m+1; if IsPrimitive(Pb) then k; l; m; IsPrimitive(Pb); end if; end for; end for; end for; Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:25:42 on modular [Seed = 1916955326] ------------------------------------- 1 2 11 true 1 3 4 true 1 4 46 true 1 6 49 true 1 6 50 true 1 7 12 true 1 7 25 true 1 8 35 true 1 8 51 true 1 8 63 true 1 9 58 true 1 10 31 true 1 10 46 true 1 11 30 true 1 13 34 true 1 13 54 true 1 15 18 true 1 15 29 true 1 15 46 true 1 16 19 true 1 16 54 true 1 18 29 true 1 18 50 true 1 19 30 true 1 19 58 true 1 22 57 true 1 23 29 true 1 23 35 true 1 23 56 true 1 25 39 true 1 26 42 true 1 26 54 true 1 27 40 true 1 27 61 true 1 28 34 true 1 31 55 true 1 34 55 true 1 35 48 true 1 35 62 true 1 38 56 true 1 39 49 true 1 42 52 true 1 44 51 true 1 47 51 true 1 48 54 true 1 55 57 true 1 56 59 true 1 56 62 true 1 56 63 true 1 58 60 true 2 3 4 true 2 3 14 true 2 3 28 true 2 3 52 true 2 4 57 true 2 5 10 true 2 5 40 true 2 5 55 true 2 6 37 true 2 7 42 true 2 7 59 true 2 8 39 true 2 8 63 true 2 9 37 true 2 11 27 true 2 11 37 true 2 12 25 true 2 12 49 true 2 12 53 true 2 14 43 true 2 17 34 true 2 17 39 true 2 17 42 true 2 23 25 true 2 24 47 true 2 25 33 true 2 25 57 true 2 26 61 true 2 29 39 true 2 29 63 true 2 30 37 true 2 30 53 true 2 33 43 true 2 35 36 true 2 37 44 true 2 38 55 true 2 41 55 true 2 43 53 true 2 43 60 true 2 45 52 true 2 47 60 true 2 51 56 true 2 53 54 true 2 60 61 true 3 4 37 true 3 4 62 true 3 5 44 true 3 6 49 true 3 8 41 true 3 10 30 true 3 10 39 true 3 13 16 true 3 13 54 true 3 15 18 true 3 16 25 true 3 17 58 true 3 18 51 true 3 18 57 true 3 19 25 true 3 19 41 true 3 20 29 true 3 21 24 true 3 21 45 true 3 24 58 true 3 25 26 true 3 25 51 true 3 26 43 true 3 27 49 true 3 28 57 true 3 29 47 true 3 30 55 true 3 34 47 true 3 34 50 true 3 34 53 true 3 36 45 true 3 37 53 true 3 37 63 true 3 38 43 true 3 38 62 true 3 40 41 true 3 41 46 true 3 49 51 true 3 49 54 true 3 49 57 true 3 55 57 true 4 5 47 true 4 5 59 true 4 6 9 true 4 6 49 true 4 6 51 true 4 6 63 true 4 9 11 true 4 10 31 true 4 11 50 true 4 14 47 true 4 15 45 true 4 17 62 true 4 18 35 true 4 19 21 true 4 21 35 true 4 21 62 true 4 22 49 true 4 27 33 true 4 30 51 true 4 34 55 true 4 43 58 true 5 6 53 true 5 7 8 true 5 7 24 true 5 8 63 true 5 9 38 true 5 9 47 true 5 11 13 true 5 12 23 true 5 14 30 true 5 15 17 true 5 15 26 true 5 17 46 true 5 20 43 true 5 21 47 true 5 23 42 true 5 23 43 true 5 25 54 true 5 26 55 true 5 29 30 true 5 31 51 true 5 31 57 true 5 39 49 true 5 44 46 true 5 47 48 true 5 53 58 true 5 54 55 true 5 57 62 true 5 59 60 true 6 8 35 true 6 9 24 true 6 9 33 true 6 10 31 true 6 11 35 true 6 11 59 true 6 13 55 true 6 15 22 true 6 15 34 true 6 17 47 true 6 20 25 true 6 21 60 true 6 25 47 true 6 27 49 true 6 30 33 true 6 40 57 true 6 40 61 true 6 41 43 true 6 42 57 true 6 43 56 true 6 45 63 true 6 47 61 true 6 49 56 true 6 55 63 true 7 9 12 true 7 9 21 true 7 9 56 true 7 9 61 true 7 9 63 true 7 10 43 true 7 13 25 true 7 13 48 true 7 15 61 true 7 17 41 true 7 18 57 true 7 20 41 true 7 21 30 true 7 21 46 true 7 22 58 true 7 24 58 true 7 26 30 true 7 27 41 true 7 29 51 true 7 33 43 true 7 33 59 true 7 36 61 true 7 39 62 true 7 40 46 true 7 41 56 true 7 42 48 true 7 42 63 true 7 46 57 true 7 46 61 true 7 60 62 true 8 10 41 true 8 11 45 true 8 13 62 true 8 14 33 true 8 14 37 true 8 15 58 true 8 17 54 true 8 19 54 true 8 21 58 true 8 23 57 true 8 26 55 true 8 26 63 true 8 29 39 true 8 35 37 true 8 35 49 true 8 37 39 true 8 41 63 true 8 49 54 true 8 55 57 true 9 10 59 true 9 12 39 true 9 13 51 true 9 14 35 true 9 16 35 true 9 17 55 true 9 18 51 true 9 19 29 true 9 19 31 true 9 23 49 true 9 23 62 true 9 26 62 true 9 27 33 true 9 27 45 true 9 28 42 true 9 28 51 true 9 30 60 true 9 30 63 true 9 31 33 true 9 33 63 true 9 34 61 true 9 36 54 true 9 38 56 true 9 38 59 true 9 39 52 true 9 43 47 true 9 47 50 true 9 47 55 true 9 50 53 true 9 51 58 true 9 59 62 true 10 11 50 true 10 11 62 true 10 12 21 true 10 13 43 true 10 15 34 true 10 15 56 true 10 15 61 true 10 16 63 true 10 18 29 true 10 19 43 true 10 22 27 true 10 25 34 true 10 25 36 true 10 28 43 true 10 28 55 true 10 29 39 true 10 29 47 true 10 30 35 true 10 33 46 true 10 35 38 true 10 38 63 true 10 39 41 true 10 39 48 true 10 39 59 true 10 45 48 true 10 45 56 true 10 47 50 true 10 47 56 true 10 48 63 true 10 51 61 true 10 51 63 true 11 13 35 true 11 13 39 true 11 14 21 true 11 14 55 true 11 17 34 true 11 18 23 true 11 18 34 true 11 20 25 true 11 21 28 true 11 21 62 true 11 22 50 true 11 25 44 true 11 27 61 true 11 30 61 true 11 31 33 true 11 33 35 true 11 34 35 true 11 34 62 true 11 36 38 true 11 40 45 true 11 41 51 true 11 41 52 true 11 45 50 true 11 46 48 true 11 52 62 true 11 58 59 true 12 13 39 true 12 19 34 true 12 19 62 true 12 22 63 true 12 23 53 true 12 25 31 true 12 25 55 true 12 27 45 true 12 33 43 true 12 34 51 true 12 61 62 true 13 15 29 true 13 15 35 true 13 15 40 true 13 15 61 true 13 17 63 true 13 19 43 true 13 20 30 true 13 20 63 true 13 21 39 true 13 22 43 true 13 23 53 true 13 27 32 true 13 28 43 true 13 30 52 true 13 33 39 true 13 33 59 true 13 34 46 true 13 34 60 true 13 35 41 true 13 35 57 true 13 36 55 true 13 39 48 true 13 39 61 true 13 46 55 true 13 46 61 true 13 51 55 true 13 56 63 true 13 58 60 true 14 15 50 true 14 16 45 true 14 17 54 true 14 17 55 true 14 19 53 true 14 20 31 true 14 20 45 true 14 22 29 true 14 30 35 true 14 30 61 true 14 31 45 true 14 42 49 true 14 42 53 true 14 46 63 true 14 49 50 true 14 53 54 true 14 53 60 true 14 58 63 true 15 17 38 true 15 21 40 true 15 22 50 true 15 25 46 true 15 25 59 true 15 25 63 true 15 27 45 true 15 28 45 true 15 29 56 true 15 37 58 true 15 37 61 true 15 41 55 true 15 42 60 true 15 52 62 true 15 58 60 true 15 58 61 true 15 58 63 true 16 17 59 true 16 18 53 true 16 19 54 true 16 22 57 true 16 25 51 true 16 25 54 true 16 26 39 true 16 29 63 true 16 45 47 true 16 51 57 true 17 18 23 true 17 19 32 true 17 19 48 true 17 21 55 true 17 24 46 true 17 26 46 true 17 28 47 true 17 30 35 true 17 30 61 true 17 35 54 true 17 35 61 true 17 36 47 true 17 39 58 true 17 40 62 true 17 43 59 true 17 47 58 true 17 50 60 true 17 55 59 true 17 59 60 true 18 20 59 true 18 23 46 true 18 23 61 true 18 24 57 true 18 27 28 true 18 29 43 true 18 30 51 true 18 31 54 true 18 34 45 true 18 35 43 true 18 37 38 true 18 38 47 true 18 39 49 true 18 40 47 true 18 41 46 true 18 43 45 true 18 43 57 true 18 47 59 true 18 49 63 true 18 54 63 true 18 60 63 true 19 20 29 true 19 21 46 true 19 23 45 true 19 24 53 true 19 25 33 true 19 28 61 true 19 30 31 true 19 30 46 true 19 33 35 true 19 33 50 true 19 36 41 true 19 36 49 true 19 37 49 true 19 37 52 true 19 37 55 true 19 41 45 true 19 43 61 true 19 44 50 true 19 48 50 true 19 49 60 true 19 53 56 true 20 22 33 true 20 25 27 true 20 27 41 true 20 27 62 true 20 39 53 true 20 59 61 true 21 22 41 true 21 23 28 true 21 23 58 true 21 26 43 true 21 26 61 true 21 29 46 true 21 30 33 true 21 31 52 true 21 31 57 true 21 31 62 true 21 35 46 true 21 36 51 true 21 36 54 true 21 38 43 true 21 38 61 true 21 41 59 true 21 42 51 true 21 44 59 true 21 45 51 true 21 45 54 true 21 50 62 true 21 51 54 true 21 54 57 true 22 23 33 true 22 29 35 true 22 33 35 true 22 36 55 true 22 37 39 true 22 38 63 true 22 41 59 true 22 47 62 true 22 57 62 true 23 24 61 true 23 25 54 true 23 28 45 true 23 29 30 true 23 29 37 true 23 29 51 true 23 37 44 true 23 37 57 true 23 42 43 true 23 44 57 true 23 45 61 true 23 47 57 true 23 54 56 true 23 56 61 true 24 25 31 true 24 25 38 true 24 29 31 true 24 35 37 true 24 37 63 true 24 43 49 true 24 49 51 true 24 59 62 true 25 27 42 true 25 27 56 true 25 31 51 true 25 35 36 true 25 35 54 true 25 35 56 true 25 35 62 true 25 38 48 true 25 39 63 true 25 43 51 true 25 47 62 true 25 51 52 true 25 51 53 true 25 52 55 true 25 54 61 true 25 56 62 true 26 27 46 true 26 28 53 true 26 29 54 true 26 39 40 true 26 47 49 true 26 55 59 true 27 29 40 true 27 29 56 true 27 34 62 true 27 35 41 true 27 50 56 true 27 53 62 true 27 55 62 true 27 58 62 true 27 60 61 true 28 29 39 true 28 29 62 true 28 39 54 true 29 30 53 true 29 31 42 true 29 31 45 true 29 31 53 true 29 34 47 true 29 34 50 true 29 34 54 true 29 35 42 true 29 41 63 true 29 43 60 true 29 46 60 true 29 48 55 true 29 49 51 true 29 50 55 true 29 51 53 true 29 53 58 true 29 56 58 true 29 56 63 true 30 36 63 true 30 39 54 true 30 45 52 true 30 46 53 true 30 47 53 true 30 47 62 true 30 49 54 true 30 49 58 true 30 51 63 true 31 33 53 true 31 33 55 true 31 34 43 true 31 34 58 true 31 37 55 true 31 37 60 true 31 39 45 true 31 39 62 true 31 41 42 true 31 42 44 true 31 50 56 true 31 55 58 true 32 37 51 true 32 45 47 true 33 34 45 true 33 35 40 true 33 39 40 true 33 39 52 true 33 44 50 true 33 45 55 true 33 54 58 true 33 54 60 true 33 54 63 true 34 35 41 true 34 35 59 true 34 38 57 true 34 43 57 true 34 44 51 true 34 45 63 true 34 50 59 true 34 53 63 true 34 54 61 true 35 41 63 true 35 42 50 true 35 44 45 true 35 44 61 true 35 45 55 true 35 46 54 true 35 46 63 true 35 49 51 true 35 49 63 true 36 37 46 true 36 41 43 true 36 43 53 true 36 61 62 true 37 39 44 true 37 42 54 true 37 53 62 true 38 39 61 true 38 49 59 true 39 41 62 true 39 44 53 true 39 44 58 true 39 45 61 true 39 48 61 true 39 51 57 true 39 52 62 true 39 57 63 true 40 43 61 true 40 55 58 true 40 57 59 true 41 46 47 true 41 46 53 true 41 52 59 true 42 49 58 true 43 45 60 true 43 50 53 true 43 52 54 true 43 55 57 true 45 48 63 true 46 49 61 true 46 49 63 true 47 49 59 true 48 51 61 true 50 61 62 true 51 53 59 true 52 55 57 true 52 57 63 true 53 55 60 true 53 62 63 true 54 59 62 true 55 58 60 true 56 57 59 true 60 61 62 true 60 61 63 true >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 1.889 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:28:38 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Output: Magma V2.11-6 Sat Oct 16 2004 13:28:38 on modular [Seed = 1834841713] ------------------------------------- true Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:28:56 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; z; Output: Magma V2.11-6 Sat Oct 16 2004 13:28:55 on modular [Seed = 1716944235] ------------------------------------- true z Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:29:12 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; z^64; Output: Magma V2.11-6 Sat Oct 16 2004 13:29:12 on modular [Seed = 455802921] ------------------------------------- true z^64 Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:29:22 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; z^-1; Output: Magma V2.11-6 Sat Oct 16 2004 13:29:22 on modular [Seed = 489489973] ------------------------------------- true >> z^-1;; ^ Runtime error in '^': Argument 2 (-1) should be >= 0 Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:29:46 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; z^(2^64-1); Output: Magma V2.11-6 Sat Oct 16 2004 13:29:45 on modular [Seed = 371592645] ------------------------------------- true >> z^(2^64-1);; ^ Runtime error in '^': Argument 1 (18446744073709551615) is too large Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:30:01 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; b^(2^64-1); Output: Magma V2.11-6 Sat Oct 16 2004 13:30:01 on modular [Seed = 188420296] ------------------------------------- true 1 Total time: 0.190 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:30:09 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; b^(2^64-2); Output: Magma V2.11-6 Sat Oct 16 2004 13:30:08 on modular [Seed = 205264886] ------------------------------------- true b^63 + b^10 + b + 1 Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:32:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=2; m:=11; Pb := z^64+z^k+z^l+z^m+1; Pb; IsPrimitive(Pb); Fb := ext< F2 | Pb >; b^(2^64-2); Output: Magma V2.11-6 Sat Oct 16 2004 13:32:33 on modular [Seed = 87367534] ------------------------------------- z^64 + z^11 + z^2 + z + 1 true b^63 + b^10 + b + 1 Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:35:55 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); k:=1; l:=3; m:=4; Pb := z^64+z^k+z^l+z^m+1; Pb; IsPrimitive(Pb); Fb := ext< F2 | Pb >; b^(2^64-2); Output: Magma V2.11-6 Sat Oct 16 2004 13:35:55 on modular [Seed = 1041114271] ------------------------------------- z^64 + z^4 + z^3 + z + 1 true b^63 + b^3 + b^2 + 1 Total time: 0.200 seconds, Total memory usage: 4.27MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:59:53 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); z^8+z^7+z^5+z^3+1; Fb := ext< F2 | z^8+z^7+z^5+z^3+1 >; Output: Magma V2.11-6 Sat Oct 16 2004 13:59:52 on modular [Seed = 3990736175] ------------------------------------- z^8 + z^7 + z^5 + z^3 + 1 Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 13:59:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Fb := ext< F2 | z^8+z^7+z^5+z^3+1 >; Output: Magma V2.11-6 Sat Oct 16 2004 13:59:58 on modular [Seed = 2561194076] ------------------------------------- Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:01:23 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fb := ext< F2 | z^8+z^7+z^5+z^3+1 >; Rb := PolynomialRing(Fb); IsPrimitive(y^4+b^23*y^245+b^48*y^48+b^239); Output: Magma V2.11-6 Sat Oct 16 2004 14:01:23 on modular [Seed = 2912783620] ------------------------------------- >> IsPrimitive(y^4+b^23*y^245+b^48*y^48+b^239); ^ Runtime error in 'IsPrimitive': Argument 1 is not monic Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:01:55 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fb := ext< F2 | z^8+z^7+z^5+z^3+1 >; Rb := PolynomialRing(Fb); Fb := ext< Fb | y^4+b^23*y^245+b^48*y^48+b^239 >; Output: Magma V2.11-6 Sat Oct 16 2004 14:01:54 on modular [Seed = 2794882542] ------------------------------------- >> Fb := ext< Fb | y^4+b^23*y^245+b^48*y^48+b^239 >; ^ Runtime error in ext< ... >: Argument 1 is not monic Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:02:36 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:02:35 on modular [Seed = 1500084799] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:02:43 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^239; alfa := 1+y; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:02:43 on modular [Seed = 1415870282] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:03:41 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^3 + b^48*y + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:03:41 on modular [Seed = 1399025779] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:03:49 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:03:48 on modular [Seed = 1316908439] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:03:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^3 + b^48*y^2 + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:03:58 on modular [Seed = 1165321878] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:04:23 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:04:22 on modular [Seed = 1081107387] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:04:28 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + 1; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:04:28 on modular [Seed = 2135907470] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:04:38 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^235; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:04:38 on modular [Seed = 2051692945] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:05:26 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 256 do Pa :=y^4 + b^23*y^2 + b^48*y + b^k; IsPrimitive(Pa); end for; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:05:26 on modular [Seed = 1900106442] ------------------------------------- false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:05:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 256 do Pa :=y^4 + b^23*y^2 + b^48*y + b^k; if IsPrimitive(Pa) then k; end if; end for; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:05:57 on modular [Seed = 1817988660] ------------------------------------- >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:06:09 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 256 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then k; end if; end for; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:06:09 on modular [Seed = 1632715565] ------------------------------------- 14 17 20 21 22 27 32 34 41 45 49 51 54 58 63 67 68 75 90 91 92 95 96 97 99 110 115 116 121 125 126 127 131 132 142 146 152 153 158 161 165 167 168 171 172 174 175 176 177 183 185 186 188 190 191 201 202 204 209 210 218 220 222 227 229 231 242 246 253 254 >> Fa := ext; ^ Runtime error in ext< ... >: Argument is not irreducible Total time: 0.210 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:06:47 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^k*y + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:06:46 on modular [Seed = 523189620] ------------------------------------- >> Pa :=y^4 + b^23*y^2 + b^k*y + b^239; ^ User error: Identifier 'k' has not been declared or assigned >> Fa := ext; ^ User error: Identifier 'Pa' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:06:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Output: Magma V2.11-6 Sat Oct 16 2004 14:06:58 on modular [Seed = 438974469] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:08:11 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); IsPrimitive(p^10 + a); Output: Magma V2.11-6 Sat Oct 16 2004 14:08:11 on modular [Seed = 3154646] ------------------------------------- false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:08:26 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); IsPrimitive(p^10 + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:08:25 on modular [Seed = 1057955323] ------------------------------------- false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:08:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); a^-1; IsPrimitive(p^10 + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:08:32 on modular [Seed = 973740231] ------------------------------------- b^16*a^3 + b^39*a + b^65 false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:09:34 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); a^-1; IsPrimitive(p^10 + p^7*a + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:09:34 on modular [Seed = 588448160] ------------------------------------- b^16*a^3 + b^39*a + b^65 false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:09:40 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); a^-1; IsPrimitive(p^10 + p^8*a + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:09:40 on modular [Seed = 3740204135] ------------------------------------- b^16*a^3 + b^39*a + b^65 false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:09:47 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); a^-1; IsPrimitive(p^10 + p^6*a + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:09:46 on modular [Seed = 3588618082] ------------------------------------- b^16*a^3 + b^39*a + b^65 false Total time: 0.210 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:09:52 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); a^-1; IsPrimitive(p^10 + p^5*a + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:09:52 on modular [Seed = 3504403069] ------------------------------------- b^16*a^3 + b^39*a + b^65 false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:09:57 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); a^-1; IsPrimitive(p^10 + p^4*a + a^-1); Output: Magma V2.11-6 Sat Oct 16 2004 14:09:57 on modular [Seed = 3489656167] ------------------------------------- b^16*a^3 + b^39*a + b^65 false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:10:34 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do IsPrimitive(p^10 + p^m*a + a^-1); end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:10:34 on modular [Seed = 3405442957] ------------------------------------- false false false false false false false false false Total time: 0.200 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:10:50 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^49*y + b^239; Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do IsPrimitive(p^10 + p^m*a^-1 + a); end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:10:49 on modular [Seed = 3253855413] ------------------------------------- false false false false false false false false false Total time: 0.210 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:12:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 256 do Pa :=y^4 + b^23*y^2 + b^49*y + b^239; if IsPrimitive(Pa) Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do Pp:=p^10 + p^m*a^-1 + a; if IsPrimitive(Pp); k; m; Pa; Pp; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:12:45 on modular [Seed = 4123381813] ------------------------------------- >> Fa := ext; ^ User error: bad syntax >> Rp

:= PolynomialRing(Fa); ^ User error: Identifier 'Fa' has not been declared or assigned >> if IsPrimitive(Pp); ^ User error: bad syntax >> k; m; Pa; Pp; ^ User error: Identifier 'k' has not been declared or assigned >> k; m; Pa; Pp; ^ User error: Identifier 'm' has not been declared or assigned >> k; m; Pa; Pp; ^ User error: Identifier 'Pa' has not been declared or assigned >> k; m; Pa; Pp; ^ User error: Identifier 'Pp' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:13:10 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 256 do Pa :=y^4 + b^23*y^2 + b^49*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do Pp:=p^10 + p^m*a^-1 + a; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:13:09 on modular [Seed = 4007578374] ------------------------------------- >> end for; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:13:52 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 256 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do Pp:=p^10 + p^m*a^-1 + a; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:13:51 on modular [Seed = 3822306913] ------------------------------------- Total time: 0.470 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:14:22 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^2 + b^49*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do Pp:=p^10 + p^m*a^-1 + a; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:14:21 on modular [Seed = 2611723835] ------------------------------------- Total time: 0.390 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:14:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^49*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for m:=1 to 9 do Pp:=p^10 + p^m*a^-1 + a; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:14:33 on modular [Seed = 2527507138] ------------------------------------- Total time: 0.400 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:14:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^49*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for m:=1 to 9 do Pp:=p^10 + p^m*a^-1 + a; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:14:44 on modular [Seed = 2378017220] ------------------------------------- 1 2 7 13 22 23 26 28 29 32 37 38 43 44 47 49 59 61 62 64 67 71 77 79 89 91 92 97 101 113 118 121 122 127 131 137 139 142 143 148 157 158 161 172 181 194 196 197 206 212 223 224 226 229 232 239 242 247 253 254 Total time: 0.410 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:16:14 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^49*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=l+1 to 9 do Pp:=p^10 + p^l*a^-1 + p^m*a + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:16:08 on modular [Seed = 2293804221] ------------------------------------- Total time: 3.080 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:16:36 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=l+1 to 9 do Pp:=p^10 + p^l*a^-1 + p^m*a + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:16:29 on modular [Seed = 2260116134] ------------------------------------- Total time: 3.169 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:17:57 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=l+1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:17:51 on modular [Seed = 3213859629] ------------------------------------- Total time: 3.160 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:18:25 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:18:13 on modular [Seed = 3129646594] ------------------------------------- Total time: 6.240 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:18:37 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^23*y^2 + b^15*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:18:36 on modular [Seed = 2978059536] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:19:16 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^2 + b^15*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:19:00 on modular [Seed = 2895940581] ------------------------------------- Total time: 8.029 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:19:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^2*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:19:34 on modular [Seed = 2879098048] ------------------------------------- Total time: 5.719 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:20:05 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^3*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:19:54 on modular [Seed = 2794881457] ------------------------------------- Total time: 5.620 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:20:25 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^4*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:20:13 on modular [Seed = 1500085848] ------------------------------------- Total time: 6.160 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:20:44 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:20:32 on modular [Seed = 1449554298] ------------------------------------- Total time: 6.009 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:21:28 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^2 + b^k*y + b^29; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:21:17 on modular [Seed = 1283222413] ------------------------------------- Total time: 5.459 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:21:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^2 + b^k*y + b^7; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:21:34 on modular [Seed = 1232694971] ------------------------------------- Total time: 5.280 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:22:09 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^2 + b^53*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:21:56 on modular [Seed = 1182163422] ------------------------------------- Total time: 6.740 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:22:15 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^2 + b^57*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:22:15 on modular [Seed = 2119064053] ------------------------------------- Total time: 0.200 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:22:30 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^3 + b^57*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:22:23 on modular [Seed = 2068536568] ------------------------------------- Total time: 3.350 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:22:43 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^5*y^3 + b^52*y + b^k; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:22:36 on modular [Seed = 1883264960] ------------------------------------- Total time: 3.459 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:22:51 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^52*y + b^85; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:22:50 on modular [Seed = 1834830539] ------------------------------------- Total time: 0.200 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:22:56 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^53*y + b^85; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:22:55 on modular [Seed = 1615873987] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:23:02 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^53*y + b^87; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:23:01 on modular [Seed = 523188550] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:23:10 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^53*y + b^93; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:23:09 on modular [Seed = 337916485] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:23:27 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^53*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:23:15 on modular [Seed = 287389534] ------------------------------------- Total time: 6.000 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:24:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 14:24:03 on modular [Seed = 238954513] ------------------------------------- Errors: /bin/sh: line 1: 7506 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:25:49 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=1 to 100 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 14:25:07 on modular [Seed = 19998686] ------------------------------------- Errors: /bin/sh: line 1: 7517 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:26:39 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=1 to 10 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 14:26:15 on modular [Seed = 805312171] ------------------------------------- Errors: /bin/sh: line 1: 7532 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:27:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=1 to 5 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 14:26:52 on modular [Seed = 723193243] ------------------------------------- Errors: /bin/sh: line 1: 7543 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:28:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=1 to 4 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 14:27:51 on modular [Seed = 3740202917] ------------------------------------- Errors: /bin/sh: line 1: 7554 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:31:52 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=1 to 3 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:28:30 on modular [Seed = 3655987403] ------------------------------------- Total time: 18.000 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:32:49 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=4 to 7 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 14:32:07 on modular [Seed = 3439125687] ------------------------------------- Errors: /bin/sh: line 1: 7568 Killed nice -n 19 /usr/local/bin/magma '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:57:51 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=4 to 6 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:57:13 on modular [Seed = 3822308790] ------------------------------------- Total time: 18.800 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:58:16 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=1 to 255 do for t:=4 to 6 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:58:15 on modular [Seed = 2527508621] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.68MB '68.60.2' ************** MAGMA ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 14:59:04 2004 Input: sin x=1/2 Output: Magma V2.11-6 Sat Oct 16 2004 14:59:02 on modular [Seed = 3129644176] ------------------------------------- >> sin x=1/2 ^ User error: bad syntax Total time: 0.180 seconds, Total memory usage: 3.50MB '68.60.2' ************** MAGMA ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 14:59:29 2004 Input: sin 64=1/2xy Output: Magma V2.11-6 Sat Oct 16 2004 14:59:29 on modular [Seed = 2961219197] ------------------------------------- >> sin 64=1/2xy ^ User error: bad syntax Total time: 0.200 seconds, Total memory usage: 3.50MB '68.60.2' ************** MAGMA ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 14:59:37 2004 Input: sin 64=1/2xy Output: Magma V2.11-6 Sat Oct 16 2004 14:59:37 on modular [Seed = 2710671204] ------------------------------------- >> sin 64=1/2xy ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:59:42 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:59:41 on modular [Seed = 1567454108] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 14:59:46 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 14:59:46 on modular [Seed = 1483241125] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.68MB '68.60.2' ************** MAGMA ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 15:00:00 2004 Input: 64=1/2xy Output: Magma V2.11-6 Sat Oct 16 2004 14:59:59 on modular [Seed = 1300063165] ------------------------------------- >> 64=1/2xy ^ User error: Invalid hexadecimal integer Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:00:12 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:00:12 on modular [Seed = 1215850155] ------------------------------------- Total time: 0.210 seconds, Total memory usage: 3.68MB '68.60.2' ************** MAGMA ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 15:00:18 2004 Input: 64=1/2 x Output: Magma V2.11-6 Sat Oct 16 2004 15:00:18 on modular [Seed = 2102219744] ------------------------------------- >> 64=1/2 x ^ User error: bad syntax Total time: 0.200 seconds, Total memory usage: 3.50MB '68.60.2' ************** MAGMA ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 15:00:29 2004 Input: 64=1/n Output: Magma V2.11-6 Sat Oct 16 2004 15:00:28 on modular [Seed = 2018006763] ------------------------------------- >> 64=1/n ^ User error: Identifier 'n' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:00:35 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:00:35 on modular [Seed = 1883266812] ------------------------------------- false Total time: 0.210 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:00:44 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^4+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:00:44 on modular [Seed = 506343581] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Ra := PolynomialRing(Fb); ^ User error: Identifier 'Fb' has not been declared or assigned >> Pa :=y^4 + b^k*y^3 + b^t*y + b^239; ^ User error: Identifier 'y' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:00:51 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^3+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:00:50 on modular [Seed = 422131620] ------------------------------------- false Total time: 0.220 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:07 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^2+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:05 on modular [Seed = 287391679] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Ra := PolynomialRing(Fb); ^ User error: Identifier 'Fb' has not been declared or assigned >> Pa :=y^4 + b^k*y^3 + b^t*y + b^239; ^ User error: Identifier 'y' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:09 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^2+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:00:58 on modular [Seed = 337918624] ------------------------------------- true 3 4 6 7 8 13 19 26 27 34 36 38 53 61 63 65 66 68 70 74 76 79 80 87 90 107 108 120 123 124 127 130 133 141 145 149 153 164 171 176 185 186 189 199 201 206 207 210 211 213 217 219 221 223 232 234 239 Total time: 5.250 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:22 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^3+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:22 on modular [Seed = 70530393] ------------------------------------- false Total time: 0.220 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:23 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^2+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:12 on modular [Seed = 188425644] ------------------------------------- true 3 4 6 7 8 13 19 26 27 34 36 38 53 61 63 65 66 68 70 74 76 79 80 87 90 107 108 120 123 124 127 130 133 141 145 149 153 164 171 176 185 186 189 199 201 206 207 210 211 213 217 219 221 223 232 234 239 Total time: 5.219 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:29 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:28 on modular [Seed = 1041108841] ------------------------------------- false Total time: 0.210 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:35 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:35 on modular [Seed = 956893289] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Ra := PolynomialRing(Fb); ^ User error: Identifier 'Fb' has not been declared or assigned >> Pa :=y^4 + b^k*y^3 + b^t*y + b^239; ^ User error: Identifier 'y' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:39 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^3+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:39 on modular [Seed = 872678776] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Ra := PolynomialRing(Fb); ^ User error: Identifier 'Fb' has not been declared or assigned >> Pa :=y^4 + b^k*y^3 + b^t*y + b^239; ^ User error: Identifier 'y' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:46 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^1+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:43 on modular [Seed = 790568552] ------------------------------------- false >> Fb := ext< F2 | Pb >; ^ Runtime error in ext< ... >: Argument is not irreducible >> Ra := PolynomialRing(Fb); ^ User error: Identifier 'Fb' has not been declared or assigned >> Pa :=y^4 + b^k*y^3 + b^t*y + b^239; ^ User error: Identifier 'y' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:49 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^2+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:18 on modular [Seed = 121055654] ------------------------------------- true 3 4 6 7 8 13 19 26 27 34 36 38 53 61 63 65 66 68 70 74 76 79 80 87 90 107 108 120 123 124 127 130 133 141 145 149 153 164 171 176 185 186 189 199 201 206 207 210 211 213 217 219 221 223 232 234 239 Total time: 5.110 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:01:58 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:01:57 on modular [Seed = 689510483] ------------------------------------- false Total time: 0.210 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:02:18 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:02:09 on modular [Seed = 3672828852] ------------------------------------- true 1 11 14 34 42 49 57 73 86 88 93 94 97 103 104 107 115 117 124 126 127 135 136 137 138 142 146 148 154 156 162 164 167 170 177 182 183 188 191 195 196 201 203 205 217 218 221 222 227 229 233 244 Total time: 4.389 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:02:29 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:02:03 on modular [Seed = 537923924] ------------------------------------- true 1 11 14 34 42 49 57 73 86 88 93 94 97 103 104 107 115 117 124 126 127 135 136 137 138 142 146 148 154 156 162 164 167 170 177 182 183 188 191 195 196 201 203 205 217 218 221 222 227 229 233 244 Total time: 4.519 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:02:35 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^3+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:02:34 on modular [Seed = 3571770817] ------------------------------------- false Total time: 0.210 seconds, Total memory usage: 3.68MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:02:55 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; IsPrimitive(Pb); Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); k; for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:02:43 on modular [Seed = 3489660611] ------------------------------------- true 3 6 13 14 19 22 26 28 29 36 39 47 58 60 61 62 66 69 70 76 78 79 87 94 97 105 110 115 117 132 134 137 138 140 141 155 157 158 159 165 170 171 172 176 178 186 187 201 206 210 211 221 225 227 232 235 255 Total time: 6.209 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:03:22 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:03:10 on modular [Seed = 3405446139] ------------------------------------- Total time: 6.169 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:04:05 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^5; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:04:05 on modular [Seed = 3321230399] ------------------------------------- Total time: 0.200 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:04:24 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); t:=23; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^7; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:04:11 on modular [Seed = 3237015859] ------------------------------------- Total time: 6.009 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:04:50 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24; for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^7; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:04:49 on modular [Seed = 4224436853] ------------------------------------- >> for t:=23 to 24; ^ User error: bad syntax >> Pa :=y^4 + b^k*y^3 + b^t*y + b^7; ^ User error: Identifier 't' has not been declared or assigned >> end for; ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:05:20 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^7; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:04:57 on modular [Seed = 4140222320] ------------------------------------- Total time: 11.179 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:05:29 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^9; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:05:28 on modular [Seed = 4056006742] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:06:03 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^11; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:05:38 on modular [Seed = 3973897393] ------------------------------------- Total time: 12.400 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:06:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^13; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:06:09 on modular [Seed = 3889682329] ------------------------------------- Total time: 11.929 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:06:38 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^17; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:06:37 on modular [Seed = 3788624259] ------------------------------------- Total time: 0.220 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:07:16 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^19; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:06:54 on modular [Seed = 2628562061] ------------------------------------- Total time: 11.189 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:08:39 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^3 + b^t*y + b^21; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:08:39 on modular [Seed = 2460131962] ------------------------------------- Total time: 0.220 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:08:45 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^21; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:08:45 on modular [Seed = 2378022255] ------------------------------------- Total time: 0.220 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:09:14 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=23 to 24 do for k:=1 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^23; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:08:52 on modular [Seed = 2293807123] ------------------------------------- Total time: 11.310 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:10:04 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=1 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^23; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:09:29 on modular [Seed = 2209592117] ------------------------------------- Total time: 17.359 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:11:21 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^53; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:10:46 on modular [Seed = 3197013463] ------------------------------------- Total time: 17.059 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:11:28 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^54; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:11:28 on modular [Seed = 3095956359] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:11:33 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^55; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:11:32 on modular [Seed = 3011739784] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:12:11 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^56; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:11:37 on modular [Seed = 2929630616] ------------------------------------- Total time: 17.300 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:12:22 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^57; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:12:21 on modular [Seed = 2845416035] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:13:01 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^58; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:12:25 on modular [Seed = 2761201506] ------------------------------------- Total time: 17.929 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:15:07 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^59; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:14:33 on modular [Seed = 1567452954] ------------------------------------- Total time: 16.940 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:17:30 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^61; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:16:55 on modular [Seed = 1466394030] ------------------------------------- Total time: 17.649 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:18:15 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^62; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:17:40 on modular [Seed = 1316912324] ------------------------------------- Total time: 17.719 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:18:29 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^63; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:18:29 on modular [Seed = 1266384400] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:19:08 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^64; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:18:34 on modular [Seed = 1148481808] ------------------------------------- Total time: 16.609 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:19:16 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^65; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:19:15 on modular [Seed = 1097954348] ------------------------------------- Total time: 0.230 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:19:21 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^66; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:19:20 on modular [Seed = 2051690268] ------------------------------------- Total time: 0.220 seconds, Total memory usage: 3.76MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:20:02 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^67; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsPrimitive(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:19:27 on modular [Seed = 2001158678] ------------------------------------- Total time: 17.640 seconds, Total memory usage: 4.55MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:20:24 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^5+z^3+z+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^67; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsIrreducible(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:20:13 on modular [Seed = 1817991519] ------------------------------------- 13 239 7 y^4 + b^13*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^201*a + b^172)*p^7 + a*p^2 + 1 13 239 7 y^4 + b^13*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^201*a + b^172)*p^7 + a*p^4 + 1 13 239 3 y^4 + b^13*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^201*a + b^172)*p^3 + 1 13 239 3 y^4 + b^13*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^201*a + b^172)*p^3 + 1 20 239 2 y^4 + b^20*y^2 + b^239*y + b^67 p^10 + a*p^3 + (b^188*a^3 + b^208*a + b^172)*p^2 + 1 20 239 8 y^4 + b^20*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^208*a + b^172)*p^8 + a*p^7 + 1 24 239 1 y^4 + b^24*y^2 + b^239*y + b^67 p^10 + a*p^2 + (b^188*a^3 + b^212*a + b^172)*p + 1 24 239 9 y^4 + b^24*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^212*a + b^172)*p^9 + a*p^8 + 1 27 239 1 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + a*p^2 + (b^188*a^3 + b^215*a + b^172)*p + 1 27 239 7 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^215*a + b^172)*p^7 + a*p^2 + 1 27 239 7 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^215*a + b^172)*p^7 + a*p^4 + 1 27 239 3 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + a*p^5 + (b^188*a^3 + b^215*a + b^172)*p^3 + 1 27 239 7 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^215*a + b^172)*p^7 + a*p^5 + 1 27 239 3 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^215*a + b^172)*p^3 + 1 27 239 3 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^215*a + b^172)*p^3 + 1 27 239 9 y^4 + b^27*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^215*a + b^172)*p^9 + a*p^8 + 1 33 239 5 y^4 + b^33*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^221*a + b^172)*p^5 + a*p + 1 33 239 5 y^4 + b^33*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^221*a + b^172)*p^5 + 1 34 239 1 y^4 + b^34*y^2 + b^239*y + b^67 p^10 + a*p^4 + (b^188*a^3 + b^222*a + b^172)*p + 1 34 239 9 y^4 + b^34*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^222*a + b^172)*p^9 + a*p^6 + 1 41 239 3 y^4 + b^41*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^229*a + b^172)*p^3 + a*p + 1 41 239 7 y^4 + b^41*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^229*a + b^172)*p^7 + a*p^2 + 1 41 239 3 y^4 + b^41*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^229*a + b^172)*p^3 + 1 41 239 7 y^4 + b^41*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^229*a + b^172)*p^7 + 1 52 239 7 y^4 + b^52*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^240*a + b^172)*p^7 + a*p^4 + 1 52 239 3 y^4 + b^52*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^240*a + b^172)*p^3 + 1 55 239 9 y^4 + b^55*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^243*a + b^172)*p^9 + a*p^2 + 1 55 239 1 y^4 + b^55*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^243*a + b^172)*p + 1 59 239 2 y^4 + b^59*y^2 + b^239*y + b^67 p^10 + a*p^3 + (b^188*a^3 + b^247*a + b^172)*p^2 + 1 59 239 6 y^4 + b^59*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^247*a + b^172)*p^6 + a*p^3 + 1 59 239 4 y^4 + b^59*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^247*a + b^172)*p^4 + 1 59 239 8 y^4 + b^59*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^247*a + b^172)*p^8 + a*p^7 + 1 70 239 7 y^4 + b^70*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^3*a + b^172)*p^7 + a*p^4 + 1 70 239 3 y^4 + b^70*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^3*a + b^172)*p^3 + 1 74 239 7 y^4 + b^74*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^7*a + b^172)*p^7 + a*p^4 + 1 74 239 3 y^4 + b^74*y^2 + b^239*y + b^67 p^10 + a*p^5 + (b^188*a^3 + b^7*a + b^172)*p^3 + 1 74 239 7 y^4 + b^74*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^7*a + b^172)*p^7 + a*p^5 + 1 74 239 3 y^4 + b^74*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^7*a + b^172)*p^3 + 1 81 239 3 y^4 + b^81*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^14*a + b^172)*p^3 + a*p^2 + 1 81 239 2 y^4 + b^81*y^2 + b^239*y + b^67 p^10 + a*p^5 + (b^188*a^3 + b^14*a + b^172)*p^2 + 1 81 239 8 y^4 + b^81*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^14*a + b^172)*p^8 + a*p^5 + 1 81 239 7 y^4 + b^81*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^14*a + b^172)*p^7 + 1 82 239 5 y^4 + b^82*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^15*a + b^172)*p^5 + a*p + 1 82 239 9 y^4 + b^82*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^15*a + b^172)*p^9 + a*p^3 + 1 82 239 1 y^4 + b^82*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^15*a + b^172)*p + 1 82 239 5 y^4 + b^82*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^15*a + b^172)*p^5 + 1 96 239 3 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^29*a + b^172)*p^3 + a*p + 1 96 239 1 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + a*p^2 + (b^188*a^3 + b^29*a + b^172)*p + 1 96 239 9 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^29*a + b^172)*p^9 + a*p^3 + 1 96 239 7 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^29*a + b^172)*p^7 + a*p^4 + 1 96 239 3 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^29*a + b^172)*p^3 + 1 96 239 1 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^29*a + b^172)*p + 1 96 239 9 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^29*a + b^172)*p^9 + a*p^8 + 1 96 239 7 y^4 + b^96*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^29*a + b^172)*p^7 + 1 101 239 2 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^2 + a*p + 1 101 239 3 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^3 + a*p + 1 101 239 4 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^4 + a*p + 1 101 239 7 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^7 + a*p + 1 101 239 2 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^3 + (b^188*a^3 + b^34*a + b^172)*p^2 + 1 101 239 5 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^5 + a*p^3 + 1 101 239 8 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^8 + a*p^3 + 1 101 239 2 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^34*a + b^172)*p^2 + 1 101 239 5 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^34*a + b^172)*p^5 + 1 101 239 8 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^34*a + b^172)*p^8 + a*p^7 + 1 101 239 3 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^34*a + b^172)*p^3 + 1 101 239 6 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^34*a + b^172)*p^6 + 1 101 239 7 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^34*a + b^172)*p^7 + 1 101 239 8 y^4 + b^101*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^34*a + b^172)*p^8 + 1 105 239 2 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^38*a + b^172)*p^2 + a*p + 1 105 239 7 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^38*a + b^172)*p^7 + a*p + 1 105 239 8 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^38*a + b^172)*p^8 + a*p + 1 105 239 8 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^38*a + b^172)*p^8 + a*p^3 + 1 105 239 2 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^38*a + b^172)*p^2 + 1 105 239 2 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^38*a + b^172)*p^2 + 1 105 239 3 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^38*a + b^172)*p^3 + 1 105 239 8 y^4 + b^105*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^38*a + b^172)*p^8 + 1 106 239 5 y^4 + b^106*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^39*a + b^172)*p^5 + a*p^3 + 1 106 239 6 y^4 + b^106*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^39*a + b^172)*p^6 + a*p^3 + 1 106 239 4 y^4 + b^106*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^39*a + b^172)*p^4 + 1 106 239 5 y^4 + b^106*y^2 + b^239*y + b^67 p^10 + a*p^7 + (b^188*a^3 + b^39*a + b^172)*p^5 + 1 109 239 3 y^4 + b^109*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^42*a + b^172)*p^3 + a*p + 1 109 239 7 y^4 + b^109*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^42*a + b^172)*p^7 + 1 110 239 7 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^43*a + b^172)*p^7 + a*p + 1 110 239 3 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^43*a + b^172)*p^3 + a*p^2 + 1 110 239 9 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^43*a + b^172)*p^9 + a*p^2 + 1 110 239 1 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + a*p^3 + (b^188*a^3 + b^43*a + b^172)*p + 1 110 239 9 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^43*a + b^172)*p^9 + a*p^7 + 1 110 239 1 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^43*a + b^172)*p + 1 110 239 7 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + a*p^8 + (b^188*a^3 + b^43*a + b^172)*p^7 + 1 110 239 3 y^4 + b^110*y^2 + b^239*y + b^67 p^10 + a*p^9 + (b^188*a^3 + b^43*a + b^172)*p^3 + 1 113 239 1 y^4 + b^113*y^2 + b^239*y + b^67 p^10 + a*p^2 + (b^188*a^3 + b^46*a + b^172)*p + 1 113 239 2 y^4 + b^113*y^2 + b^239*y + b^67 p^10 + a*p^3 + (b^188*a^3 + b^46*a + b^172)*p^2 + 1 113 239 8 y^4 + b^113*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^46*a + b^172)*p^8 + a*p^7 + 1 113 239 9 y^4 + b^113*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^46*a + b^172)*p^9 + a*p^8 + 1 118 239 1 y^4 + b^118*y^2 + b^239*y + b^67 p^10 + a*p^5 + (b^188*a^3 + b^51*a + b^172)*p + 1 118 239 9 y^4 + b^118*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^51*a + b^172)*p^9 + a*p^5 + 1 119 239 1 y^4 + b^119*y^2 + b^239*y + b^67 p^10 + a*p^2 + (b^188*a^3 + b^52*a + b^172)*p + 1 119 239 9 y^4 + b^119*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^52*a + b^172)*p^9 + a*p^8 + 1 126 239 8 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^59*a + b^172)*p^8 + a*p + 1 126 239 1 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + a*p^2 + (b^188*a^3 + b^59*a + b^172)*p + 1 126 239 9 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^59*a + b^172)*p^9 + a*p^2 + 1 126 239 1 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + a*p^4 + (b^188*a^3 + b^59*a + b^172)*p + 1 126 239 7 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^59*a + b^172)*p^7 + a*p^4 + 1 126 239 3 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + a*p^6 + (b^188*a^3 + b^59*a + b^172)*p^3 + 1 126 239 9 y^4 + b^126*y^2 + b^239*y + b^67 p^10 + (b^188*a^3 + b^59*a + b^172)*p^9 + a*p^6 + 1 126 239 1 y^4 + b^126*y^2 + b^239*y + b^67 p^1 ** WARNING: Output too long, hence truncated. '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:22:08 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for t:=239 to 241 do for k:=0 to 255 do Pa :=y^4 + b^k*y^2 + b^t*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsIrreducible(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:21:57 on modular [Seed = 1716933613] ------------------------------------- 1 239 5 y^4 + b*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^17*a + 1)*p^5 + a*p^2 + 1 1 239 2 y^4 + b*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^17*a + 1)*p^2 + 1 1 239 8 y^4 + b*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^17*a + 1)*p^8 + a*p^3 + 1 1 239 2 y^4 + b*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^17*a + 1)*p^2 + 1 1 239 8 y^4 + b*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^17*a + 1)*p^8 + a*p^7 + 1 1 239 5 y^4 + b*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^17*a + 1)*p^5 + 1 11 239 3 y^4 + b^11*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^27*a + 1)*p^3 + a*p^2 + 1 11 239 7 y^4 + b^11*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^27*a + 1)*p^7 + 1 14 239 8 y^4 + b^14*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^30*a + 1)*p^8 + a*p + 1 14 239 6 y^4 + b^14*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^30*a + 1)*p^6 + a*p^3 + 1 14 239 4 y^4 + b^14*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^30*a + 1)*p^4 + 1 14 239 2 y^4 + b^14*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^30*a + 1)*p^2 + 1 16 239 1 y^4 + b^16*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^32*a + 1)*p + 1 16 239 9 y^4 + b^16*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^32*a + 1)*p^9 + a*p^5 + 1 20 239 4 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^36*a + 1)*p^4 + a*p + 1 20 239 8 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^36*a + 1)*p^8 + a*p + 1 20 239 8 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^36*a + 1)*p^8 + a*p^3 + 1 20 239 1 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + a*p^4 + (b^16*a^3 + b^36*a + 1)*p + 1 20 239 9 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^36*a + 1)*p^9 + a*p^6 + 1 20 239 2 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^36*a + 1)*p^2 + 1 20 239 2 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^36*a + 1)*p^2 + 1 20 239 6 y^4 + b^20*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^36*a + 1)*p^6 + 1 21 239 2 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^37*a + 1)*p^2 + a*p + 1 21 239 5 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^37*a + 1)*p^5 + a*p^2 + 1 21 239 5 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^37*a + 1)*p^5 + a*p^3 + 1 21 239 1 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^37*a + 1)*p + 1 21 239 9 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^37*a + 1)*p^9 + a*p^5 + 1 21 239 5 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^37*a + 1)*p^5 + 1 21 239 5 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^37*a + 1)*p^5 + 1 21 239 8 y^4 + b^21*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^37*a + 1)*p^8 + 1 27 239 9 y^4 + b^27*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^43*a + 1)*p^9 + a*p^2 + 1 27 239 1 y^4 + b^27*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^43*a + 1)*p + 1 27 239 2 y^4 + b^27*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^43*a + 1)*p^2 + 1 27 239 8 y^4 + b^27*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^43*a + 1)*p^8 + a*p^7 + 1 27 239 9 y^4 + b^27*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^43*a + 1)*p^9 + a*p^7 + 1 27 239 1 y^4 + b^27*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^43*a + 1)*p + 1 28 239 4 y^4 + b^28*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^44*a + 1)*p^4 + a*p + 1 28 239 1 y^4 + b^28*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^44*a + 1)*p + 1 28 239 9 y^4 + b^28*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^44*a + 1)*p^9 + a*p^7 + 1 28 239 6 y^4 + b^28*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^44*a + 1)*p^6 + 1 31 239 3 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^47*a + 1)*p^3 + a*p^2 + 1 31 239 5 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^47*a + 1)*p^5 + a*p^2 + 1 31 239 2 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^47*a + 1)*p^2 + 1 31 239 5 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^47*a + 1)*p^5 + a*p^3 + 1 31 239 1 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^47*a + 1)*p + 1 31 239 9 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^47*a + 1)*p^9 + a*p^5 + 1 31 239 5 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^47*a + 1)*p^5 + 1 31 239 8 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^47*a + 1)*p^8 + a*p^7 + 1 31 239 5 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^47*a + 1)*p^5 + 1 31 239 7 y^4 + b^31*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^47*a + 1)*p^7 + 1 34 239 4 y^4 + b^34*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^50*a + 1)*p^4 + a*p + 1 34 239 6 y^4 + b^34*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^50*a + 1)*p^6 + 1 38 239 4 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^54*a + 1)*p^4 + a*p + 1 38 239 5 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^54*a + 1)*p^5 + a*p + 1 38 239 7 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^54*a + 1)*p^7 + a*p + 1 38 239 7 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^54*a + 1)*p^7 + a*p^2 + 1 38 239 3 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^54*a + 1)*p^3 + 1 38 239 3 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^54*a + 1)*p^3 + 1 38 239 5 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^54*a + 1)*p^5 + 1 38 239 6 y^4 + b^38*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^54*a + 1)*p^6 + 1 52 239 3 y^4 + b^52*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^68*a + 1)*p^3 + a*p^2 + 1 52 239 1 y^4 + b^52*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^68*a + 1)*p + 1 52 239 9 y^4 + b^52*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^68*a + 1)*p^9 + a*p^7 + 1 52 239 7 y^4 + b^52*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^68*a + 1)*p^7 + 1 55 239 5 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^71*a + 1)*p^5 + a*p^2 + 1 55 239 6 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^71*a + 1)*p^6 + a*p^3 + 1 55 239 8 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^71*a + 1)*p^8 + a*p^3 + 1 55 239 2 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^71*a + 1)*p^2 + 1 55 239 8 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^71*a + 1)*p^8 + a*p^5 + 1 55 239 2 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^71*a + 1)*p^2 + 1 55 239 4 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^71*a + 1)*p^4 + 1 55 239 5 y^4 + b^55*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^71*a + 1)*p^5 + 1 56 239 7 y^4 + b^56*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^72*a + 1)*p^7 + a*p^2 + 1 56 239 1 y^4 + b^56*y^2 + b^239*y + b^239 p^10 + a*p^4 + (b^16*a^3 + b^72*a + 1)*p + 1 56 239 1 y^4 + b^56*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^72*a + 1)*p + 1 56 239 9 y^4 + b^56*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^72*a + 1)*p^9 + a*p^5 + 1 56 239 9 y^4 + b^56*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^72*a + 1)*p^9 + a*p^6 + 1 56 239 3 y^4 + b^56*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^72*a + 1)*p^3 + 1 57 239 3 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^73*a + 1)*p^3 + a*p^2 + 1 57 239 5 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^73*a + 1)*p^5 + a*p^3 + 1 57 239 6 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^73*a + 1)*p^6 + a*p^3 + 1 57 239 2 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^73*a + 1)*p^2 + 1 57 239 8 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^73*a + 1)*p^8 + a*p^5 + 1 57 239 4 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^73*a + 1)*p^4 + 1 57 239 5 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^73*a + 1)*p^5 + 1 57 239 7 y^4 + b^57*y^2 + b^239*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^73*a + 1)*p^7 + 1 61 239 5 y^4 + b^61*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^77*a + 1)*p^5 + a*p + 1 61 239 7 y^4 + b^61*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^77*a + 1)*p^7 + a*p + 1 61 239 2 y^4 + b^61*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^77*a + 1)*p^2 + 1 61 239 8 y^4 + b^61*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^77*a + 1)*p^8 + a*p^7 + 1 61 239 3 y^4 + b^61*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^77*a + 1)*p^3 + 1 61 239 5 y^4 + b^61*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^77*a + 1)*p^5 + 1 70 239 2 y^4 + b^70*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^86*a + 1)*p^2 + 1 70 239 5 y^4 + b^70*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^86*a + 1)*p^5 + a*p^3 + 1 70 239 2 y^4 + b^70*y^2 + b^239*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^86*a + 1)*p^2 + 1 70 239 8 y^4 + b^70*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^86*a + 1)*p^8 + a*p^5 + 1 70 239 5 y^4 + b^70*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^86*a + 1)*p^5 + 1 70 239 8 y^4 + b^70*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^86*a + 1)*p^8 + a*p^7 + 1 71 239 2 y^4 + b^71*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^87*a + 1)*p^2 + 1 71 239 8 y^4 + b^71*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^87*a + 1)*p^8 + a*p^7 + 1 72 239 5 y^4 + b^72*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^88*a + 1)*p^5 + a*p + 1 72 239 8 y^4 + b^72*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^88*a + 1)*p^8 + a*p + 1 72 239 2 y^4 + b^72*y^2 + b^239*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^88*a + 1)*p^2 + 1 72 239 8 y^4 + b^72*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^88*a + 1)*p^8 + a*p^7 + 1 72 239 2 y^4 + b^72*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^88*a + 1)*p^2 + 1 72 239 5 y^4 + b^72*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^88*a + 1)*p^5 + 1 75 239 8 y^4 + b^75*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^91*a + 1)*p^8 + a*p^3 + 1 75 239 2 y^4 + b^75*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^91*a + 1)*p^2 + 1 76 239 7 y^4 + b^76*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^92*a + 1)*p^7 + a*p + 1 76 239 5 y^4 + b^76*y^2 + b^239*y + b^239 p^10 + (b^16*a^3 + b^92*a + 1)*p^5 + a*p^3 + 1 76 239 5 y^4 + b^76*y^2 + b^239*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^92*a + 1)*p^5 + 1 76 239 3 y^4 + b^76*y^2 + b^239*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^92*a ** WARNING: Output too long, hence truncated. '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:22:30 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=0 to 255 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsIrreducible(Pp) then k; t; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:22:30 on modular [Seed = 1666406091] ------------------------------------- >> k; t; m; Pa; Pp; ^ User error: Identifier 't' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.5.15 (130.235.5.15) Time: Sat Oct 16 15:22:42 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); for k:=0 to 255 do Pa :=y^4 + b^23*y^2 + b^k*y + b^239; if IsPrimitive(Pa) then Fa := ext; Rp

:= PolynomialRing(Fa); for l:=1 to 9 do for m:=1 to 9 do Pp:=p^10 + p^l*a + p^m*a^-1 + 1; if IsIrreducible(Pp) then k; m; Pa; Pp; end if; end for; end for; end if; end for; Output: Magma V2.11-6 Sat Oct 16 2004 15:22:37 on modular [Seed = 472656319] ------------------------------------- 17 5 y^4 + b^23*y^2 + b^17*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^33)*p^5 + a*p + 1 17 8 y^4 + b^23*y^2 + b^17*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^33)*p^8 + a*p + 1 17 3 y^4 + b^23*y^2 + b^17*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^33)*p^3 + a*p^2 + 1 17 7 y^4 + b^23*y^2 + b^17*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^33)*p^7 + 1 17 2 y^4 + b^23*y^2 + b^17*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^33)*p^2 + 1 17 5 y^4 + b^23*y^2 + b^17*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^33)*p^5 + 1 20 7 y^4 + b^23*y^2 + b^20*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^36)*p^7 + a*p + 1 20 7 y^4 + b^23*y^2 + b^20*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^36)*p^7 + a*p^2 + 1 20 6 y^4 + b^23*y^2 + b^20*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^36)*p^6 + a*p^3 + 1 20 4 y^4 + b^23*y^2 + b^20*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^36)*p^4 + 1 20 3 y^4 + b^23*y^2 + b^20*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^36)*p^3 + 1 20 3 y^4 + b^23*y^2 + b^20*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^36)*p^3 + 1 21 6 y^4 + b^23*y^2 + b^21*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^37)*p^6 + a*p^3 + 1 21 1 y^4 + b^23*y^2 + b^21*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^37)*p + 1 21 9 y^4 + b^23*y^2 + b^21*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^37)*p^9 + a*p^5 + 1 21 4 y^4 + b^23*y^2 + b^21*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^37)*p^4 + 1 22 8 y^4 + b^23*y^2 + b^22*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^38)*p^8 + a*p + 1 22 2 y^4 + b^23*y^2 + b^22*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^38)*p^2 + 1 27 1 y^4 + b^23*y^2 + b^27*y + b^239 p^10 + a*p^4 + (b^16*a^3 + b^39*a + b^43)*p + 1 27 2 y^4 + b^23*y^2 + b^27*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^43)*p^2 + 1 27 8 y^4 + b^23*y^2 + b^27*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^43)*p^8 + a*p^5 + 1 27 9 y^4 + b^23*y^2 + b^27*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^43)*p^9 + a*p^6 + 1 32 8 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^48)*p^8 + a*p + 1 32 5 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^48)*p^5 + a*p^2 + 1 32 1 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^48)*p + 1 32 2 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^48)*p^2 + 1 32 8 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^48)*p^8 + a*p^5 + 1 32 9 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^48)*p^9 + a*p^5 + 1 32 5 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^48)*p^5 + 1 32 2 y^4 + b^23*y^2 + b^32*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^48)*p^2 + 1 34 5 y^4 + b^23*y^2 + b^34*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^50)*p^5 + a*p + 1 34 3 y^4 + b^23*y^2 + b^34*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^50)*p^3 + 1 34 7 y^4 + b^23*y^2 + b^34*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^50)*p^7 + a*p^5 + 1 34 5 y^4 + b^23*y^2 + b^34*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^50)*p^5 + 1 41 7 y^4 + b^23*y^2 + b^41*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^57)*p^7 + a*p^2 + 1 41 6 y^4 + b^23*y^2 + b^41*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^57)*p^6 + a*p^3 + 1 41 3 y^4 + b^23*y^2 + b^41*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^57)*p^3 + 1 41 7 y^4 + b^23*y^2 + b^41*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^57)*p^7 + a*p^5 + 1 41 4 y^4 + b^23*y^2 + b^41*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^57)*p^4 + 1 41 3 y^4 + b^23*y^2 + b^41*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^57)*p^3 + 1 45 7 y^4 + b^23*y^2 + b^45*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^61)*p^7 + a*p^2 + 1 45 9 y^4 + b^23*y^2 + b^45*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^61)*p^9 + a*p^2 + 1 45 1 y^4 + b^23*y^2 + b^45*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^39*a + b^61)*p + 1 45 9 y^4 + b^23*y^2 + b^45*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^61)*p^9 + a*p^7 + 1 45 1 y^4 + b^23*y^2 + b^45*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^61)*p + 1 45 3 y^4 + b^23*y^2 + b^45*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^61)*p^3 + 1 51 3 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^67)*p^3 + a*p + 1 51 3 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^67)*p^3 + a*p^2 + 1 51 5 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^67)*p^5 + a*p^2 + 1 51 7 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^67)*p^7 + a*p^2 + 1 51 3 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^67)*p^3 + 1 51 5 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^67)*p^5 + 1 51 7 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^67)*p^7 + 1 51 7 y^4 + b^23*y^2 + b^51*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^67)*p^7 + 1 54 5 y^4 + b^23*y^2 + b^54*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^70)*p^5 + a*p^3 + 1 54 5 y^4 + b^23*y^2 + b^54*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^70)*p^5 + 1 58 1 y^4 + b^23*y^2 + b^58*y + b^239 p^10 + a*p^2 + (b^16*a^3 + b^39*a + b^74)*p + 1 58 9 y^4 + b^23*y^2 + b^58*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^74)*p^9 + a*p^8 + 1 63 5 y^4 + b^23*y^2 + b^63*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^79)*p^5 + a*p + 1 63 5 y^4 + b^23*y^2 + b^63*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^79)*p^5 + 1 67 2 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^83)*p^2 + a*p + 1 67 1 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + a*p^2 + (b^16*a^3 + b^39*a + b^83)*p + 1 67 1 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^39*a + b^83)*p + 1 67 7 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^83)*p^7 + a*p^4 + 1 67 3 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^83)*p^3 + 1 67 7 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^83)*p^7 + a*p^5 + 1 67 3 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + a*p^6 + (b^16*a^3 + b^39*a + b^83)*p^3 + 1 67 9 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^83)*p^9 + a*p^7 + 1 67 9 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^83)*p^9 + a*p^8 + 1 67 8 y^4 + b^23*y^2 + b^67*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^83)*p^8 + 1 68 5 y^4 + b^23*y^2 + b^68*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^84)*p^5 + a*p^2 + 1 68 5 y^4 + b^23*y^2 + b^68*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^84)*p^5 + 1 90 8 y^4 + b^23*y^2 + b^90*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^106)*p^8 + a*p + 1 90 2 y^4 + b^23*y^2 + b^90*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^106)*p^2 + 1 90 8 y^4 + b^23*y^2 + b^90*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^106)*p^8 + a*p^5 + 1 90 2 y^4 + b^23*y^2 + b^90*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^106)*p^2 + 1 91 9 y^4 + b^23*y^2 + b^91*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^107)*p^9 + a*p^2 + 1 91 1 y^4 + b^23*y^2 + b^91*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^107)*p + 1 92 5 y^4 + b^23*y^2 + b^92*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^108)*p^5 + a*p + 1 92 4 y^4 + b^23*y^2 + b^92*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^108)*p^4 + 1 92 6 y^4 + b^23*y^2 + b^92*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^108)*p^6 + a*p^5 + 1 92 5 y^4 + b^23*y^2 + b^92*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^108)*p^5 + 1 95 9 y^4 + b^23*y^2 + b^95*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^111)*p^9 + a*p^2 + 1 95 1 y^4 + b^23*y^2 + b^95*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^111)*p + 1 97 4 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^113)*p^4 + a*p + 1 97 9 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^113)*p^9 + a*p^3 + 1 97 1 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + a*p^4 + (b^16*a^3 + b^39*a + b^113)*p + 1 97 3 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^113)*p^3 + 1 97 7 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^113)*p^7 + a*p^5 + 1 97 9 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^113)*p^9 + a*p^6 + 1 97 1 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^113)*p + 1 97 6 y^4 + b^23*y^2 + b^97*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^113)*p^6 + 1 99 1 y^4 + b^23*y^2 + b^99*y + b^239 p^10 + a*p^2 + (b^16*a^3 + b^39*a + b^115)*p + 1 99 9 y^4 + b^23*y^2 + b^99*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^115)*p^9 + a*p^8 + 1 110 7 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^126)*p^7 + a*p + 1 110 5 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^126)*p^5 + a*p^2 + 1 110 1 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^39*a + b^126)*p + 1 110 8 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^126)*p^8 + a*p^3 + 1 110 2 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^126)*p^2 + 1 110 9 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^126)*p^9 + a*p^7 + 1 110 5 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^126)*p^5 + 1 110 3 y^4 + b^23*y^2 + b^110*y + b^239 p^10 + a*p^9 + (b^16*a^3 + b^39*a + b^126)*p^3 + 1 115 2 y^4 + b^23*y^2 + b^115*y + b^239 p^10 + a*p^3 + (b^16*a^3 + b^39*a + b^131)*p^2 + 1 115 9 y^4 + b^23*y^2 + b^115*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^131)*p^9 + a*p^3 + 1 115 1 y^4 + b^23*y^2 + b^115*y + b^239 p^10 + a*p^7 + (b^16*a^3 + b^39*a + b^131)*p + 1 115 8 y^4 + b^23*y^2 + b^115*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^131)*p^8 + a*p^7 + 1 116 3 y^4 + b^23*y^2 + b^116*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^132)*p^3 + a*p^2 + 1 116 1 y^4 + b^23*y^2 + b^116*y + b^239 p^10 + a*p^4 + (b^16*a^3 + b^39*a + b^132)*p + 1 116 9 y^4 + b^23*y^2 + b^116*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^132)*p^9 + a*p^6 + 1 116 7 y^4 + b^23*y^2 + b^116*y + b^239 p^10 + a*p^8 + (b^16*a^3 + b^39*a + b^132)*p^7 + 1 121 1 y^4 + b^23*y^2 + b^121*y + b^239 p^10 + a*p^5 + (b^16*a^3 + b^39*a + b^137)*p + 1 121 9 y^4 + b^23*y^2 + b^121*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^137)*p^9 + a*p^5 + 1 125 4 y^4 + b^23*y^2 + b^125*y + b^239 p^10 + (b^16*a^3 + b^39*a + b^141)*p^4 + a*p + 1 125 5 y^4 + b^23*y^2 + b^125*y + b^2 ** WARNING: Output too long, hence truncated. '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 15:55:16 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 15:54:42 on modular [Seed = 838995950] ------------------------------------- 7 4 Point [ 1, 215, 764, 567 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 270, 656, 773 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 395, 656, 474 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 416, 638, 757 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.750 seconds, Total memory usage: 15.43MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 15:55:54 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 15:55:42 on modular [Seed = 790565583] ------------------------------------- 7 4 Point [ 1, 166, 868, 166 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 442, 36, 235 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 816, 846, 44 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 5.950 seconds, Total memory usage: 6.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 15:56:39 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 15:56:10 on modular [Seed = 723195567] ------------------------------------- 7 4 Point [ 1, 1048, 3026, 2226 ] was singular mod 5003 and ignored at the #3 lift Point [ 1, 1609, 3270, 4049 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 3779, 3639, 4401 ] was singular mod 5003 and ignored at the #3 lift Point [ 1, 4488, 2282, 4802 ] was singular mod 5003 and ignored at the #3 lift Point [ 1, 4575, 784, 4708 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 4973, 1737, 1087 ] was singular mod 5003 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.449 seconds, Total memory usage: 6.95MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 15:57:52 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 15:57:11 on modular [Seed = 588455786] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 5000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.699 seconds, Total memory usage: 9.91MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 15:58:52 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 15:58:10 on modular [Seed = 3757040595] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 5003 and ignored at the #3 lift Point [ 1, 3691, 3917, 1023 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 3691, 1086, 3980 ] was singular mod 5003 and ignored at the #1 lift Errors: /bin/sh: line 1: 8065 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 16:00:56 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,4000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 16:00:15 on modular [Seed = 2628558861] ------------------------------------- 7 4 Point [ 1, 0, 0, 0 ] was singular mod 4001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.460 seconds, Total memory usage: 9.00MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 16:01:51 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,4000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 16:01:09 on modular [Seed = 2561189827] ------------------------------------- 7 4 Point [ 1, 787, 691, 3183 ] was singular mod 4001 and ignored at the #1 lift Point [ 1, 900, 612, 3038 ] was singular mod 4001 and ignored at the #3 lift Errors: /bin/sh: line 1: 8134 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 16:03:10 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sat Oct 16 2004 16:02:29 on modular [Seed = 3095955379] ------------------------------------- 7 4 Point [ 1, 770, 2585, 2052 ] was singular mod 3001 and ignored at the #3 lift Point [ 1, 1461, 2758, 1815 ] was singular mod 3001 and ignored at the #1 lift Point [ 1, 2178, 448, 1042 ] was singular mod 3001 and ignored at the #1 lift Point [ 1, 2527, 2512, 1041 ] was singular mod 3001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.670 seconds, Total memory usage: 10.06MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 16:04:53 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 16:04:11 on modular [Seed = 1097957019] ------------------------------------- 7 Errors: /bin/sh: line 1: 8224 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 16:09:38 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,2500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 16:05:43 on modular [Seed = 1567449899] ------------------------------------- 7 Errors: /bin/sh: line 1: 8252 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.128 (66.63.133.128) Time: Sat Oct 16 16:13:12 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,2000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sat Oct 16 2004 16:12:30 on modular [Seed = 4291771953] ------------------------------------- 7 Errors: /bin/sh: line 1: 8607 Killed nice -n 19 /usr/local/bin/magma '216.254' ************** MAGMA ***************** Host 216.254.23.142 (216.254.23.142) Time: Sun Oct 17 04:39:46 2004 Input: A := AffineSpace(Rationals(),2); C := Curve(A,x^3+y^3-1); EllipticCurve(C,C![1,0]); Output: Magma V2.11-6 Sun Oct 17 2004 04:39:45 on modular [Seed = 3706696293] ------------------------------------- >> EllipticCurve(C,C![1,0]);; ^ Runtime error in 'EllipticCurve': Curve must be projective Total time: 0.280 seconds, Total memory usage: 3.56MB '216.254' ************** MAGMA ***************** Host 216.254.23.142 (216.254.23.142) Time: Sun Oct 17 04:40:08 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(A,x^3+y^3-z^3); EllipticCurve(C,C![1,0,0]); Output: Magma V2.11-6 Sun Oct 17 2004 04:40:07 on modular [Seed = 3521298270] ------------------------------------- >> C := Curve(A,x^3+y^3-z^3); ^ User error: Identifier 'A' has not been declared or assigned >> EllipticCurve(C,C![1,0,0]);; ^ User error: Identifier 'C' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '216.254' ************** MAGMA ***************** Host 216.254.23.142 (216.254.23.142) Time: Sun Oct 17 04:40:17 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^3+y^3-z^3); EllipticCurve(C,C![1,0,0]); Output: Magma V2.11-6 Sun Oct 17 2004 04:40:16 on modular [Seed = 3605379150] ------------------------------------- >> EllipticCurve(C,C![1,0,0]);; ^ Runtime error in '!': Illegal coercion Total time: 0.200 seconds, Total memory usage: 3.50MB '216.254' ************** MAGMA ***************** Host 216.254.23.142 (216.254.23.142) Time: Sun Oct 17 04:40:30 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^3+y^3-z^3); EllipticCurve(C,C![1,0,1]); Output: Magma V2.11-6 Sun Oct 17 2004 04:40:29 on modular [Seed = 2878915902] ------------------------------------- Elliptic Curve defined by y^2 - 9*y = x^3 - 27 over Rational Field Mapping from: Crv: C to Elliptic Curve defined by y^2 - 9*y = x^3 - 27 over Rational Field with equations : 3*y -9*x -x + z and inverse $.2 -3*$.1 $.2 - 9*$.3 Total time: 0.230 seconds, Total memory usage: 3.86MB '134.22.' ************** MAGMA ***************** Host 134.22.70.40 (134.22.70.40) Time: Sun Oct 17 04:45:14 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Sun Oct 17 2004 04:45:13 on modular [Seed = 2761413845] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.50MB '207.189' ************** MAGMA ***************** Host 207.189.100.168 (207.189.100.168) Time: Sun Oct 17 04:56:14 2004 Input: Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^3+y^3-n*z^3); EllipticCurve(C,C![1,0,1]); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. '207.189' ************** MAGMA ***************** Host 207.189.100.168 (207.189.100.168) Time: Sun Oct 17 04:56:38 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^3+y^3-n*z^3); EllipticCurve(C,C![1,0,1]); Output: Magma V2.11-6 Sun Oct 17 2004 04:56:37 on modular [Seed = 2411527458] ------------------------------------- >> C := Curve(P,x^3+y^3-n*z^3); ^ User error: Identifier 'n' has not been declared or assigned >> EllipticCurve(C,C![1,0,1]); ^ User error: Identifier 'C' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.50MB '216.254' ************** MAGMA ***************** Host 216.254.23.142 (216.254.23.142) Time: Sun Oct 17 05:09:14 2004 Input: R := RationalFunctionField(Rationals()); P := ProjectiveSpace(R,2); C := Curve(P,x^3 + y^3 - n*z^3); EllipticCurve(C,C![1,-1,0]); Output: Magma V2.11-6 Sun Oct 17 2004 05:09:13 on modular [Seed = 1616058289] ------------------------------------- Elliptic Curve defined by y^2 - 9/n^2*y = x^3 - 27/n^4 over Univariate rational function field over Rational Field Mapping from: Crv: C to Elliptic Curve defined by y^2 - 9/n^2*y = x^3 - 27/n^4 over Univariate rational function field over Rational Field with equations : 3/n*z 9/n^2*x x + y and inverse -$.2 $.2 - 9/n^2*$.3 -3/n*$.1 Total time: 0.230 seconds, Total memory usage: 3.86MB '216.254' ************** MAGMA ***************** Host 216.254.23.142 (216.254.23.142) Time: Sun Oct 17 05:12:45 2004 Input: R := RationalFunctionField(Rationals()); P := ProjectiveSpace(R,2); C := Curve(P, X^3 + Y^3 - n*Z^3); EllipticCurve(C,C![1,-1,0]); Output: Magma V2.11-6 Sun Oct 17 2004 05:12:45 on modular [Seed = 2051607708] ------------------------------------- Elliptic Curve defined by y^2 - 9/n^2*y = x^3 - 27/n^4 over Univariate rational function field over Rational Field Mapping from: Crv: C to Elliptic Curve defined by y^2 - 9/n^2*y = x^3 - 27/n^4 over Univariate rational function field over Rational Field with equations : 3/n*Z 9/n^2*X X + Y and inverse -$.2 $.2 - 9/n^2*$.3 -3/n*$.1 Total time: 0.230 seconds, Total memory usage: 3.86MB '145.254' ************** MAGMA ***************** Host 145.254.116.247 (145.254.116.247) Time: Sun Oct 17 05:20:48 2004 Input: F:= FreeGroup(3); for i in [1..10] do Q := NilpotentQuotient(F, i :Engel := 4); NilpotencyClass(Q); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sun Oct 17 2004 05:20:06 on modular [Seed = 1984237147] ------------------------------------- 1 2 3 4 5 6 Errors: /bin/sh: line 1: 10781 Killed nice -n 19 /usr/local/bin/magma '145.254' ************** MAGMA ***************** Host 145.254.116.247 (145.254.116.247) Time: Sun Oct 17 05:24:23 2004 Input: F:= FreeGroup(3); for i in [1..10] do Q := NilpotentQuotient(F, i :Engel := 4); NilpotencyClass(Q); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sun Oct 17 2004 05:23:41 on modular [Seed = 1131427893] ------------------------------------- 1 2 3 4 5 6 Errors: /bin/sh: line 1: 10792 Killed nice -n 19 /usr/local/bin/magma '82.84.1' ************** MAGMA ***************** Host 82.84.156.82 (82.84.156.82) Time: Sun Oct 17 12:01:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Sun Oct 17 2004 11:59:12 on modular [Seed = 1818213321] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.040 seconds, Total memory usage: 3.50MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:32:44 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:28:34 on modular [Seed = 689632746] ------------------------------------- 7 4 Point [ 1, 5, 933, 118 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 115, 84, 584 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 474, 998, 892 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 666, 859, 165 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 10.990 seconds, Total memory usage: 11.61MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:37:13 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:34:09 on modular [Seed = 287493985] ------------------------------------- 7 4 Point [ 1, 311, 701, 844 ] was singular mod 1009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 11.000 seconds, Total memory usage: 11.58MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:41:46 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:38:04 on modular [Seed = 371574923] ------------------------------------- 7 4 Point [ 1, 1379, 479, 788 ] was singular mod 3001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.220 seconds, Total memory usage: 11.63MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:45:43 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[3]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:42:20 on modular [Seed = 489618560] ------------------------------------- 7 4 Point [ 1, 342, 2834, 2623 ] was singular mod 3001 and ignored at the #3 lift Point [ 1, 1676, 2202, 317 ] was singular mod 3001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.220 seconds, Total memory usage: 11.59MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:46:18 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); Output: Magma V2.11-6 Sun Oct 17 2004 12:46:00 on modular [Seed = 20111800] ------------------------------------- Total time: 0.970 seconds, Total memory usage: 5.73MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:46:43 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); g; Output: Magma V2.11-6 Sun Oct 17 2004 12:46:33 on modular [Seed = 70771868] ------------------------------------- [ 391*$.1^4 + 1301*$.1^3 + 3468*$.1^2 - 3844*$.1 + 7616, -2287*$.1^4 + 27444*$.1^2 - 9148, 4*$.1^4 + 27444*$.1^2 + 5230369, $.1^4 + 5230369, 2*$.1^4 - 4*$.1^3 - 6858*$.1^2 + 6860*$.1 + 652081, 2337*$.1^4 + 2720*$.1^3 + 28044*$.1^2 + 5440*$.1 + 9348, $.1^4 - 27444*$.1^2 + 20921476 ] Total time: 0.960 seconds, Total memory usage: 5.73MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:51:36 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:49:21 on modular [Seed = 138144747] ------------------------------------- 7 4 Point [ 1, 1004, 2053, 1386 ] was singular mod 3001 and ignored at the #1 lift Point [ 1, 1125, 546, 1027 ] was singular mod 3001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 11.830 seconds, Total memory usage: 8.21MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 12:56:55 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:53:25 on modular [Seed = 4056027909] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 18.739 seconds, Total memory usage: 16.50MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 13:01:13 2004 Input: E := EllipticCurve( [0,0,0,-20921476,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,4000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 12:57:55 on modular [Seed = 4190772251] ------------------------------------- 7 4 Point [ 1, 40, 2620, 3084 ] was singular mod 4001 and ignored at the #3 lift Point [ 1, 985, 3444, 1807 ] was singular mod 4001 and ignored at the #1 lift Point [ 1, 2584, 3575, 1007 ] was singular mod 4001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 20921476*x over Rational Field function(p) ... end function (-17318640362013683485875991560022318748039483520083866694767/80674810430872166\ 64499665131654811815809003570700037184 : -428807691410872637178736957845857852426919684680536185333634202152499109080872\ 2918351033/22914317710741539630837119800751976458421994688101365769786669265457\ 144726275829248 : 1) 127.30560847271769375765 Total time: 17.579 seconds, Total memory usage: 11.56MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 13:07:58 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S;, F := S[1]; pts := Points(F,4000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sun Oct 17 2004 13:04:01 on modular [Seed = 3571921831] ------------------------------------- 7 4 >> #S;, ^ User error: bad syntax Errors: /bin/sh: line 1: 12453 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 13:12:13 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S;, F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sun Oct 17 2004 13:08:16 on modular [Seed = 3455986620] ------------------------------------- 7 4 >> #S;, ^ User error: bad syntax Point [ 1, 638, 241, 1000 ] was singular mod 3001 and ignored at the #1 lift Errors: /bin/sh: line 1: 12476 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.140 (66.63.133.140) Time: Sun Oct 17 13:24:34 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S;, F := S[1]; pts := Points(F,2000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Sun Oct 17 2004 13:18:43 on modular [Seed = 270792725] ------------------------------------- 7 4 >> #S;, ^ User error: bad syntax Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.480 seconds, Total memory usage: 15.45MB '62.123.' ************** MAGMA ***************** Host 62.123.114.34 (62.123.114.34) Time: Sun Oct 17 15:22:25 2004 Input: 12323 Output: Magma V2.11-6 Sun Oct 17 2004 15:20:48 on modular [Seed = 1950872336] ------------------------------------- 12323 Total time: 0.050 seconds, Total memory usage: 3.50MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:30:35 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; beta := PrimitiveElement(Fx)^5; beta; Output: Magma V2.11-6 Sun Oct 17 2004 19:30:34 on modular [Seed = 2761352518] ------------------------------------- >> Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + ( ^ User error: Identifier 'y' has not been declared or assigned >> Fy<_y> := ext< Fz | Py>; ^ User error: Identifier 'Py' has not been declared or assigned >> Rx := PolynomialRing(Fy); ^ User error: Identifier 'Fy' has not been declared or assigned >> Px := x^17 + x^15 + x^4 + _y; ^ User error: Identifier 'x' has not been declared or assigned >> Fx<_x> := ext< Fy | Px >; ^ User error: Identifier 'Fy' has not been declared or assigned >> beta := PrimitiveElement(Fx)^5; ^ User error: Identifier 'Fx' has not been declared or assigned >> beta;; ^ User error: Identifier 'beta' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.66MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:31:10 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; beta := PrimitiveElement(Fx)^5; beta; Output: Magma V2.11-6 Sun Oct 17 2004 19:31:10 on modular [Seed = 2578176095] ------------------------------------- _x^5 Total time: 0.250 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:34:05 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; beta := PrimitiveElement(Fx)^5; Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); Pt; Output: Magma V2.11-6 Sun Oct 17 2004 19:34:05 on modular [Seed = 2460013191] ------------------------------------- t^17 + t^15 + t^14 + _y*t^12 + (_y + 1)*t^11 + _y^2*t^5 + t^4 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^3 + _z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^45 Total time: 0.280 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:37:06 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; beta := PrimitiveElement(Fx)^10; Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); Pt; Output: Magma V2.11-6 Sun Oct 17 2004 19:37:06 on modular [Seed = 2293943250] ------------------------------------- t^17 + t^15 + t^14 + _y^2*t^12 + (_y^2 + 1)*t^11 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^5 + t^4 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^3 + _z^165*_y^3 + _z^98*_y^2 + _z^192*_y + _z^113 Total time: 0.280 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:37:52 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; beta := PrimitiveElement(Fx)^15; Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); Pt; Output: Magma V2.11-6 Sun Oct 17 2004 19:37:52 on modular [Seed = 2378157733] ------------------------------------- t^17 + t^16 + (_y + 1)*t^15 + (_y + 1)*t^14 + (_y^2 + _y)*t^13 + (_y^3 + _y^2)*t^12 + (_z^246*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^11 + (_z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^82)*t^10 + (_z^75*_y^3 + _z^196*_y^2 + _z^211*_y + _z^169)*t^9 + (_z^140*_y^3 + _z^186*_y^2 + _z^158*_y + _z^64)*t^8 + (_z^3*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^7 + (_z^107*_y^3 + _z^241*_y^2 + _z^198*_y + _z^247)*t^6 + (_z^96*_y^3 + _z^208*_y^2 + _z^5*_y + _z^96)*t^5 + (_z^143*_y^3 + _z^27*_y^2 + _z^133*_y + _z^170)*t^4 + (_z^223*_y^3 + _z^96*_y^2 + _z^155*_y + _z^132)*t^3 + (_z^44*_y^3 + _z^86*_y^2 + _z^207*_y + _z^153)*t^2 + (_z^20*_y^3 + _z^191*_y + _z^33)*t + _z^76*_y^3 + _z^112*_y^2 + _z^97*_y + _z^9 Total time: 0.280 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:38:20 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; beta := PrimitiveElement(Fx)^20; Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); Pt; Output: Magma V2.11-6 Sun Oct 17 2004 19:38:19 on modular [Seed = 2276836500] ------------------------------------- t^17 + t^15 + t^14 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^12 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^11 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^5 + t^4 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^3 + _z^31*_y^3 + _z^42*_y^2 + _z^87*_y + _z^170 Total time: 0.280 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:39:51 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; for pwr:=1 to 10 do beta := PrimitiveElement(Fx)^(5*pwr); Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); 5*pwr; Pt; end for; Output: Magma V2.11-6 Sun Oct 17 2004 19:39:50 on modular [Seed = 2135768258] ------------------------------------- 5 t^17 + t^15 + t^14 + _y*t^12 + (_y + 1)*t^11 + _y^2*t^5 + t^4 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^3 + _z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^45 10 t^17 + t^15 + t^14 + _y^2*t^12 + (_y^2 + 1)*t^11 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^5 + t^4 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^3 + _z^165*_y^3 + _z^98*_y^2 + _z^192*_y + _z^113 15 t^17 + t^16 + (_y + 1)*t^15 + (_y + 1)*t^14 + (_y^2 + _y)*t^13 + (_y^3 + _y^2)*t^12 + (_z^246*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^11 + (_z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^82)*t^10 + (_z^75*_y^3 + _z^196*_y^2 + _z^211*_y + _z^169)*t^9 + (_z^140*_y^3 + _z^186*_y^2 + _z^158*_y + _z^64)*t^8 + (_z^3*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^7 + (_z^107*_y^3 + _z^241*_y^2 + _z^198*_y + _z^247)*t^6 + (_z^96*_y^3 + _z^208*_y^2 + _z^5*_y + _z^96)*t^5 + (_z^143*_y^3 + _z^27*_y^2 + _z^133*_y + _z^170)*t^4 + (_z^223*_y^3 + _z^96*_y^2 + _z^155*_y + _z^132)*t^3 + (_z^44*_y^3 + _z^86*_y^2 + _z^207*_y + _z^153)*t^2 + (_z^20*_y^3 + _z^191*_y + _z^33)*t + _z^76*_y^3 + _z^112*_y^2 + _z^97*_y + _z^9 20 t^17 + t^15 + t^14 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^12 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^11 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^5 + t^4 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^3 + _z^31*_y^3 + _z^42*_y^2 + _z^87*_y + _z^170 25 t^17 + (_y + 1)*t^16 + t^15 + (_y^2 + _y + 1)*t^14 + (_y^2 + _y)*t^13 + (_z^36*_y^3 + _z^145*_y^2 + _z^31*_y + _z^235)*t^12 + (_z^113*_y^3 + _z^165*_y^2 + _z^67*_y + _z^114)*t^11 + (_z^32*_y^3 + _z^139*_y^2 + _z^25*_y + _z^156)*t^10 + (_z^34*_y^3 + _z^187*_y^2 + _z^66*_y + _z^157)*t^9 + (_z^30*_y^3 + _z^194*_y^2 + _z^162*_y + _z^100)*t^8 + (_z^170*_y^3 + _z^71*_y^2 + _z^141*_y + _z^141)*t^7 + (_z^41*_y^3 + _z^223*_y^2 + _z^10*_y + _z^251)*t^6 + (_z^64*_y^3 + _z^149*_y^2 + _z^216*_y + _z^5)*t^5 + (_z^244*_y^3 + _z^71*_y^2 + _z^124*_y + _z^163)*t^4 + (_z^98*_y^3 + _z^54*_y^2 + _z^96*_y + _z^157)*t^3 + (_z^141*_y^3 + _z^39*_y^2 + _z^108*_y + _z^231)*t^2 + (_z^62*_y^3 + _z^95*_y^2 + _z^251*_y + _z^113)*t + _z^45*_y^3 + _z^180*_y^2 + _z^243*_y + _z^6 30 t^17 + t^16 + (_y^2 + 1)*t^15 + (_y^2 + 1)*t^14 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^244)*t^13 + (_z^234*_y^3 + _z^203*_y^2 + _z^232*_y + _z^62)*t^12 + (_z^70*_y^3 + _z^2*_y^2 + _z^100*_y + _z^162)*t^11 + (_z^165*_y^3 + _z^98*_y^2 + _z^192*_y + _z^16)*t^10 + (_z^164*_y^3 + _z^5*_y^2 + _z^6*_y + _z^115)*t^9 + (_z^25*_y^3 + _z^163*_y^2 + _z^114*_y + _z^242)*t^8 + (_z^166*_y^3 + _z^172*_y^2 + _z^159*_y + _z^115)*t^7 + (_z^240*_y^3 + _z^54*_y^2 + _z^102*_y + _z^10)*t^6 + (_z^66*_y^3 + _z^33*_y^2 + _z^233*_y + _z^100)*t^5 + (_z^198*_y^3 + _z^12*_y^2 + _z^68*_y + _z^236)*t^4 + (_z^123*_y^3 + _z^168*_y^2 + _z^191*_y + _z^58)*t^3 + (_z^172*_y^3 + _z^87*_y^2 + _z^212*_y + _z^34)*t^2 + (_z^115*_y^3 + _z^86*_y^2 + _z^249*_y + _z^191)*t + _z^101*_y^3 + _z^154*_y^2 + _z^31*_y + _z^245 35 t^17 + (_y + 1)*t^16 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^15 + (_z^56*_y^3 + _z^163*_y^2 + _z^37*_y + _z^116)*t^14 + (_z^13*_y^3 + _z^2*_y^2 + _z^100*_y + _z^42)*t^13 + (_z^234*_y^3 + _z^203*_y^2 + _z^232*_y + _z^245)*t^12 + (_z^194*_y^3 + _z^77*_y^2 + _z^155*_y + _z^160)*t^11 + (_z^65*_y^3 + _z^107*_y^2 + _z^105*_y + _z^216)*t^10 + (_z^200*_y^3 + _z^89*_y^2 + _z^154*_y + _z^90)*t^9 + (_z^20*_y^3 + _z^194*_y^2 + _z^3*_y + _z^79)*t^8 + (_z^26*_y^3 + _z^124*_y^2 + _z^33*_y + _z^90)*t^7 + (_z^147*_y^3 + _z^37*_y^2 + _z^40*_y + _z^227)*t^6 + (_z^40*_y^3 + _z^232*_y^2 + _z^2*_y + _z^45)*t^5 + (_z^85*_y^3 + _z^100*_y^2 + _z^182*_y + _z^40)*t^4 + (_z^239*_y^3 + _z^102*_y^2 + _z^107*_y + _z^59)*t^3 + (_z^17*_y^3 + _z^168*_y^2 + _z^85)*t^2 + (_z*_y^3 + _z^55*_y^2 + _z^226*_y + _z^104)*t + _z^101*_y^3 + _z^142*_y^2 + _z^159*_y + _z^110 40 t^17 + t^15 + t^14 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^12 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^53)*t^11 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^5 + t^4 + (_z^137*_y^3 + _z^156*_y^2 + _z^233*_y + _z^249)*t^3 + _z^243*_y^3 + _z^80*_y^2 + _z^17*_y + _z^103 45 t^17 + t^16 + (_z^56*_y^3 + _z^167*_y^2 + _z^37*_y + _z^116)*t^15 + (_z^218*_y^3 + _z^51*_y^2 + _z^73*_y + _z^194)*t^14 + (_z^172*_y^3 + _z^231*_y^2 + _z^243*_y + _z^38)*t^13 + (_z^201*_y^3 + _z^21*_y^2 + _z^23*_y + _z^7)*t^12 + (_z^251*_y^3 + _z^136*_y^2 + _z^30*_y + _z^252)*t^11 + (_z^101*_y^3 + _z^205*_y^2 + _z^121*_y + _z^187)*t^10 + (_z^56*_y^3 + _z^6*_y^2 + _z^103*_y + _z^237)*t^9 + (_z^20*_y^3 + _z^22*_y^2 + _z^237*_y + _z^96)*t^8 + (_z^53*_y^3 + _z^98*_y^2 + _z^141*_y + _z^112)*t^7 + (_z^45*_y^3 + _z^254*_y^2 + _z^239*_y + _z^31)*t^6 + (_z^85*_y^3 + _z^71*_y^2 + _z^62*_y + _z^133)*t^5 + (_z^113*_y^3 + _z^204*_y^2 + _z^137*_y + _z^191)*t^4 + (_z^97*_y^3 + _z^253*_y^2 + _z^95*_y + _z^25)*t^3 + (_z^67*_y^3 + _z^81*_y^2 + _z^65*_y + _z^83)*t^2 + (_z^100*_y^3 + _z^144*_y^2 + _z^32*_y + _z^121)*t + _z^136*_y^3 + _z^218*_y^2 + _z^17*_y + _z^80 50 t^17 + (_y^2 + 1)*t^16 + t^15 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^116)*t^14 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^244)*t^13 + (_z^82*_y^3 + _z^214*_y^2 + _z^250*_y + _z^226)*t^12 + (_z^216*_y^3 + _z^116*_y^2 + _z^71*_y + _z^74)*t^11 + (_z^58*_y^3 + _z^52*_y^2 + _z^11*_y + _z^222)*t^10 + (_z^114*_y^3 + _z^99*_y^2 + _z^47*_y + _z^195)*t^9 + (_z^85*_y^3 + _z^168*_y^2 + _z^179*_y + _z^250)*t^8 + (_z^6*_y^3 + _z^72*_y^2 + _z^161*_y + _z^187)*t^7 + (_z^66*_y^3 + _z^74*_y^2 + _z^213*_y + _z^161)*t^6 + (_z^149*_y^3 + _z^81*_y^2 + _z^67*_y + _z^49)*t^5 + (_z^120*_y^3 + _z^203*_y^2 + _z^6*_y + _z^34)*t^4 + (_z^91*_y^3 + _z^61*_y^2 + _z^33*_y + _z^214)*t^3 + (_z^73*_y^3 + _z^50*_y^2 + _z^6*_y + _z^90)*t^2 + (_z^91*_y^3 + _z^8*_y^2 + _z^223*_y + _z^78)*t + _z^253*_y^3 + _z^139*_y^2 + _z^157*_y + _z^133 Total time: 0.560 seconds, Total memory usage: 4.54MB '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:41:04 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; for pwr:=1 to 100 do beta := PrimitiveElement(Fx)^(5*pwr); Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); 5*pwr; Pt; end for; Output: Magma V2.11-6 Sun Oct 17 2004 19:41:00 on modular [Seed = 1916809221] ------------------------------------- 5 t^17 + t^15 + t^14 + _y*t^12 + (_y + 1)*t^11 + _y^2*t^5 + t^4 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^3 + _z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^45 10 t^17 + t^15 + t^14 + _y^2*t^12 + (_y^2 + 1)*t^11 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^5 + t^4 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^3 + _z^165*_y^3 + _z^98*_y^2 + _z^192*_y + _z^113 15 t^17 + t^16 + (_y + 1)*t^15 + (_y + 1)*t^14 + (_y^2 + _y)*t^13 + (_y^3 + _y^2)*t^12 + (_z^246*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^11 + (_z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^82)*t^10 + (_z^75*_y^3 + _z^196*_y^2 + _z^211*_y + _z^169)*t^9 + (_z^140*_y^3 + _z^186*_y^2 + _z^158*_y + _z^64)*t^8 + (_z^3*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^7 + (_z^107*_y^3 + _z^241*_y^2 + _z^198*_y + _z^247)*t^6 + (_z^96*_y^3 + _z^208*_y^2 + _z^5*_y + _z^96)*t^5 + (_z^143*_y^3 + _z^27*_y^2 + _z^133*_y + _z^170)*t^4 + (_z^223*_y^3 + _z^96*_y^2 + _z^155*_y + _z^132)*t^3 + (_z^44*_y^3 + _z^86*_y^2 + _z^207*_y + _z^153)*t^2 + (_z^20*_y^3 + _z^191*_y + _z^33)*t + _z^76*_y^3 + _z^112*_y^2 + _z^97*_y + _z^9 20 t^17 + t^15 + t^14 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^12 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^11 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^5 + t^4 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^3 + _z^31*_y^3 + _z^42*_y^2 + _z^87*_y + _z^170 25 t^17 + (_y + 1)*t^16 + t^15 + (_y^2 + _y + 1)*t^14 + (_y^2 + _y)*t^13 + (_z^36*_y^3 + _z^145*_y^2 + _z^31*_y + _z^235)*t^12 + (_z^113*_y^3 + _z^165*_y^2 + _z^67*_y + _z^114)*t^11 + (_z^32*_y^3 + _z^139*_y^2 + _z^25*_y + _z^156)*t^10 + (_z^34*_y^3 + _z^187*_y^2 + _z^66*_y + _z^157)*t^9 + (_z^30*_y^3 + _z^194*_y^2 + _z^162*_y + _z^100)*t^8 + (_z^170*_y^3 + _z^71*_y^2 + _z^141*_y + _z^141)*t^7 + (_z^41*_y^3 + _z^223*_y^2 + _z^10*_y + _z^251)*t^6 + (_z^64*_y^3 + _z^149*_y^2 + _z^216*_y + _z^5)*t^5 + (_z^244*_y^3 + _z^71*_y^2 + _z^124*_y + _z^163)*t^4 + (_z^98*_y^3 + _z^54*_y^2 + _z^96*_y + _z^157)*t^3 + (_z^141*_y^3 + _z^39*_y^2 + _z^108*_y + _z^231)*t^2 + (_z^62*_y^3 + _z^95*_y^2 + _z^251*_y + _z^113)*t + _z^45*_y^3 + _z^180*_y^2 + _z^243*_y + _z^6 30 t^17 + t^16 + (_y^2 + 1)*t^15 + (_y^2 + 1)*t^14 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^244)*t^13 + (_z^234*_y^3 + _z^203*_y^2 + _z^232*_y + _z^62)*t^12 + (_z^70*_y^3 + _z^2*_y^2 + _z^100*_y + _z^162)*t^11 + (_z^165*_y^3 + _z^98*_y^2 + _z^192*_y + _z^16)*t^10 + (_z^164*_y^3 + _z^5*_y^2 + _z^6*_y + _z^115)*t^9 + (_z^25*_y^3 + _z^163*_y^2 + _z^114*_y + _z^242)*t^8 + (_z^166*_y^3 + _z^172*_y^2 + _z^159*_y + _z^115)*t^7 + (_z^240*_y^3 + _z^54*_y^2 + _z^102*_y + _z^10)*t^6 + (_z^66*_y^3 + _z^33*_y^2 + _z^233*_y + _z^100)*t^5 + (_z^198*_y^3 + _z^12*_y^2 + _z^68*_y + _z^236)*t^4 + (_z^123*_y^3 + _z^168*_y^2 + _z^191*_y + _z^58)*t^3 + (_z^172*_y^3 + _z^87*_y^2 + _z^212*_y + _z^34)*t^2 + (_z^115*_y^3 + _z^86*_y^2 + _z^249*_y + _z^191)*t + _z^101*_y^3 + _z^154*_y^2 + _z^31*_y + _z^245 35 t^17 + (_y + 1)*t^16 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^15 + (_z^56*_y^3 + _z^163*_y^2 + _z^37*_y + _z^116)*t^14 + (_z^13*_y^3 + _z^2*_y^2 + _z^100*_y + _z^42)*t^13 + (_z^234*_y^3 + _z^203*_y^2 + _z^232*_y + _z^245)*t^12 + (_z^194*_y^3 + _z^77*_y^2 + _z^155*_y + _z^160)*t^11 + (_z^65*_y^3 + _z^107*_y^2 + _z^105*_y + _z^216)*t^10 + (_z^200*_y^3 + _z^89*_y^2 + _z^154*_y + _z^90)*t^9 + (_z^20*_y^3 + _z^194*_y^2 + _z^3*_y + _z^79)*t^8 + (_z^26*_y^3 + _z^124*_y^2 + _z^33*_y + _z^90)*t^7 + (_z^147*_y^3 + _z^37*_y^2 + _z^40*_y + _z^227)*t^6 + (_z^40*_y^3 + _z^232*_y^2 + _z^2*_y + _z^45)*t^5 + (_z^85*_y^3 + _z^100*_y^2 + _z^182*_y + _z^40)*t^4 + (_z^239*_y^3 + _z^102*_y^2 + _z^107*_y + _z^59)*t^3 + (_z^17*_y^3 + _z^168*_y^2 + _z^85)*t^2 + (_z*_y^3 + _z^55*_y^2 + _z^226*_y + _z^104)*t + _z^101*_y^3 + _z^142*_y^2 + _z^159*_y + _z^110 40 t^17 + t^15 + t^14 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^12 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^53)*t^11 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^5 + t^4 + (_z^137*_y^3 + _z^156*_y^2 + _z^233*_y + _z^249)*t^3 + _z^243*_y^3 + _z^80*_y^2 + _z^17*_y + _z^103 45 t^17 + t^16 + (_z^56*_y^3 + _z^167*_y^2 + _z^37*_y + _z^116)*t^15 + (_z^218*_y^3 + _z^51*_y^2 + _z^73*_y + _z^194)*t^14 + (_z^172*_y^3 + _z^231*_y^2 + _z^243*_y + _z^38)*t^13 + (_z^201*_y^3 + _z^21*_y^2 + _z^23*_y + _z^7)*t^12 + (_z^251*_y^3 + _z^136*_y^2 + _z^30*_y + _z^252)*t^11 + (_z^101*_y^3 + _z^205*_y^2 + _z^121*_y + _z^187)*t^10 + (_z^56*_y^3 + _z^6*_y^2 + _z^103*_y + _z^237)*t^9 + (_z^20*_y^3 + _z^22*_y^2 + _z^237*_y + _z^96)*t^8 + (_z^53*_y^3 + _z^98*_y^2 + _z^141*_y + _z^112)*t^7 + (_z^45*_y^3 + _z^254*_y^2 + _z^239*_y + _z^31)*t^6 + (_z^85*_y^3 + _z^71*_y^2 + _z^62*_y + _z^133)*t^5 + (_z^113*_y^3 + _z^204*_y^2 + _z^137*_y + _z^191)*t^4 + (_z^97*_y^3 + _z^253*_y^2 + _z^95*_y + _z^25)*t^3 + (_z^67*_y^3 + _z^81*_y^2 + _z^65*_y + _z^83)*t^2 + (_z^100*_y^3 + _z^144*_y^2 + _z^32*_y + _z^121)*t + _z^136*_y^3 + _z^218*_y^2 + _z^17*_y + _z^80 50 t^17 + (_y^2 + 1)*t^16 + t^15 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^116)*t^14 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^244)*t^13 + (_z^82*_y^3 + _z^214*_y^2 + _z^250*_y + _z^226)*t^12 + (_z^216*_y^3 + _z^116*_y^2 + _z^71*_y + _z^74)*t^11 + (_z^58*_y^3 + _z^52*_y^2 + _z^11*_y + _z^222)*t^10 + (_z^114*_y^3 + _z^99*_y^2 + _z^47*_y + _z^195)*t^9 + (_z^85*_y^3 + _z^168*_y^2 + _z^179*_y + _z^250)*t^8 + (_z^6*_y^3 + _z^72*_y^2 + _z^161*_y + _z^187)*t^7 + (_z^66*_y^3 + _z^74*_y^2 + _z^213*_y + _z^161)*t^6 + (_z^149*_y^3 + _z^81*_y^2 + _z^67*_y + _z^49)*t^5 + (_z^120*_y^3 + _z^203*_y^2 + _z^6*_y + _z^34)*t^4 + (_z^91*_y^3 + _z^61*_y^2 + _z^33*_y + _z^214)*t^3 + (_z^73*_y^3 + _z^50*_y^2 + _z^6*_y + _z^90)*t^2 + (_z^91*_y^3 + _z^8*_y^2 + _z^223*_y + _z^78)*t + _z^253*_y^3 + _z^139*_y^2 + _z^157*_y + _z^133 55 t^17 + (_y^2 + _y)*t^16 + (_z^148*_y^3 + _z^196*_y^2 + _z^211*_y + _z^12)*t^15 + (_z^127*_y^3 + _z^254*_y^2 + _z^147*_y + _z^239)*t^14 + (_z^249*_y^3 + _z^62*_y^2 + _z^130*_y + _z^30)*t^13 + (_z^123*_y^3 + _z^147*_y^2 + _z^121*_y + _z^134)*t^12 + (_z^173*_y^3 + _z^38*_y^2 + _z^190*_y + _z^168)*t^11 + (_z^68*_y^3 + _z^198*_y^2 + _z^157*_y + _z^57)*t^10 + (_z^248*_y^3 + _z^85*_y^2 + _z^89*_y + _z^104)*t^9 + (_z^43*_y^3 + _z^209*_y^2 + _z^48*_y + _z^40)*t^8 + (_z^86*_y^3 + _z^34*_y^2 + _z^225*_y + _z^118)*t^7 + (_z^158*_y^3 + _z^205*_y^2 + _z^25*_y + _z^142)*t^6 + (_z^164*_y^3 + _z^156*_y^2 + _z^174*_y + _z^32)*t^5 + (_z^236*_y^3 + _z^136*_y^2 + _z^5*_y + _z^168)*t^4 + (_z^175*_y^3 + _z^59*_y^2 + _z^240*_y + _z^10)*t^3 + (_y^3 + _z^80*_y^2 + _z^22*_y + _z^198)*t^2 + (_z^27*_y^3 + _z^183*_y^2 + _z^90*_y + _z^168)*t + _z^2*_y^3 + _z^185*_y^2 + _z^10*_y + _z^200 60 t^17 + t^16 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^15 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^14 + (_z^160*_y^3 + _z^153*_y^2 + _z^5*_y + _z^15)*t^13 + (_z^228*_y^3 + _z^50*_y^2 + _z^135*_y + _z^49)*t^12 + (_z^168*_y^3 + _z^5*_y^2 + _z^52*_y + _z^169)*t^11 + (_z^31*_y^3 + _z^42*_y^2 + _z^87*_y + _z^85)*t^10 + (_z^111*_y^3 + _z^199*_y^2 + _z^210*_y + _z^66)*t^9 + (_z^171*_y^3 + _z^214*_y^2 + _z^3*_y + _z^119)*t^8 + (_z^112*_y^3 + _z^249*_y^2 + _z^101*_y + _z^150)*t^7 + (_z^11*_y^3 + _z^104*_y^2 + _z^52*_y + _z^117)*t^6 + (_z^37*_y^3 + _z^143*_y^2 + _z^30*_y + _z^248)*t^5 + (_z^182*_y^3 + _z^140*_y^2 + _z^223*_y + _z^82)*t^4 + (_z^145*_y^3 + _z^19*_y^2 + _z^126*_y + _z^68)*t^3 + (_z^244*_y^3 + _z^29*_y^2 + _z^141*_y + _z^213)*t^2 + (_z^69*_y^3 + _z^118*_y^2 + _z^114*_y + _z^246)*t + _z^247*_y^3 + _z^19*_y^2 + _z^83*_y + _z^75 65 t^17 + (_y^2 + _y + 1)*t^16 + (_z^73*_y^3 + _z^20*_y^2 + _z^157*_y + _z^45)*t^15 + (_z^129*_y^3 + _z^28*_y^2 + _z^5*_y + _z^158)*t^14 + (_z^215*_y^3 + _z^159*_y^2 + _z^209*_y + _z^227)*t^13 + (_z^188*_y^3 + _z^152*_y^2 + _z^237*_y + _z^107)*t^12 + (_z^3*_y^3 + _z^38*_y^2 + _z^57*_y + _z^246)*t^11 + (_z*_y^3 + _z^239*_y^2 + _z^145*_y + _z^176)*t^10 + (_z^243*_y^3 + _z^94*_y^2 + _z^137*_y + _z^124)*t^9 + (_z^81*_y^3 + _z^36*_y^2 + _z^199*_y + _z^79)*t^8 + (_z^196*_y^3 + _z^91*_y^2 + _z^164*_y + _z^223)*t^7 + (_z^88*_y^3 + _z^24*_y^2 + _z^191*_y + _z^9)*t^6 + (_z^228*_y^3 + _z^152*_y + _z^238)*t^5 + (_z^190*_y^3 + _z^251*_y^2 + _z^237*_y + _z^238)*t^4 + (_z^52*_y^3 + _z^208*_y^2 + _z^227*_y + _z^206)*t^3 + (_z^130*_y^3 + _z^139*_y^2 + _z^123*_y + _z^253)*t^2 + (_z^141*_y^3 + _z^161*_y^2 + _z^16*_y + _z^78)*t + _z^58*_y^3 + _z^83*_y^2 + _z^51*_y + _z^6 70 t^17 + (_y^2 + 1)*t^16 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^129)*t^15 + (_z^106*_y^3 + _z^87*_y^2 + _z^59*_y + _z^53)*t^14 + (_z^210*_y^3 + _z^138*_y^2 + _z^40*_y + 1)*t^13 + (_z^228*_y^3 + _z^50*_y^2 + _z^135*_y + _z^43)*t^12 + (_z^254*_y^3 + _z^47*_y^2 + _z^86*_y + _z^41)*t^11 + (_z^214*_y^3 + _z^218*_y^2 + _z^254*_y + _z^174)*t^10 + (_z^154*_y^3 + _z^53*_y^2 + _z^252*_y + _z^78)*t^9 + (_z^25*_y^3 + _z^217*_y^2 + _z^33*_y + _z^172)*t^8 + (_z^237*_y^3 + _z^105*_y^2 + _z^70*_y + _z^117)*t^7 + (_z^227*_y^3 + _z^231*_y^2 + _z^253*_y + _z^214)*t^6 + (_z^77*_y^3 + _z^43*_y^2 + _z^52*_y + _z^82)*t^5 + (_z^117*_y^3 + _y^2 + _z^119*_y + _z^121)*t^4 + (_z^106*_y^3 + _z^233*_y^2 + _z^34*_y + _z^190)*t^3 + (_z^232*_y^3 + _z^164*_y^2 + _z^154*_y + _z^96)*t^2 + (_z^214*_y^3 + _z^94*_y^2 + _z^170*_y + _z^74)*t + _z^239*_y^3 + _z^91*_y^2 + _z^180*_y + _z^93 75 t^17 + (_y^3 + _y + 1)*t^16 + (_z^14*_y^3 + _z^11*_y^2 + _z^115*_y + _z^225)*t^15 + (_z^43*_y^3 + _z^54 ** WARNING: Output too long, hence truncated. '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:45:26 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; for pwr:=15 to 100 do beta := PrimitiveElement(Fx)^(5*pwr); Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); 5*pwr; Pt; end for; Output: Magma V2.11-6 Sun Oct 17 2004 19:45:23 on modular [Seed = 1767582721] ------------------------------------- 75 t^17 + (_y^3 + _y + 1)*t^16 + (_z^14*_y^3 + _z^11*_y^2 + _z^115*_y + _z^225)*t^15 + (_z^43*_y^3 + _z^54*_y^2 + _z^10*_y + _z^52)*t^14 + (_z^243*_y^3 + _z^145*_y^2 + _z^56*_y + _z^28)*t^13 + (_z^234*_y^3 + _z^179*_y^2 + _z^221*_y + _z^87)*t^12 + (_z^202*_y^3 + _z^21*_y^2 + _z^142*_y + _z^42)*t^11 + (_z^93*_y^3 + _z^28*_y^2 + _z^142*_y + _z^29)*t^10 + (_z^45*_y^3 + _z^10*_y^2 + _z^100*_y + _z^77)*t^9 + (_z^47*_y^3 + _z^251*_y^2 + _z^210*_y + _z^9)*t^8 + (_z^122*_y^3 + _z^17*_y^2 + _z^25*_y + _z^254)*t^7 + (_z^141*_y^3 + _z^52*_y^2 + _z^64*_y + _z^211)*t^6 + (_z^140*_y^3 + _z^135*_y^2 + _z^99*_y + _z^130)*t^5 + (_z^199*_y^3 + _z^91*_y^2 + _z^221*_y + _z^133)*t^4 + (_z^247*_y^3 + _z^166*_y^2 + _z^110*_y + _z^153)*t^3 + (_z^114*_y^3 + _z^119*_y^2 + _z^110*_y + _z^157)*t^2 + (_z^120*_y^3 + _z^155*_y^2 + _z^81*_y + _z^15)*t + _z^23*_y^3 + _z^71*_y^2 + _y + _z^30 80 t^17 + t^15 + t^14 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^12 + (_z*_y^3 + _y^2 + _z^8*_y + _z^9)*t^11 + (_z^137*_y^3 + _z^156*_y^2 + _z^233*_y + _z^249)*t^5 + t^4 + (_z^17*_y^3 + _z^244*_y^2 + _z^67*_y + _z^43)*t^3 + _z^125*_y^3 + _z^103*_y^2 + _z^128*_y + _z^201 85 t^17 + (_z^5*_y^3 + _z^145*_y^2 + _z^31*_y + _z^235)*t^16 + (_z^230*_y^3 + _z^238*_y^2 + _z^56*_y + _z^115)*t^15 + (_z^149*_y^3 + _z^97*_y^2 + _z^42*_y + _z^114)*t^14 + (_z^152*_y^3 + _z^163*_y^2 + _z^19*_y + _z^228)*t^13 + (_z^244*_y^3 + _z^121*_y^2 + _z^102*_y + _z^86)*t^12 + (_z^66*_y^3 + _z^239*_y^2 + _z*_y + _z^252)*t^11 + (_z^36*_y^3 + _z^159*_y^2 + _z^81*_y + _z^69)*t^10 + (_z^75*_y^3 + _z^150*_y^2 + _z^136*_y + _z^254)*t^9 + (_z^113*_y^3 + _z^162*_y^2 + _z^105*_y + _z^140)*t^8 + (_z^222*_y^3 + _z^187*_y^2 + _z^114*_y + _z^168)*t^7 + (_z^28*_y^3 + _z^195*_y^2 + _z^87*_y + _z^227)*t^6 + (_z^60*_y^3 + _z^35*_y^2 + _z^34*_y + _z^165)*t^5 + (_z^4*_y^3 + _z^187*_y^2 + _z^157*_y + _z^64)*t^4 + (_z^190*_y^3 + _z^76*_y^2 + _z^158*_y + _z^18)*t^3 + (_z^215*_y^3 + _z^53*_y^2 + _z^121*_y + _z^19)*t^2 + (_z^252*_y^3 + _z^61*_y^2 + _z^145*_y + _z^102)*t + _z^241*_y^3 + _z^154*_y^2 + _z^122*_y + _z^247 90 t^17 + t^16 + (_z^160*_y^3 + _z^34*_y^2 + _z^5*_y + _z^186)*t^15 + (_z^244*_y^3 + _z^184*_y^2 + _z^245*_y + _z^237)*t^14 + (_z^129*_y^3 + _z^195*_y^2 + _z^9*_y + _z^253)*t^13 + (_z^78*_y^3 + _z^56*_y^2 + _z^47*_y + _z^49)*t^12 + (_z^24*_y^3 + _z^103*_y^2 + _z^86*_y + _z^207)*t^11 + (_z^36*_y^3 + _z^145*_y^2 + _z^112*_y + _z^77)*t^10 + (_z^34*_y^3 + _z^83*_y^2 + _z^187*_y + _z^101)*t^9 + (_z^31*_y^3 + _z^7*_y^2 + _z^30*_y + _z^188)*t^8 + (_z^5*_y^3 + _z^249*_y^2 + _z^241*_y + _z^112)*t^7 + (_z^185*_y^3 + _z^244*_y^2 + _z^134*_y + _z^115)*t^6 + (_z^90*_y^3 + _z^161*_y^2 + _z^72*_y + _z^110)*t^5 + (_z^213*_y^3 + _z^101*_y^2 + _z^118*_y + _z^103)*t^4 + (_z^115*_y^3 + _z^58*_y^2 + _z^15*_y + _z^223)*t^3 + (_z^19*_y^3 + _z^189*_y^2 + _z^149*_y + _z^201)*t^2 + (_z^104*_y^3 + _z^165*_y^2 + _z^36*_y + _z^81)*t + _z^159*_y^3 + _z^168*_y^2 + _z^45*_y + _z^188 95 t^17 + _y^2*t^16 + (_z^239*_y^3 + _z^8*_y^2 + _z^141*_y + _z^104)*t^15 + (_z^220*_y^3 + _z^33*_y^2 + _z^125*_y + _z^79)*t^14 + (_z^120*_y^3 + _z^153*_y^2 + _z^35*_y + _z^234)*t^13 + (_z^39*_y^3 + _z^230*_y^2 + _z^122*_y + _z^187)*t^12 + (_z^194*_y^3 + _z^169*_y^2 + _z^175*_y + _z^13)*t^11 + (_z^158*_y^3 + _z^38*_y^2 + _z^188*_y + _z^181)*t^10 + (_z^191*_y^3 + _z^30*_y^2 + _z^172*_y + _z^138)*t^9 + (_z^254*_y^3 + _z^40*_y + _z^92)*t^8 + (_z^101*_y^3 + _z^244*_y^2 + _z^217*_y + _z^164)*t^7 + (_z^117*_y^3 + _z^47*_y^2 + _z^225*_y + _z^130)*t^6 + (_z^177*_y^3 + _z^157*_y^2 + _z^251*_y + _z^19)*t^5 + (_z^240*_y^3 + _z^155*_y^2 + _z^143*_y + _z^64)*t^4 + (_z^223*_y^3 + _z^148*_y^2 + _z^17*_y + 1)*t^3 + (_z^248*_y^3 + _z^170*_y^2 + _z^215*_y + _z^3)*t^2 + (_z^50*_y^3 + _z^90*_y^2 + _z^144*_y + _z^194)*t + _z^140*_y^3 + _z^91*_y^2 + _z^174*_y + _z^235 100 t^17 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^16 + t^15 + (_z^160*_y^3 + _z^153*_y^2 + _z^5*_y + _z^186)*t^14 + (_z^160*_y^3 + _z^153*_y^2 + _z^5*_y + _z^15)*t^13 + (_z^46*_y^3 + _z^185*_y^2 + _z^190*_y + _z^251)*t^12 + (_z^2*_y^3 + _z^169*_y^2 + _z^122*_y + _z^203)*t^11 + (_z^155*_y^3 + _z^32*_y^2 + _z^186*_y + _z^56)*t^10 + (_z^42*_y^3 + _z^208*_y^2 + _z^214*_y + _z^17)*t^9 + (_z^37*_y^3 + _z^38*_y^2 + _z^32*_y + _z^179)*t^8 + (_z^103*_y^3 + _z^70*_y^2 + _z^157*_y + _z^192)*t^7 + (_z^55*_y^3 + _z^53*_y^2 + _z^35*_y + _z^199)*t^6 + (_z^71*_y^3 + _z^107*_y^2 + _z^210*_y + _z^143)*t^5 + (_z^107*_y^3 + _z^158*_y^2 + _z^102*_y + _z^25)*t^4 + (_z^249*_y^3 + _z^31*_y^2 + _z^53*_y + _z^132)*t^3 + (_z^165*_y^3 + _z^157*_y^2 + _z^137*_y + _z^97)*t^2 + (_z^15*_y^3 + _z^210*_y^2 + _z^45*_y + _z^18)*t + _y^3 + _z^128*_y^2 + _z^73*_y + _z^145 105 t^17 + (_z^73*_y^3 + _z^144*_y^2 + _z^243*_y + _z^45)*t^16 + (_z^156*_y^3 + _z^228*_y^2 + _z^171*_y + _z^219)*t^15 + (_z^14*_y^3 + _z^204*_y^2 + _z^60*_y + _z^234)*t^14 + (_z^253*_y^3 + _z^190*_y^2 + _z^249*_y + _z^227)*t^13 + (_z^28*_y^3 + _z^184*_y^2 + _z^83*_y + _z^55)*t^12 + (_z^28*_y^3 + _z^153*_y^2 + _z^156*_y + _z^73)*t^11 + (_z^10*_y^3 + _z^121*_y^2 + _z*_y + _z^221)*t^10 + (_z^226*_y^3 + _z^151*_y^2 + _z^242*_y + _z^250)*t^9 + (_z^224*_y^3 + _z^114*_y^2 + _z^148*_y + _z^81)*t^8 + (_z^125*_y^3 + _z^56*_y^2 + _z^129*_y + _z^249)*t^7 + (_z^183*_y^3 + _z^73*_y^2 + _z^158*_y + _z^51)*t^6 + (_z^237*_y^3 + _z^91*_y^2 + _z^91*_y + 1)*t^5 + (_z^158*_y^3 + _z^90*_y^2 + _z^152*_y + _z^199)*t^4 + (_z^166*_y^3 + _z^125*_y^2 + _z^190*_y + _z^112)*t^3 + (_z^184*_y^3 + _z^188*_y^2 + _z^119*_y + _z^116)*t^2 + (_z^12*_y^3 + _z^95*_y^2 + _z^25*_y + _z^138)*t + _z^70*_y^3 + _z^163*_y^2 + _z^10*_y + _z^71 110 t^17 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^244)*t^16 + (_z^212*_y^3 + _z^138*_y^2 + _z^234*_y + _z^9)*t^15 + (_z^198*_y^3 + _z^183*_y^2 + _z^145)*t^14 + (_z^93*_y^3 + _z^252*_y^2 + _z^31*_y + _z^128)*t^13 + (_z^127*_y^3 + _z^98*_y^2 + _z^243*_y + _z^254)*t^12 + (_z^30*_y^3 + _z^177*_y^2 + _z^220*_y + _z^223)*t^11 + (_z^131*_y^3 + _z^75*_y^2 + _z^47*_y + _z^160)*t^10 + (_z^135*_y^3 + _z^232*_y^2 + _z^138*_y + _z^47)*t^9 + (_z^28*_y^3 + _z^104*_y^2 + _z^228*_y + _z^164)*t^8 + (_z^152*_y^3 + _z^83*_y^2 + _z^20*_y + _z^70)*t^7 + (_z^29*_y^3 + _z^209*_y^2 + _z^242*_y + _z^149)*t^6 + (_z^247*_y^3 + _z^178*_y^2 + _z^198*_y + _z)*t^5 + (_z^42*_y^3 + _z^57*_y^2 + _z^162*_y + _z^132)*t^4 + (_z^7*_y^3 + _z^109*_y^2 + _z^132*_y + _z^168)*t^3 + (_z^190*_y^3 + _z^211*_y^2 + _z^154*_y + _z^35)*t^2 + (_z^230*_y^3 + _z^214*_y^2 + _z^130*_y + _z^228)*t + _z^83*_y^3 + _z^36*_y^2 + _z^195*_y + _z^194 115 t^17 + (_z^60*_y^3 + _z^228*_y^2 + _z^232*_y + _z^62)*t^16 + (_z^115*_y^3 + _z^223*_y^2 + _z^217*_y + _z^102)*t^15 + (_z^249*_y^3 + _z^192*_y^2 + _z^152*_y + _z^190)*t^14 + (_z^208*_y^3 + _z^172*_y^2 + _z^228*_y + _z^26)*t^13 + (_z^182*_y^3 + _z^107*_y^2 + _z^215*_y + _z^216)*t^12 + (_z^192*_y^3 + _z^138*_y^2 + _z^188*_y + _z^120)*t^11 + (_z^181*_y^3 + _z^123*_y^2 + _z^77*_y + _z^100)*t^10 + (_z^62*_y^3 + _z^85*_y^2 + _z^231*_y + _z^14)*t^9 + (_z^157*_y^3 + _z^47*_y^2 + _z^107*_y + _z^21)*t^8 + (_z^211*_y^3 + _z^120*_y^2 + _z^120*_y + _z^139)*t^7 + (_z^95*_y^3 + _z^251*_y^2 + _z^89*_y + _z^234)*t^6 + (_z^61*_y^3 + _z^19*_y^2 + _z^121*_y + _z^128)*t^5 + (_z^129*_y^3 + _z^148*_y^2 + _z^143*_y + _z^11)*t^4 + (_z^247*_y^3 + _z^190*_y^2 + _z^219*_y + _z^213)*t^3 + (_z^59*_y^3 + _z^62*_y^2 + _z^129*_y + _z^189)*t^2 + (_z^177*_y^3 + _z^183*_y^2 + _z^196*_y + _z^201)*t + _z^156*_y^3 + _z^192*_y^2 + _z^166*_y + _z^164 120 t^17 + t^16 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^53)*t^15 + (_z^106*_y^3 + _z^225*_y^2 + _z^59*_y + _z^53)*t^14 + (_z^147*_y^3 + _z^87*_y^2 + _z^76*_y + _z^7)*t^13 + (_z^114*_y^3 + _z^138*_y^2 + _z^8*_y + _z^209)*t^12 + (_z^230*_y^3 + _z^70*_y^2 + _z^233*_y + _z^175)*t^11 + (_z^243*_y^3 + _z^80*_y^2 + _z^17*_y + _z^252)*t^10 + (_z^30*_y^3 + _z^193*_y^2 + _z^31*_y + _z^136)*t^9 + (_z^52*_y^3 + _z^207*_y^2 + _z^11*_y + _z^156)*t^8 + (_z^115*_y^2 + _z^67*_y + _z^205)*t^7 + (_z^5*_y^3 + _z^179*_y^2 + _z^214*_y + _z^246)*t^6 + (_z^77*_y^3 + _z^81*_y^2 + _z^148*_y + _z^189)*t^5 + (_z^78*_y^3 + _z^166*_y^2 + _z^4*_y + _z^249)*t^4 + (_z^207*_y^3 + _z^77*_y^2 + _z^81*_y + _z^159)*t^3 + (_z^82*_y^3 + _z^121*_y^2 + _z^208*_y + _z^240)*t^2 + (_z^29*_y^3 + _z^114*_y^2 + _z^57*_y + _z^22)*t + _z^193*_y^3 + _z^138*_y^2 + _z^154*_y + _z^141 125 t^17 + (_z^246*_y^3 + _z^163*_y^2 + _z^37*_y + _z^116)*t^16 + (_z^60*_y^3 + _z^177*_y^2 + _z^150*_y + _z^82)*t^15 + (_z^189*_y^3 + _z^43*_y^2 + _z^84*_y + _z^232)*t^14 + (_z^159*_y^3 + _z^47*_y^2 + _z^97*_y + _z^226)*t^13 + (_z^216*_y^3 + _z^41*_y^2 + _z^65*_y + _z^169)*t^12 + (_z^161*_y^3 + _z^177*_y^2 + _z^243*_y + _z^100)*t^11 + (_z^34*_y^3 + _z^62*_y^2 + _z^4*_y + _z^111)*t^10 + (_z^158*_y^3 + _z^44*_y^2 + _z^194*_y + _z^143)*t^9 + (_z^88*_y^3 + _z^225*_y^2 + _z^82*_y + _z^157)*t^8 + (_z^4*_y^3 + _z^24*_y^2 + _z^8*_y + _z^124)*t^7 + (_z^67*_y^3 + _z^60*_y^2 + _z^168*_y + _z^119)*t^6 + (_z^106*_y^3 + _z^73*_y^2 + _z^170*_y + _z^224)*t^5 + (_z^246*_y^3 + _z^178*_y^2 + _z^142*_y + _z^187)*t^4 + (_z^130*_y^3 + _z^227*_y^2 + _z^67*_y + _z^244)*t^3 + (_z^2*_y^3 + _z^78*_y^2 + _z^12*_y + _z^66)*t^2 + (_z^102*_y^3 + _z^58*_y^2 + _z^51*_y + _z^232)*t + _z^157*_y^3 + _z^24*_y^2 + _z^218*_y + _z^46 130 t^17 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^116)*t^16 + (_z^239*_y^3 + _z^8*_y^2 + _z^141*_y + _z^104)*t^15 + (_z^231*_y^3 + _z^198*_y^2 + _z^162*_y ** WARNING: Output too long, hence truncated. '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:46:59 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; for pwr:=26 to 100 do beta := PrimitiveElement(Fx)^(5*pwr); Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); 5*pwr; Pt; end for; Output: Magma V2.11-6 Sun Oct 17 2004 19:46:56 on modular [Seed = 1666262632] ------------------------------------- 130 t^17 + (_z^56*_y^3 + _z^167*_y^2 + _z^210*_y + _z^116)*t^16 + (_z^239*_y^3 + _z^8*_y^2 + _z^141*_y + _z^104)*t^15 + (_z^231*_y^3 + _z^198*_y^2 + _z^162*_y + _z^92)*t^14 + (_z^230*_y^3 + _z^181*_y^2 + _z^149*_y + _z^161)*t^13 + (_z^31*_y^3 + _z^92*_y^2 + _z^83*_y + _z^66)*t^12 + (_z^149*_y^3 + _z^163*_y^2 + _z^39*_y + _z^18)*t^11 + (_z^153*_y^3 + _z^210*_y^2 + _z^218*_y + _z^61)*t^10 + (_z^234*_y^3 + _z^102*_y^2 + _z^50*_y + _z^21)*t^9 + (_z^87*_y^3 + _z^101*_y^2 + _z^164*_y + _z^40)*t^8 + (_z^97*_y^3 + _z^13*_y^2 + _z^93*_y + _z^116)*t^7 + (_z^151*_y^3 + _z^188*_y^2 + _z^14*_y + _z^93)*t^6 + (_z^21*_y^3 + _z^184*_y^2 + _z^155*_y + _z^118)*t^5 + (_z^197*_y^3 + _z^61*_y^2 + _z^107*_y + _z^55)*t^4 + (_z^25*_y^3 + _z^207*_y^2 + _z^180*_y + _z^238)*t^3 + (_z^102*_y^3 + _z^170*_y^2 + _z^137*_y + _z^118)*t^2 + (_z^183*_y^3 + _z^174*_y^2 + _z^131*_y + _z^247)*t + _z^186*_y^3 + _z^83*_y^2 + _z^138*_y + _z^212 135 t^17 + (_z^98*_y^3 + _z^40*_y^2 + _z^42*_y + _z^43)*t^16 + (_z^153*_y^3 + _z^175*_y^2 + _z^181*_y + _z^28)*t^15 + (_z*_y^3 + _z^81*_y^2 + _z^157*_y + _z^193)*t^14 + (_z^248*_y^3 + _z^95*_y^2 + _z^244*_y + _z^181)*t^13 + (_z^127*_y^3 + _z^230*_y^2 + _z^34*_y + _z^39)*t^12 + (_z^170*_y^3 + _z^167*_y^2 + _z^87*_y + _z^121)*t^11 + (_z^224*_y^3 + _z^123*_y^2 + _z^128*_y + _z^73)*t^10 + (_z^219*_y^3 + _z^161*_y^2 + _z^131*_y + _z^116)*t^9 + (_z^13*_y^3 + _z^84*_y^2 + _z^71*_y + _z^136)*t^8 + (_z^78*_y^3 + _z^140*_y^2 + _z^60*_y + _z^193)*t^7 + (_z^63*_y^3 + _z^49*_y^2 + _z^85*_y + _z^157)*t^6 + (_z^89*_y^3 + _z^144*_y^2 + _z^107*_y + _z^115)*t^5 + (_z^139*_y^3 + _z^54*_y^2 + _z^162*_y + _z^211)*t^4 + (_z^56*_y^3 + _z^22*_y^2 + _z*_y + _z^78)*t^3 + (_z^140*_y^3 + _z^249*_y^2 + _z^21*_y + _z^234)*t^2 + (_z^139*_y^3 + _z^172*_y^2 + _z^73*_y + _z^88)*t + _z^23*_y^3 + _z^40*_y^2 + _z^90*_y + _z^232 140 t^17 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^116)*t^16 + (_z*_y^3 + _y^2 + _z^8*_y + _z^65)*t^15 + (_z^217*_y^3 + _z^167*_y^2 + _z^84*_y + _z^133)*t^14 + (_z^244*_y^3 + _z^189*_y^2 + _z^101*_y + _z^39)*t^13 + (_z^114*_y^3 + _z^138*_y^2 + _z^8*_y + _z^211)*t^12 + (_z^169*_y^3 + _z^14*_y^2 + _z^191*_y + _z^95)*t^11 + (_z^109*_y^3 + _z^123*_y^2 + _z^192*_y + _z^223)*t^10 + (_z^26*_y^3 + _z^14*_y^2 + _z^212*_y + _z^210)*t^9 + (_z^47*_y^3 + _z^112*_y^2 + _z^22*_y + _z^136)*t^8 + (_z^134*_y^3 + _z^166*_y^2 + _z^94*_y + _z^39)*t^7 + (_z^135*_y^3 + _z^236*_y^2 + _z^218*_y + _z^142)*t^6 + (_z^112*_y^3 + _z^42*_y^2 + _z^186*_y + _z^88)*t^5 + (_z^100*_y^3 + _z^22*_y^2 + _z^187*_y + _z^174)*t^4 + (_z^156*_y^3 + _z^85*_y^2 + _z^173)*t^3 + (_z^237*_y^3 + _z^227*_y^2 + _z^121*_y + _z^129)*t^2 + (_z^81*_y^3 + _z^200*_y^2 + _z^240*_y + _z^145)*t + _z^217*_y^3 + _z^146*_y^2 + _z^170*_y + _z^236 145 t^17 + (_z^36*_y^3 + _z^67*_y^2 + _z^250*_y + _z^235)*t^16 + (_z^189*_y^3 + _z^95*_y^2 + _z^251*_y + _z^81)*t^15 + (_z^158*_y^3 + _z^62*_y^2 + _z^82*_y + _z^159)*t^14 + (_z^198*_y^3 + _z^49*_y^2 + _z^91*_y + _z^15)*t^13 + (_z^14*_y^3 + _z^111*_y^2 + _z^129*_y + _z^18)*t^12 + (_z^201*_y^3 + _z^14*_y^2 + _z^15*_y + _z^174)*t^11 + (_z^183*_y^3 + _z^18*_y^2 + _z^111*_y + _z^240)*t^10 + (_z^207*_y^3 + _z^98*_y^2 + _z^96*_y + _z^187)*t^9 + (_z^121*_y^3 + _z^179*_y^2 + _z^201*_y + _z^6)*t^8 + (_z^51*_y^3 + _z^20*_y^2 + _z^119*_y + _z^119)*t^7 + (_z^238*_y^3 + _z^178*_y^2 + _z^136*_y + _z^148)*t^6 + (_z^168*_y^3 + _z^241*_y^2 + _z^38*_y + _z^29)*t^5 + (_z^50*_y^3 + _z^127*_y^2 + _z^138*_y + _z^145)*t^4 + (_z^129*_y^3 + _z^101*_y^2 + _z^254*_y + _z^47)*t^3 + (_z^10*_y^3 + _z^5*_y^2 + _z^209*_y + _z^188)*t^2 + (_z^246*_y^3 + _z^101*_y^2 + _z^227*_y + _z^4)*t + _z^102*_y^3 + _z^206*_y^2 + _z^222*_y + _z^238 150 t^17 + (_z^75*_y^3 + _z^172*_y^2 + _z^209*_y + _z^12)*t^16 + (_z^130*_y^3 + _z^18*_y^2 + _z^13*_y + _z^38)*t^15 + (_z^12*_y^3 + _z^48*_y^2 + _z^41*_y + _z^197)*t^14 + (_z^84*_y^3 + _z^18*_y^2 + _z^164*_y + _z^36)*t^13 + (_z^212*_y^3 + _z^204*_y^2 + _z^17*_y + _z^199)*t^12 + (_z^22*_y^3 + _z^105*_y^2 + _y + _z^47)*t^11 + (_z^9*_y^3 + _z^165*_y^2 + _z^64*_y + _z^31)*t^10 + (_z^213*_y^3 + _z^69*_y^2 + _z^59*_y + _z^14)*t^9 + (_z^204*_y^3 + _z^189*_y^2 + _z^240*_y + _z^201)*t^8 + (_z^204*_y^3 + _z^93*_y^2 + _z^200*_y + _z^205)*t^7 + (_z^224*_y^3 + _z^8*_y^2 + _z^169*_y + _z^186)*t^6 + (_z^132*_y^3 + _z^4*_y^2 + _z^35*_y + _z^190)*t^5 + (_z^107*_y^3 + _z^146*_y^2 + _z^130*_y + _z^155)*t^4 + (_z^224*_y^3 + _z^188*_y^2 + _z^232*_y + _z^222)*t^3 + (_z^104*_y^3 + _z^72*_y^2 + _z^54*_y + _z^103)*t^2 + (_z^128*_y^3 + _z^21*_y^2 + _z^18*_y + _z^163)*t + _z^217*_y^3 + _z^17*_y^2 + _z^239*_y + _z^86 155 t^17 + (_z^197*_y^3 + _z^237*_y^2 + _z^19*_y + _z^104)*t^16 + (_z^150*_y^2 + _z^235*_y + _z^151)*t^15 + (_z^9*_y^3 + _z^45*_y^2 + _z^159*_y + _z^51)*t^14 + (_z^57*_y^3 + _z^38*_y^2 + _z^169*_y + _z^165)*t^13 + (_z^239*_y^3 + _z^30*_y^2 + _z^161*_y + _z)*t^12 + (_z^236*_y^3 + _z^21*_y^2 + _z^129*_y + _z^49)*t^11 + (_z^210*_y^3 + _z^71*_y^2 + _z^9*_y + _z^205)*t^10 + (_z^194*_y^3 + _z^54*_y^2 + _z^224*_y + _z^57)*t^9 + (_z^203*_y^3 + _z^159*_y^2 + _z^233*_y + _z^253)*t^8 + (_y^3 + _z^230*_y^2 + _z^31*_y + _z^238)*t^7 + (_z^77*_y^3 + _z^22*_y^2 + _z^81*_y + _z^160)*t^6 + (_z^211*_y^3 + _z^170*_y^2 + _z^82*_y + _z^183)*t^5 + (_z^182*_y^3 + _z^169*_y^2 + _z^34*_y + _z^17)*t^4 + (_z^69*_y^2 + _z^191*_y + _z^144)*t^3 + (_z^210*_y^3 + _z^64*_y^2 + _z^147*_y + _z^20)*t^2 + (_z^120*_y^3 + _z^6*_y^2 + _z^141*_y + _z^13)*t + _z^45*_y^3 + _z^251*_y^2 + _z^3*_y + _z^131 160 t^17 + t^15 + t^14 + (_z^137*_y^3 + _z^156*_y^2 + _z^233*_y + _z^249)*t^12 + (_z^137*_y^3 + _z^156*_y^2 + _z^233*_y + _z^206)*t^11 + (_z^17*_y^3 + _z^244*_y^2 + _z^67*_y + _z^43)*t^5 + t^4 + (_z^182*_y^3 + _z^154*_y^2 + _z^149*_y + _z^119)*t^3 + _z^224*_y^3 + _z^212*_y^2 + _z^210*_y + _z^61 165 t^17 + (_z^81*_y^3 + _z^179*_y^2 + _z^33*_y + _z^32)*t^16 + (_z^119*_y^3 + _z^116*_y^2 + _z^34*_y + _z^39)*t^15 + (_z^124*_y^3 + _z^79*_y^2 + _z^129*_y + _z^3)*t^14 + (_z^34*_y^3 + _z^254*_y^2 + _z^142*_y + _z^153)*t^13 + (_z^179*_y^3 + _z^11*_y^2 + _z^14*_y + _z^133)*t^12 + (_z^57*_y^3 + _z^123*_y^2 + _z^129*_y + _z^69)*t^11 + (_z^184*_y^3 + _z^201*_y^2 + _z^34*_y + _z^241)*t^10 + (_z^95*_y^3 + _z^183*_y^2 + _z^4*_y + _z^249)*t^9 + (_z^115*_y^3 + _z^144*_y^2 + _z^114*_y + _z^69)*t^8 + (_z^63*_y^3 + _z^130*_y^2 + _z^163*_y + _z^193)*t^7 + (_z^208*_y^3 + _z^175*_y^2 + _z^207*_y + _z^192)*t^6 + (_z^62*_y^3 + _z^5*_y^2 + _z^69*_y + _z^195)*t^5 + (_z^177*_y^3 + _z^103*_y^2 + _z^130*_y + _z^64)*t^4 + (_z^37*_y^3 + _z^82*_y^2 + _z^45*_y + _z^194)*t^3 + (_z^230*_y^3 + _z^192*_y^2 + _z^83*_y + _z^185)*t^2 + (_z^73*_y^3 + _z^252*_y^2 + _z^223*_y + _z^172)*t + _z^148*_y^3 + _z^120*_y^2 + _z^152*_y + _z^83 170 t^17 + (_z^42*_y^3 + _z^71*_y^2 + _z^104*_y + _z^156)*t^16 + (_z^128*_y^3 + _z^231*_y^2 + _z^108*_y + _z^243)*t^15 + (_z^23*_y^3 + _z^11*_y^2 + _z^146*_y + _z^86)*t^14 + (_z^230*_y^3 + _z^89*_y^2 + _z^4*_y + _z^224)*t^13 + (_z^115*_y^3 + _z^10*_y^2 + _z^4*_y + _z^170)*t^12 + (_z^217*_y^3 + _z^185*_y^2 + _z^90*_y + _z^202)*t^11 + (_z^242*_y^3 + _z^194*_y^2 + _z^202*_y + _z^76)*t^10 + (_z^81*_y^3 + _z^67*_y^2 + _z^50*_y + _z^32)*t^9 + (_z^117*_y^3 + _z^74*_y^2 + _z^145*_y + _z^213)*t^8 + (_z^57*_y^3 + _z^41*_y^2 + _z^158*_y + _z^203)*t^7 + (_z^110*_y^3 + _z^240*_y^2 + _z^76*_y + _z^117)*t^6 + (_z^210*_y^3 + _z^82*_y^2 + _z^68*_y + _z^202)*t^5 + (_z^87*_y^3 + _z^247*_y^2 + _z^199*_y + _z^70)*t^4 + (_z^129*_y^3 + _z^15*_y^2 + _z^202*_y + _z^164)*t^3 + (_z^158*_y^3 + _z^154*_y^2 + _z^112*_y + _z^222)*t^2 + (_z^28*_y^3 + _z^46*_y^2 + _z*_y + _z^187)*t + _z^37*_y^3 + _z^153*_y^2 + _z^226*_y + _z^240 175 t^17 + (_z^16*_y^3 + _z^165*_y^2 + _z^145*_y + _z^114)*t^16 + (_z^88*_y^3 + _z^84*_y^2 + _z^220*_y + _z^205)*t^15 + (_z^51*_y^3 + _z^78*_y^2 + _z^58*_y + _z^51)*t^14 + (_z^56*_y^3 + _z^75*_y^2 + _z^7*_y + _z^12)*t^13 + (_z^192*_y^3 + _z^90*_y^2 + _z^139*_y + _z^101)*t^12 + (_z^74*_y^3 + _z^23*_y^2 + _z^65*_y + _z^98)*t^11 + (_z^10*_y^3 + _z^107*_y^2 + _z^32*_y + _z^230)*t^10 + (_z^65*_y^3 + _z^56*_y^2 + _z^57*_y + 1)*t^9 + (_z^5*_y^3 + _z^109*_y^2 + _z^154*_y + _z^161)*t^8 + (_z^181*_y^3 + _z^158*_y^2 + _z^170*_y + _z^135)*t^7 + (_z^165*_y^3 + _z^97*_y^2 + _z^150*_y + _z^21)*t^6 + (_z^93*_y^3 + _z^234*_y^2 + _z^28*_y + _z^243)*t^5 + (_z^49*_y^3 + _z^190*_y^2 + _z^212*_y + _z^145)*t^4 + (_z^75*_y^3 + _z^137*_y^2 + _z^92*_y + _z^229)*t^3 + (_z^29*_y^3 + _z^59*_y^2 + _z^231*_y + _z^73)*t^2 + (_z^250*_y^3 + _z^2*_y^2 + _z^49*_y + _z^239)*t + _z^208*_y^3 + _z^179*_y^2 + _z^135*_y + _z^182 180 t^17 + t^16 + (_z^237*_y^3 + _z^34*_y^2 + _z^111*_y + _z^221)*t^15 + (_z^42*_y^3 + _z^128*_y^2 + _z^34*_y + _z^63)*t^14 + (_z^94*_y^3 + _z^123*_y^2 + _z^148*_y + _z^90)*t^13 + (_z^130*_y^3 + _z^93*_y^2 + _z^116*_y + _z^105)*t^12 + (_z^251*_y^3 + _z^165*_y^2 + _z^238*_y + _z^38)*t^11 + (_z^82*_y^3 + _z^26*_y^2 + _z^250*_y + _z^232)*t^10 + (_z^214*_y^3 + _z^56*_y^2 + _z^242*_y + _z^246)*t^9 + (_z^215*_y^3 + _z^228*_y^2 + _z^116*_y + _z^36)*t^8 + (_z^194*_y^3 + _z^253*_y^2 + _z^24*_y + _z^38)*t^7 + (_z^155*_y^3 + _z^133*_y^2 + _z^35*_y + _z^87)*t^6 + (_z^28*_y^3 + _z^22*_y^2 + _z^4*_y + _z^119)*t^5 + (_z^160*_y^3 + _z^222*_y^2 + _z^96*_y + _z^40)*t^4 + (_z^108*_y^3 + _z^180*_y^2 + _z^87*_y + _z^120)*t^3 + (_z^193*_y^3 + _z^98*_y^2 + _z^90*_y + _z^46)*t^2 + (_z^25*_y^3 + _z^181*_y^2 + _z^190*_y + _z^245)*t + _z^160*_y^3 + _z^5*_y^2 + _z^195*_y + ** WARNING: Output too long, hence truncated. '130.235' ************** MAGMA ***************** Host 130.235.59.12 (130.235.59.12) Time: Sun Oct 17 19:51:00 2004 Input: F2 := FiniteField(2); Rz := PolynomialRing(F2); Fz<_z> := ext< F2 | z^8+z^6+z^3+z^2+1>; Ry := PolynomialRing(Fz); Py := y^4 + (_z^4+_z^6+_z^7)*y^3 + (1+_z+_z^3+_z^5)*y^2 + (1+_z+_z^6)*y + (1+_z+_z^2+_z^5+_z^6); Fy<_y> := ext< Fz | Py>; Rx := PolynomialRing(Fy); Px := x^17 + x^15 + x^4 + _y; Fx<_x> := ext< Fy | Px >; pwr:=2^32; beta := PrimitiveElement(Fx)^(5*pwr); Rt := PolynomialRing(Fx); Pt := (t+beta)*(t+beta^((2^32)^1))*(t+beta^((2^32)^2))*(t+beta^((2^32)^3))* (t+beta^((2^32)^4))*(t+beta^((2^32)^5))*(t+beta^((2^32)^6))* (t+beta^((2^32)^7))*(t+beta^((2^32)^8))*(t+beta^((2^32)^9))* (t+beta^((2^32)^10))*(t+beta^((2^32)^11))*(t+beta^((2^32)^12))* (t+beta^((2^32)^13))*(t+beta^((2^32)^14))*(t+beta^((2^32)^15))* (t+beta^((2^32)^16)); 5*pwr; Pt; Output: Magma V2.11-6 Sun Oct 17 2004 19:50:59 on modular [Seed = 1567562050] ------------------------------------- 21474836480 t^17 + t^15 + t^14 + _y*t^12 + (_y + 1)*t^11 + _y^2*t^5 + t^4 + (_z^56*_y^3 + _z^163*_y^2 + _z^210*_y + _z^244)*t^3 + _z^180*_y^3 + _z^20*_y^2 + _z^243*_y + _z^45 Total time: 0.280 seconds, Total memory usage: 4.54MB '169.244' ************** MAGMA ***************** Host 169.244.70.148 (169.244.70.148) Time: Mon Oct 18 09:58:29 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Mon Oct 18 2004 09:58:29 on modular [Seed = 2727358379] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:28:04 2004 Input: X:=Matrix(IntegerRing(), 2, 3, [1,2,3,4,5,6]); X; X^-1; Output: Magma V2.11-6 Mon Oct 18 2004 12:28:03 on modular [Seed = 3196850338] ------------------------------------- [1 2 3] [4 5 6] >> X^-1; ^ Runtime error in '^': Argument 1 is not square Total time: 0.180 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:28:24 2004 Input: X:=Matrix(IntegerRing(), 2, 3, [1,2,3,42,5,6]); X; X^-1; Output: Magma V2.11-6 Mon Oct 18 2004 12:28:24 on modular [Seed = 3112900510] ------------------------------------- [ 1 2 3] [42 5 6] >> X^-1;; ^ Runtime error in '^': Argument 1 is not square Total time: 0.180 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:28:46 2004 Input: X:=Matrix(IntegerRing(), 2, 2, [1,2,3,42]); X; X^-1; Output: Magma V2.11-6 Mon Oct 18 2004 12:28:46 on modular [Seed = 3045530500] ------------------------------------- [ 1 2] [ 3 42] >> X^-1;; ^ Runtime error in '^': Argument 1 is not invertible Total time: 0.180 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:30:02 2004 Input: X:=Matrix(IntegerRing(), 2, 2, [1,2,3,42]); X; Y=X^-1; Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:30:02 on modular [Seed = 3489489226] ------------------------------------- [ 1 2] [ 3 42] >> Y=X^-1; ^ User error: Identifier 'Y' has not been declared or assigned >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:31:24 2004 Input: X:=Matrix(IntegerRing(), 2, 2, [1,2,3,42]); X; Y:=X^-1; Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:31:23 on modular [Seed = 3371853340] ------------------------------------- [ 1 2] [ 3 42] >> Y:=X^-1; ^ Runtime error in '^': Argument 1 is not invertible >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:32:38 2004 Input: X:=Matrix(IntegerRing(), 3, 3, [3,2,1,1,0,2,4,1,3]); X; Y:=X^-1; Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:32:38 on modular [Seed = 3287380714] ------------------------------------- [3 2 1] [1 0 2] [4 1 3] >> Y:=X^-1; ^ Runtime error in '^': Argument 1 is not invertible >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:33:02 2004 Input: X:=Matrix(IntegerRing(), 3, 3, [3,2,1,1,0,2,4,1,3]); X; Y:=Inverse(X); Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:33:02 on modular [Seed = 3756879598] ------------------------------------- [3 2 1] [1 0 2] [4 1 3] >> Y:=Inverse(X); ^ Runtime error in 'Inverse': Argument 1 must be a variable reference (use ~) Argument types given: AlgMatElt >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:33:14 2004 Input: X:=Matrix(IntegerRing(), 3, 3, [3,2,1,1,0,2,4,1,3]); X; Y:=Inverse(~X); Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:33:14 on modular [Seed = 3689507486] ------------------------------------- [3 2 1] [1 0 2] [4 1 3] >> Y:=Inverse(~X); ^ User error: References are only allowed as procedure call arguments (function call attempted) >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:33:41 2004 Input: X:=Matrix(IntegerRing(), 3, 3, [3,2,1,1,0,2,4,1,3]); X; Y:=Transpose(X); Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:33:41 on modular [Seed = 3622135485] ------------------------------------- [3 2 1] [1 0 2] [4 1 3] [3 1 4] [2 0 1] [1 2 3] Total time: 0.200 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:34:47 2004 Input: X:=Matrix(IntegerRing(), 3, 3, [3,2,1,1,0,2,4,1,3]); X; Y:=Inverse(X,IntegerRing()); Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:34:47 on modular [Seed = 3504497016] ------------------------------------- [3 2 1] [1 0 2] [4 1 3] >> Y:=Inverse(X,IntegerRing()); ^ Runtime error in 'Inverse': Bad argument types Argument types given: AlgMatElt, RngInt >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '134.147' ************** MAGMA ***************** Host 134.147.40.177 (134.147.40.177) Time: Mon Oct 18 12:35:23 2004 Input: X:=Matrix(IntegerRing(), 3, 3, [3,2,1,1,0,2,4,1,3]); X; Y:=X^-1; Y; Output: Magma V2.11-6 Mon Oct 18 2004 12:35:23 on modular [Seed = 3973995816] ------------------------------------- [3 2 1] [1 0 2] [4 1 3] >> Y:=X^-1; ^ Runtime error in '^': Argument 1 is not invertible >> Y;; ^ User error: Identifier 'Y' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:51:11 2004 Input: [12, 34]-[11, 11] Output: Magma V2.11-6 Mon Oct 18 2004 15:51:10 on modular [Seed = 2035033798] ------------------------------------- >> [12, 34]-[11, 11]; ^ Runtime error in '-': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:51:17 2004 Input: [12, 34] - [11, 11] Output: Magma V2.11-6 Mon Oct 18 2004 15:51:17 on modular [Seed = 2118853083] ------------------------------------- >> [12, 34] - [11, 11]; ^ Runtime error in '-': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:51:48 2004 Input: [12, 34] + [11, 11] Output: Magma V2.11-6 Mon Oct 18 2004 15:51:48 on modular [Seed = 1683045280] ------------------------------------- >> [12, 34] + [11, 11]; ^ Runtime error in '+': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:52:30 2004 Input: a := [12, 34];a; b := [11, 11];b; c := a+b;c; Output: Magma V2.11-6 Mon Oct 18 2004 15:52:30 on modular [Seed = 1767650951] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> c := a+b;c;; ^ Runtime error in '+': Bad argument types Argument types given: SeqEnum[RngIntElt], SeqEnum[RngIntElt] >> c := a+b;c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:55:17 2004 Input: a := [12, 34];a; b := [11, 11];b; c[1] := a[1] + b[1];c[1]; Output: Magma V2.11-6 Mon Oct 18 2004 15:55:17 on modular [Seed = 2426785317] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> c[1] := a[1] + b[1];c[1];; ^ User error: Identifier 'c' has not been declared or assigned >> c[1] := a[1] + b[1];c[1];; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:55:27 2004 Input: a := [12, 34];a; b := [11, 11];b; c := a[1] + b[1];c; Output: Magma V2.11-6 Mon Oct 18 2004 15:55:27 on modular [Seed = 2510342954] ------------------------------------- [ 12, 34 ] [ 11, 11 ] 23 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:56:29 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0, 0]; for i in [1, 2] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 15:56:29 on modular [Seed = 2209799550] ------------------------------------- [ 12, 34 ] [ 11, 11 ] [ 23, 45 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:59:11 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0, 0]; for i form 1 to 2 do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 15:59:11 on modular [Seed = 3045119018] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> for i form 1 to 2 do ^ User error: bad syntax >> c[i] := a[i] + b[i]; ^ User error: Identifier 'i' has not been declared or assigned >> end for; ^ User error: bad syntax [ 0, 0 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 15:59:18 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0, 0]; for i from 1 to 2 do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 15:59:18 on modular [Seed = 3163151674] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> for i from 1 to 2 do ^ User error: bad syntax >> c[i] := a[i] + b[i]; ^ User error: Identifier 'i' has not been declared or assigned >> end for; ^ User error: bad syntax [ 0, 0 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:01:48 2004 Input: n := 2^109-1; time Factorization(n); Output: Magma V2.11-6 Mon Oct 18 2004 16:01:48 on modular [Seed = 4207909574] ------------------------------------- [ <745988807, 1>, <870035986098720987332873, 1> ] Time: 0.020 Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:02:53 2004 Input: m := 2^111-1; n := 2^113-1; t := Cputime(); Factorization(m); Factorization(n); Cputime(t); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:03:07 2004 Input: m := 2^111-1; n := 2^113-1; Factorization(m); Factorization(n); Output: Magma V2.11-6 Mon Oct 18 2004 16:03:07 on modular [Seed = 3805774473] ------------------------------------- [ <7, 1>, <223, 1>, <321679, 1>, <26295457, 1>, <319020217, 1>, <616318177, 1> ] [ <3391, 1>, <23279, 1>, <65993, 1>, <1868569, 1>, <1066818132868207, 1> ] Total time: 0.200 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:04:05 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0, 0]; for i = 1 to 2 do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:04:04 on modular [Seed = 3889334083] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> for i = 1 to 2 do ^ User error: bad syntax >> c[i] := a[i] + b[i]; ^ User error: Identifier 'i' has not been declared or assigned >> end for; ^ User error: bad syntax [ 0, 0 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:04:16 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0, 0]; for i := 1 to 2 do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:04:16 on modular [Seed = 3973680188] ------------------------------------- [ 12, 34 ] [ 11, 11 ] [ 23, 45 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:06:53 2004 Input: n := 2^109-1; time Factorization(n); cputime(); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:07:04 2004 Input: n := 2^109-1; time Factorization(n); Cputime(); Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:07:18 2004 Input: n := 2^109-1; time Factorization(n); Realtime(); Output: Magma V2.11-6 Mon Oct 18 2004 16:07:18 on modular [Seed = 456030334] ------------------------------------- [ <745988807, 1>, <870035986098720987332873, 1> ] Time: 0.240 1098130038.733 Total time: 0.420 seconds, Total memory usage: 3.66MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:12:41 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0 | x in [1 .. 2]]; for i in [1, 2] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:12:41 on modular [Seed = 20210603] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> c := [0 | x in [1 .. 2]]; ^ User error: Identifier 'x' has not been declared or assigned >> c[i] := a[i] + b[i]; ^ User error: Identifier 'c' has not been declared or assigned >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:13:04 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0 | x in [1, 2]]; for i in [1, 2] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:13:03 on modular [Seed = 70346456] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> c := [0 | x in [1, 2]]; ^ User error: Identifier 'x' has not been declared or assigned >> c[i] := a[i] + b[i]; ^ User error: Identifier 'c' has not been declared or assigned >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:13:24 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0 | 2]; for i in [1, 2] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:13:24 on modular [Seed = 255487480] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> c := [0 | 2]; ^ Runtime error in [ ... ]: Invalid sequence universe >> c[i] := a[i] + b[i]; ^ User error: Identifier 'c' has not been declared or assigned >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:13:31 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0 : 2]; for i in [1, 2] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:13:31 on modular [Seed = 839340234] ------------------------------------- [ 12, 34 ] [ 11, 11 ] >> c := [0 : 2]; ^ User error: bad syntax >> c[i] := a[i] + b[i]; ^ User error: Identifier 'c' has not been declared or assigned >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:13:49 2004 Input: a := [12, 34];a; b := [11, 11];b; c := [0 : x in [1, 2]]; for i in [1, 2] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:13:49 on modular [Seed = 889214939] ------------------------------------- [ 12, 34 ] [ 11, 11 ] [ 23, 45 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:14:49 2004 Input: a := [1 : x in [1 .. 36]];a; b := [2 : x in [1 .. 36]];b; c := [0 : x in [1 .. 36]]; for i in [1 .. 36] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:14:48 on modular [Seed = 940399891] ------------------------------------- [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] [ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:16:12 2004 Input: n := 136; a := [1 : x in [1 .. n]];a; b := [2 : x in [1 .. n]];b; c := [0 : x in [1 .. n]]; for i in [1 .. n] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:16:12 on modular [Seed = 588662460] ------------------------------------- [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] [ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:16:58 2004 Input: n := 136; a := [1 : x := 1 to n];a; b := [2 : x in [1 .. n]];b; c := [0 : x in [1 .. n]]; for i in [1 .. n] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:16:58 on modular [Seed = 621822092] ------------------------------------- >> a := [1 : x := 1 to n];a; ^ User error: bad syntax [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] >> c[i] := a[i] + b[i]; ^ User error: Identifier 'a' has not been declared or assigned [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:17:08 2004 Input: n := 136; a := [1 | x := 1 to n];a; b := [2 : x in [1 .. n]];b; c := [0 : x in [1 .. n]]; for i in [1 .. n] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:17:08 on modular [Seed = 773540857] ------------------------------------- >> a := [1 | x := 1 to n];a; ^ User error: bad syntax [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] >> c[i] := a[i] + b[i]; ^ User error: Identifier 'a' has not been declared or assigned [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:17:32 2004 Input: n := 136; a := [1 : x := 1 to n do];a; b := [2 : x in [1 .. n]];b; c := [0 : x in [1 .. n]]; for i in [1 .. n] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:17:31 on modular [Seed = 1365521566] ------------------------------------- >> a := [1 : x := 1 to n do];a; ^ User error: bad syntax [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] >> c[i] := a[i] + b[i]; ^ User error: Identifier 'a' has not been declared or assigned [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:17:53 2004 Input: n := 136; a := [1 : [1 .. n]];a; b := [2 : x in [1 .. n]];b; c := [0 : x in [1 .. n]]; for i in [1 .. n] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:17:53 on modular [Seed = 1415655862] ------------------------------------- >> a := [1 : [1 .. n]];a; ^ User error: bad syntax [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] >> c[i] := a[i] + b[i]; ^ User error: Identifier 'a' has not been declared or assigned [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:18:07 2004 Input: n := 136; a := [1 : x in [1 .. n]];a; b := [2 : x in [1 .. n]];b; c := [0 : x in [1 .. n]]; for i in [1 .. n] do c[i] := a[i] + b[i]; end for; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:18:06 on modular [Seed = 1098130604] ------------------------------------- [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] [ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:19:27 2004 Input: n := 136; a := <11, 22>;a; Output: Magma V2.11-6 Mon Oct 18 2004 16:19:27 on modular [Seed = 1883575340] ------------------------------------- <11, 22> Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:19:53 2004 Input: n := 136; a := <11, 22>;a; b := <12, 23>;b; c := a + b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:19:53 on modular [Seed = 2068717313] ------------------------------------- <11, 22> <12, 23> >> c := a + b; c;; ^ Runtime error in '+': Bad argument types Argument types given: Tup, Tup >> c := a + b; c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:23:05 2004 Input: n := 136; a := Matrix(2,1,[11, 22]);a; b := Matrix(2,1,[12, 23]);b; c := a + b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:23:05 on modular [Seed = 1666581593] ------------------------------------- [11] [22] [12] [23] [23] [45] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:23:29 2004 Input: n := 136; a := Matrix(1,2,[11, 22]);a; b := Matrix(1,2,[12, 23]);b; c := a + b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:23:29 on modular [Seed = 1716715828] ------------------------------------- [11 22] [12 23] [23 45] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:25:20 2004 Input: n := 136; a := Matrix(1,n,[2 : x in [1..n]]);a; b := Matrix(1,n,[1 : x in [1..n]]);b; c := a + b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:25:19 on modular [Seed = 1767640789] ------------------------------------- [2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3] Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:25:34 2004 Input: n := 136; a := Matrix(1,n,[2 : x in [1..n]]);a; b := Matrix(1,n,[1 : x in [1..n]]);b; c := a - b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:25:33 on modular [Seed = 1817775042] ------------------------------------- [2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:27:02 2004 Input: n := 136; a := Vector(n,[2 : x in [1..n]]);a; b := Vector(n,[1 : x in [1..n]]);b; c := a - b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:27:02 on modular [Seed = 2527326355] ------------------------------------- (2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2) (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1) (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1) Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:27:52 2004 Input: n := 136; a := Vector(n,[2 : x in [1..n]]);a; b := Matrix(1, n,[1 : x in [1..n]]);b; c := a - b; c; Output: Magma V2.11-6 Mon Oct 18 2004 16:27:52 on modular [Seed = 2578251714] ------------------------------------- (2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2) [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] >> c := a - b; c;; ^ Runtime error in '-': Bad argument types Argument types given: ModTupRngElt, ModMatRngElt >> c := a - b; c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:30:30 2004 Input: StringToInteger("It's a beautiful day!"); Output: Magma V2.11-6 Mon Oct 18 2004 16:30:30 on modular [Seed = 2193089655] ------------------------------------- >> StringToInteger("It's a beautiful day!");; ^ Runtime error in 'StringToInteger': String "It's a beautiful day!" does not represent an number in base 10 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:30:40 2004 Input: StringToInteger( "It's a beautiful day!" ); Output: Magma V2.11-6 Mon Oct 18 2004 16:30:40 on modular [Seed = 2242962278] ------------------------------------- >> StringToInteger( "It's a beautiful day!" );; ^ Runtime error in 'StringToInteger': String "It's a beautiful day!" does not represent an number in base 10 Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:31:20 2004 Input: StringToCode( "It's a beautiful day!" ); Output: Magma V2.11-6 Mon Oct 18 2004 16:31:20 on modular [Seed = 2294145411] ------------------------------------- 73 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:32:11 2004 Input: StringToCode( "It's a beautiful day!" ); StringToInteger(5); Output: Magma V2.11-6 Mon Oct 18 2004 16:32:10 on modular [Seed = 2995248107] ------------------------------------- 73 >> StringToInteger(5);; ^ Runtime error in 'StringToInteger': Bad argument types Argument types given: RngIntElt Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:32:39 2004 Input: StringToCode( "It's a beautiful day!" ); StringToInteger(5.64); Output: Magma V2.11-6 Mon Oct 18 2004 16:32:39 on modular [Seed = 3045121217] ------------------------------------- 73 >> StringToInteger(5.64);; ^ Runtime error in 'StringToInteger': Bad argument types Argument types given: FldPrElt Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:32:47 2004 Input: StringToCode( "It's a beautiful day!" ); StringToInteger("5.64"); Output: Magma V2.11-6 Mon Oct 18 2004 16:32:47 on modular [Seed = 2727857118] ------------------------------------- 73 >> StringToInteger("5.64");; ^ Runtime error in 'StringToInteger': String "5.64" does not represent an number in base 10 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:32:55 2004 Input: StringToCode( "It's a beautiful day!" ); StringToInteger('5.64'); Output: Magma V2.11-6 Mon Oct 18 2004 16:32:55 on modular [Seed = 2777730241] ------------------------------------- 73 >> StringToInteger('5.64');; ^ User error: Identifier '5.64' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:34:19 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5.64"); Output: Magma V2.11-6 Mon Oct 18 2004 16:34:19 on modular [Seed = 2828910960] ------------------------------------- 73 >> StringToIntegerSequence("5.64");; ^ Runtime error in 'StringToIntegerSequence': String "5.64" does not consist of a sequence of integers Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:35:28 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 64"); Output: Magma V2.11-6 Mon Oct 18 2004 16:35:27 on modular [Seed = 3555113936] ------------------------------------- 73 [ 5, 64 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:35:40 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); Output: Magma V2.11-6 Mon Oct 18 2004 16:35:39 on modular [Seed = 3605249758] ------------------------------------- 73 [ 5, 6, 4 ] Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:37:47 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); StringToInteger("5 6 4"); Output: Magma V2.11-6 Mon Oct 18 2004 16:37:47 on modular [Seed = 3422462787] ------------------------------------- 73 [ 5, 6, 4 ] >> StringToInteger("5 6 4");; ^ Runtime error in 'StringToInteger': String "5 6 4" does not represent an number in base 10 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:37:54 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); StringToInteger("5 64"); Output: Magma V2.11-6 Mon Oct 18 2004 16:37:54 on modular [Seed = 3472598655] ------------------------------------- 73 [ 5, 6, 4 ] >> StringToInteger("5 64");; ^ Runtime error in 'StringToInteger': String "5 64" does not represent an number in base 10 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:38:44 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); StringToInteger("-5 64"); Output: Magma V2.11-6 Mon Oct 18 2004 16:38:44 on modular [Seed = 4156727088] ------------------------------------- 73 [ 5, 6, 4 ] >> StringToInteger("-5 64");; ^ Runtime error in 'StringToInteger': String "-5 64" does not represent an number in base 10 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:39:42 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(546,2); Output: Magma V2.11-6 Mon Oct 18 2004 16:39:42 on modular [Seed = 4207907303] ------------------------------------- 73 [ 5, 6, 4 ] 1000100010 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:40:16 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); Output: Magma V2.11-6 Mon Oct 18 2004 16:40:16 on modular [Seed = 4257781470] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:41:07 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); StringToInteger("56 4"); IntegerToString(372,2); Output: Magma V2.11-6 Mon Oct 18 2004 16:41:07 on modular [Seed = 3772091280] ------------------------------------- 73 [ 5, 6, 4 ] >> StringToInteger("56 4"); ^ Runtime error in 'StringToInteger': String "56 4" does not represent an number in base 10 101110100 Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:41:25 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); ?StringToInteger Output: Magma V2.11-6 Mon Oct 18 2004 16:41:24 on modular [Seed = 3990390410] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 2 matches: 1 I /language/IO/string/conversion/StringToInteger 2 I /language/IO/string/conversion/StringToInteger To view an entry, type ? followed by the number next to it Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:41:33 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); ?StringToInteger ?1 Output: Magma V2.11-6 Mon Oct 18 2004 16:41:33 on modular [Seed = 287603326] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 2 matches: 1 I /language/IO/string/conversion/StringToInteger 2 I /language/IO/string/conversion/StringToInteger To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/IO/string/conversion/StringToInteger KIND: Intrinsic =============================================================================== StringToInteger(s, b) : MonStgElt, MonStgElt -> RngIntElt Returns the integer corresponding to the string of digits s, all assumed to be written in base b. All non-space characters in the string s must be digits less than b (if b is greater than 10, `A' is used for 10, `B' for 11, etc.), except the first character, which is also allowed to be + or -. An error results if any other combination of characters occurs. =============================================================================== Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:42:22 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); StringToInteger("A"); ?StringToInteger() ?1 Output: Magma V2.11-6 Mon Oct 18 2004 16:42:22 on modular [Seed = 456028327] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 >> StringToInteger("A"); ^ Runtime error in 'StringToInteger': String "A" does not represent an number in base 10 No references for word "StringToInteger()" No numbers are defined Total time: 0.190 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:42:35 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); StringToInteger("A"); ?StringToInteger ?1 Output: Magma V2.11-6 Mon Oct 18 2004 16:42:35 on modular [Seed = 104033711] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 >> StringToInteger("A"); ^ Runtime error in 'StringToInteger': String "A" does not represent an number in base 10 2 matches: 1 I /language/IO/string/conversion/StringToInteger 2 I /language/IO/string/conversion/StringToInteger To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/IO/string/conversion/StringToInteger KIND: Intrinsic =============================================================================== StringToInteger(s, b) : MonStgElt, MonStgElt -> RngIntElt Returns the integer corresponding to the string of digits s, all assumed to be written in base b. All non-space characters in the string s must be digits less than b (if b is greater than 10, `A' is used for 10, `B' for 11, etc.), except the first character, which is also allowed to be + or -. An error results if any other combination of characters occurs. =============================================================================== Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:42:45 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); StringToInteger("A"); ?StringToInteger ?2 Output: Magma V2.11-6 Mon Oct 18 2004 16:42:45 on modular [Seed = 188637404] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 >> StringToInteger("A"); ^ Runtime error in 'StringToInteger': String "A" does not represent an number in base 10 2 matches: 1 I /language/IO/string/conversion/StringToInteger 2 I /language/IO/string/conversion/StringToInteger To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/IO/string/conversion/StringToInteger KIND: Intrinsic =============================================================================== StringToInteger(s) : MonStgElt -> RngIntElt Returns the integer corresponding to the string of decimal digits s. All non-space characters in the string s must be digits (0, 1, ..., 9), except the first character, which is also allowed to be + or -. An error results if any other combination of characters occurs. Leading zeros are omitted. =============================================================================== Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:43:08 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); StringToInteger("013521"); ?StringToInteger ?2 Output: Magma V2.11-6 Mon Oct 18 2004 16:43:07 on modular [Seed = 205088709] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 13521 2 matches: 1 I /language/IO/string/conversion/StringToInteger 2 I /language/IO/string/conversion/StringToInteger To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/IO/string/conversion/StringToInteger KIND: Intrinsic =============================================================================== StringToInteger(s) : MonStgElt -> RngIntElt Returns the integer corresponding to the string of decimal digits s. All non-space characters in the string s must be digits (0, 1, ..., 9), except the first character, which is also allowed to be + or -. An error results if any other combination of characters occurs. Leading zeros are omitted. =============================================================================== Total time: 0.180 seconds, Total memory usage: 3.50MB '129.137' ************** MAGMA ***************** Host 129.137.208.58 (129.137.208.58) Time: Mon Oct 18 16:43:16 2004 Input: StringToCode( "It's a beautiful day!" ); StringToIntegerSequence("5 6 4"); IntegerToString(372,2); StringToInteger("13521"); ?StringToInteger ?2 Output: Magma V2.11-6 Mon Oct 18 2004 16:43:16 on modular [Seed = 822368967] ------------------------------------- 73 [ 5, 6, 4 ] 101110100 13521 2 matches: 1 I /language/IO/string/conversion/StringToInteger 2 I /language/IO/string/conversion/StringToInteger To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/IO/string/conversion/StringToInteger KIND: Intrinsic =============================================================================== StringToInteger(s) : MonStgElt -> RngIntElt Returns the integer corresponding to the string of decimal digits s. All non-space characters in the string s must be digits (0, 1, ..., 9), except the first character, which is also allowed to be + or -. An error results if any other combination of characters occurs. Leading zeros are omitted. =============================================================================== Total time: 0.190 seconds, Total memory usage: 3.50MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:55:06 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:55:01 on modular [Seed = 1348834113] ------------------------------------- 7 4 Point [ 1, 349, 252, 928 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 472, 18, 4 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 652, 419, 637 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 711, 325, 473 ] was singular mod 1009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.649 seconds, Total memory usage: 6.30MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:55:25 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,1000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:55:22 on modular [Seed = 1567137363] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.720 seconds, Total memory usage: 6.43MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:55:48 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:55:36 on modular [Seed = 1500289637] ------------------------------------- 7 4 Point [ 1, 524, 1997, 2811 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 524, 3269, 4693 ] was singular mod 5003 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 12.039 seconds, Total memory usage: 6.43MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:56:36 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[2]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:56:20 on modular [Seed = 1165002245] ------------------------------------- 7 4 Point [ 1, 360, 1048, 671 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 360, 6134, 2829 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3131, 2167, 3746 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3131, 2900, 6755 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 4114, 6137, 1240 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 4114, 2922, 2260 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6904, 5690, 155 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6904, 4764, 3345 ] was singular mod 7001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.640 seconds, Total memory usage: 7.10MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:57:05 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[3]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:56:48 on modular [Seed = 1098154533] ------------------------------------- 7 4 Point [ 1, 360, 1048, 671 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 360, 6134, 2829 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3131, 2167, 3746 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3131, 2900, 6755 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 4114, 6137, 1240 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 4114, 2922, 2260 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6904, 5690, 155 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6904, 4764, 3345 ] was singular mod 7001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.609 seconds, Total memory usage: 7.10MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:57:34 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[1]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:57:18 on modular [Seed = 1316720084] ------------------------------------- 7 4 Point [ 1, 93, 6414, 4942 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 5119, 3516, 5577 ] was singular mod 7001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.609 seconds, Total memory usage: 6.43MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:58:02 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[4]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:57:46 on modular [Seed = 1249872372] ------------------------------------- 7 4 Point [ 1, 899, 4555, 54 ] was singular mod 7001 and ignored at the #1 lift Point [ 1, 2623, 5110, 6199 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 2901, 3785, 5335 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 5804, 5918, 998 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 5896, 4084, 3744 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6186, 166, 3251 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6336, 3908, 5828 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6477, 4720, 2972 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 6622, 3504, 3921 ] was singular mod 7001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.489 seconds, Total memory usage: 6.43MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:58:28 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[1]); #S; F := S[5]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:58:27 on modular [Seed = 1984148913] ------------------------------------- 7 4 >> F := S[5]; ^ Runtime error in '[]': Sequence element 5 not defined >> pts := Points(F,7000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field >> AssociatedEC(F); ^ User error: Identifier 'F' has not been declared or assigned >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 1.570 seconds, Total memory usage: 6.32MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:58:50 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[2]); #S; F := S[1]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 22:58:43 on modular [Seed = 1917301125] ------------------------------------- 7 4 Points( F: [ [ 0 0 0 1] [ 0 0 1 0] [ 0..., bound: 7000 ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/find_point.m", line 117, column 50: >> r := ShortVectors(Lattice(M),6*Floor(p^3) : ^ Runtime error in 'ShortVectors': Upper bound too large (would produce at least 1073741823 vectors) Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 6.870 seconds, Total memory usage: 8.98MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:59:22 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 22:59:01 on modular [Seed = 2118892959] ------------------------------------- 7 4 Errors: /bin/sh: line 1: 21866 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 22:59:56 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 22:59:35 on modular [Seed = 1683072615] ------------------------------------- 7 Errors: /bin/sh: line 1: 21872 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:00:18 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[3]); #S; F := S[1]; pts := Points(F,4000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:00:02 on modular [Seed = 1616224838] ------------------------------------- 7 4 Point [ 1, 45, 2309, 2857 ] was singular mod 4001 and ignored at the #1 lift Point [ 1, 607, 514, 1596 ] was singular mod 4001 and ignored at the #3 lift Point [ 1, 3154, 2949, 751 ] was singular mod 4001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.720 seconds, Total memory usage: 8.30MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:00:44 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[4]); #S; F := S[1]; pts := Points(F,4500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:00:36 on modular [Seed = 1817816620] ------------------------------------- 7 FourDescent( f: $.1^4 + 27478564 ) ReduceFD( fd: [ [ 5611561 11113512 -159226075724 ... ) StollReduce( desc: [ [ 0 0 23551 2560] [ 0 0 216660 23551... ) Covariant( mat1: [ 0 0 23551 2560] [ 0 0 216660 23551] ..., mat2: [ 18810654742 173050675456 -65017 588249] [ ... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 350, column 33: >> covmat *:= 1/Sqrt(&+[Norm(c) : c in Eltseq(covmat)]); ^ Runtime error in '/': Division by zero >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S[1]; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,4500); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field >> AssociatedEC(F); ^ User error: Identifier 'F' has not been declared or assigned >> m(pts[1]); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 8.109 seconds, Total memory usage: 7.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:02:10 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,4500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:01:55 on modular [Seed = 1767680990] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.730 seconds, Total memory usage: 7.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:02:43 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:02:25 on modular [Seed = 2510313280] ------------------------------------- 7 4 Point [ 1, 4621, 3547, 1575 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4621, 2460, 4432 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 17.629 seconds, Total memory usage: 7.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:03:17 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:02:57 on modular [Seed = 2443465572] ------------------------------------- 7 4 Point [ 1, 2271, 3413, 1270 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 2271, 3588, 5731 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 2539, 1428, 3273 ] was singular mod 7001 and ignored at the #1 lift Point [ 1, 2539, 5573, 3728 ] was singular mod 7001 and ignored at the #1 lift Point [ 1, 3390, 6527, 1479 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3390, 474, 5522 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3741, 3410, 1967 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3741, 3591, 5034 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3751, 1665, 1176 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3751, 5336, 5825 ] was singular mod 7001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.230 seconds, Total memory usage: 7.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:03:51 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[2]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:03:31 on modular [Seed = 2645055626] ------------------------------------- 7 4 Point [ 1, 2271, 3588, 1270 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 2271, 3413, 5731 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 2539, 5573, 3273 ] was singular mod 7001 and ignored at the #1 lift Point [ 1, 2539, 1428, 3728 ] was singular mod 7001 and ignored at the #1 lift Point [ 1, 3390, 474, 1479 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3390, 6527, 5522 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3741, 3591, 1967 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3741, 3410, 5034 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3751, 5336, 1176 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 3751, 1665, 5825 ] was singular mod 7001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.989 seconds, Total memory usage: 7.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:04:22 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[3]; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 23:04:01 on modular [Seed = 2578209964] ------------------------------------- 7 4 Point [ 1, 1655, 3726, 5067 ] was singular mod 7001 and ignored at the #3 lift Point [ 1, 1951, 1936, 2631 ] was singular mod 7001 and ignored at the #1 lift Errors: /bin/sh: line 1: 21901 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:04:53 2004 Input: E := EllipticCurve( [0,0,0,-6869641,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[3]; pts := Points(F,6800); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:04:32 on modular [Seed = 2242920657] ------------------------------------- 7 4 Point [ 1, 405, 6206, 3521 ] was singular mod 6803 and ignored at the #1 lift Point [ 1, 1596, 1827, 3223 ] was singular mod 6803 and ignored at the #1 lift Point [ 1, 2846, 5054, 3214 ] was singular mod 6803 and ignored at the #1 lift Point [ 1, 3119, 899, 4965 ] was singular mod 6803 and ignored at the #1 lift Point [ 1, 6602, 2413, 2540 ] was singular mod 6803 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field function(p) ... end function (1262572144393399142500799275479203682215327558854661231694961/9648671056064493\ 745735556173750720923938363865988980100 : -141839492620150585074979589539390292085426545749402635777753238027292398610642\ 6160748972959/29971001190836340626772937362877335642478912981786854575996907726\ 422804406849701000 : 1) 130.52603184443972850203 Total time: 20.910 seconds, Total memory usage: 7.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:05:41 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[3]; pts := Points(F,6800); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 23:05:20 on modular [Seed = 2176074981] ------------------------------------- 7 4 Point [ 1, 3268, 2517, 245 ] was singular mod 6803 and ignored at the #1 lift Errors: /bin/sh: line 1: 21909 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:06:14 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[3]; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 23:05:53 on modular [Seed = 2377664520] ------------------------------------- 7 4 Point [ 1, 466, 1853, 5501 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2124, 1756, 3643 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3288, 1780, 1797 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 21913 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:06:45 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[3]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 23:06:24 on modular [Seed = 2310818861] ------------------------------------- 7 4 Errors: /bin/sh: line 1: 21917 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:07:18 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,5000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 23:06:57 on modular [Seed = 3062068083] ------------------------------------- 7 4 Errors: /bin/sh: line 1: 21922 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:07:44 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[1]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:07:24 on modular [Seed = 2995222346] ------------------------------------- 7 4 Point [ 1, 396, 1983, 2207 ] was singular mod 3001 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.879 seconds, Total memory usage: 10.31MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:08:15 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[2]; pts := Points(F,3000); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:07:55 on modular [Seed = 3196811937] ------------------------------------- 7 4 Point [ 1, 947, 2489, 526 ] was singular mod 3001 and ignored at the #1 lift Point [ 1, 2353, 425, 1896 ] was singular mod 3001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.949 seconds, Total memory usage: 10.24MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:08:47 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[3]; pts := Points(F,3200); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:08:27 on modular [Seed = 2760990875] ------------------------------------- 7 4 Point [ 1, 2395, 61, 2141 ] was singular mod 3203 and ignored at the #3 lift Point [ 1, 2407, 398, 90 ] was singular mod 3203 and ignored at the #1 lift Point [ 1, 2903, 2830, 2460 ] was singular mod 3203 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.989 seconds, Total memory usage: 10.24MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:09:20 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[4]; pts := Points(F,3200); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:09:01 on modular [Seed = 2694145273] ------------------------------------- 7 4 Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.079 seconds, Total memory usage: 10.24MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:09:51 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[4]; pts := Points(F,3500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:09:32 on modular [Seed = 2895734996] ------------------------------------- 7 4 Point [ 1, 839, 2512, 1032 ] was singular mod 3511 and ignored at the #3 lift Point [ 1, 1714, 1883, 857 ] was singular mod 3511 and ignored at the #3 lift Point [ 1, 1797, 1883, 2654 ] was singular mod 3511 and ignored at the #3 lift Point [ 1, 2672, 2512, 2479 ] was singular mod 3511 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.070 seconds, Total memory usage: 10.13MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:10:37 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[5]); #S; F := S[4]; pts := Points(F,3900); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: Magma V2.11-6 Mon Oct 18 2004 23:10:17 on modular [Seed = 2828889125] ------------------------------------- 7 4 Point [ 1, 691, 3664, 2055 ] was singular mod 3907 and ignored at the #1 lift Point [ 1, 3216, 3664, 1852 ] was singular mod 3907 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field function(p) ... end function >> m(pts[1]); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.910 seconds, Total memory usage: 10.13MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:11:14 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,3900); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Oct 18 2004 23:10:53 on modular [Seed = 3571519613] ------------------------------------- 7 Errors: /bin/sh: line 1: 21952 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.166 (66.63.132.166) Time: Mon Oct 18 23:11:44 2004 Input: E := EllipticCurve( [0,0,0,-32982049,0] ); g := TwoDescent(E); #g; S := FourDescent(g[6]); #S; F := S[1]; pts := Points(F,3500); X,m := Scheme(F); E; AssociatedEC(F); m(pts[1]); Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so comp