'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\
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4209932336102683834830969288091053123005002292528473238170813835583063210547614\
2122185536884450912065665766145972792756443037388879438826340716274982084227704\
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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\
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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
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,
x
7
,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
x
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,
x
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x
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,
x
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,
x
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,
x
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,
x
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,
x
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,
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/\
solub