[was@modular modelsX0N]$ [was@modular modelsX0N]$ Magma V2.8-BETA   Sat Jun  9 2001 11:25:23 on modular  [Seed = 1]
Linked at:        Tue Jun 05 2001 20:16:04
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> Attach("model.m");
> CanonicalEmbeddingX0(79);
Scheme over Rational Field defined by
0
a*c - b^2 + b*f - 5/8*c*e + 9/4*c*f - 1/8*d^2 - 5/8*d*e - 5/4*d*f - 5/4*e^2 - 7/8*e*f - 3/4*f^2
a*d - b*c + b*f + 1/4*c*e - 1/2*c*f + 1/4*d^2 + 1/4*d*e + 1/2*d*f - 5/2*e^2 + 11/4*e*f - 5/2*f^2
a*e - 2*b*f - c^2 + 5/4*c*e + 3/2*c*f + 1/4*d^2 - 3/4*d*e - 3/2*d*f - 3/2*e^2 + 7/4*e*f + 1/2*f^2
a*f - b*f - c*d + 1/8*c*e + 3/4*c*f + 5/8*d^2 + 1/8*d*e - 3/4*d*f - 7/4*e^2 + 27/8*e*f - 1/4*f^2
b*d - 2*b*f - c^2 + 2*c*e + 2*c*f - 2*d*f - e^2 - 2*e*f + 3*f^2
b*e - 2*b*f - c*d + c*e + d^2 - d*f - 2*e^2 + 3*e*f
> CanonicalEmbeddingX0(79);
Scheme over Rational Field defined by
0
a*c - b^2 + b*f - 5/8*c*e + 9/4*c*f - 1/8*d^2 - 5/8*d*e - 5/4*d*f - 5/4*e^2 - 7/8*e*f - 3/4*f^2
a*d - b*c + b*f + 1/4*c*e - 1/2*c*f + 1/4*d^2 + 1/4*d*e + 1/2*d*f - 5/2*e^2 + 11/4*e*f - 5/2*f^2
a*e - 2*b*f - c^2 + 5/4*c*e + 3/2*c*f + 1/4*d^2 - 3/4*d*e - 3/2*d*f - 3/2*e^2 + 7/4*e*f + 1/2*f^2
a*f - b*f - c*d + 1/8*c*e + 3/4*c*f + 5/8*d^2 + 1/8*d*e - 3/4*d*f - 7/4*e^2 + 27/8*e*f - 1/4*f^2
b*d - 2*b*f - c^2 + 2*c*e + 2*c*f - 2*d*f - e^2 - 2*e*f + 3*f^2
b*e - 2*b*f - c*d + c*e + d^2 - d*f - 2*e^2 + 3*e*f
> C := $1;
> C;
Scheme over Rational Field defined by
0
a*c - b^2 + b*f - 5/8*c*e + 9/4*c*f - 1/8*d^2 - 5/8*d*e - 5/4*d*f - 5/4*e^2 - 7/8*e*f - 3/4*f^2
a*d - b*c + b*f + 1/4*c*e - 1/2*c*f + 1/4*d^2 + 1/4*d*e + 1/2*d*f - 5/2*e^2 + 11/4*e*f - 5/2*f^2
a*e - 2*b*f - c^2 + 5/4*c*e + 3/2*c*f + 1/4*d^2 - 3/4*d*e - 3/2*d*f - 3/2*e^2 + 7/4*e*f + 1/2*f^2
a*f - b*f - c*d + 1/8*c*e + 3/4*c*f + 5/8*d^2 + 1/8*d*e - 3/4*d*f - 7/4*e^2 + 27/8*e*f - 1/4*f^2
b*d - 2*b*f - c^2 + 2*c*e + 2*c*f - 2*d*f - e^2 - 2*e*f + 3*f^2
b*e - 2*b*f - c*d + c*e + d^2 - d*f - 2*e^2 + 3*e*f
> Dimension(C) eq 1 and IsIrreducible(C)
> ;
true
> Genus(C);

>> Genus(C);
        ^
Runtime error in 'Genus': Bad argument types
Argument types given: Sch
> BaseExtend(C,AlgebraicClosure());
Scheme over Algebraically closed field with no variables defined by
0
$.1*$.3 - $.2^2 + $.2*$.6 - 5/8*$.3*$.5 + 9/4*$.3*$.6 - 1/8*$.4^2 - 5/8*$.4*$.5 - 5/4*$.4*$.6 - 5/4*$.5^2 - 7/8*$.5*$.6 - 3/4*$.6^2
$.1*$.4 - $.2*$.3 + $.2*$.6 + 1/4*$.3*$.5 - 1/2*$.3*$.6 + 1/4*$.4^2 + 1/4*$.4*$.5 + 1/2*$.4*$.6 - 5/2*$.5^2 + 11/4*$.5*$.6 - 5/2*$.6^2
$.1*$.5 - 2*$.2*$.6 - $.3^2 + 5/4*$.3*$.5 + 3/2*$.3*$.6 + 1/4*$.4^2 - 3/4*$.4*$.5 - 3/2*$.4*$.6 - 3/2*$.5^2 + 7/4*$.5*$.6 + 1/2*$.6^2
$.1*$.6 - $.2*$.6 - $.3*$.4 + 1/8*$.3*$.5 + 3/4*$.3*$.6 + 5/8*$.4^2 + 1/8*$.4*$.5 - 3/4*$.4*$.6 - 7/4*$.5^2 + 27/8*$.5*$.6 - 1/4*$.6^2
$.2*$.4 - 2*$.2*$.6 - $.3^2 + 2*$.3*$.5 + 2*$.3*$.6 - 2*$.4*$.6 - $.5^2 - 2*$.5*$.6 + 3*$.6^2
$.2*$.5 - 2*$.2*$.6 - $.3*$.4 + $.3*$.5 + $.4^2 - $.4*$.6 - 2*$.5^2 + 3*$.5*$.6
> B := $1;
> IsIrreducible(B);


This is a particularly molten bug in Magma
Time to this point: 3.58
Segmentation fault
> quit;


This is a particularly molten bug in Magma
Time to this point: 3.59
Segmentation fault
Magma: Fatal Error: error_internal(): had enough (-5.62868e-08)
[was@modular modelsX0N]$ quit;
bash: quit: command not found
[was@modular modelsX0N]$ magma
Magma V2.7-1      Sat Jun  9 2001 15:28:29 on modular  [Seed = 336424956]
Type ? for help.  Type <Ctrl>-D to quit.

Can't open package spec file /home/was/modsym/spec for reading (No such file or 
directory)

Can't open startup file "/home/was/modsym/init-magma.m"
> SetLineEditor(false);
SetLineEditor(false);> SetLineEditor(false);
> attach("model.m");

>> Attach("model.m");
   ^
User error: Identifier 'attach' has not been declared or assigned
> > Attach("model.m");

>> > Attach("model.m");
   ^
User error: bad syntax
> > Attach("model.m");

>> > 
   ^
User error: bad syntax
> Attach("model.m");
> C := CanonicalEmbeddingX0(79);

CanonicalEmbeddingX0(
    N: 79
)
In file "/home/was/papers/modelsX0N/model.m", line 38, column 48:
>>          if Dimension(C) eq 1 and IsIrreducible(C) then 
                                                  ^
Runtime error in 'IsIrreducible': Scheme must be a hypersurface
> quit;

Total time: 1.649 seconds
[was@modular modelsX0N]$ exit
exit

Process magma finished
[was@modular modelsX0N]$ [was@modular modelsX0N]$ Magma V2.8-BETA   Sat Jun  9 2001 11:30:08 on modular  [Seed = 1]
Linked at:        Tue Jun 05 2001 20:16:04
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> S := CS(MF(79));
> Basis(S);
[
q - q^7 + O(q^8),
q^2 + 2*q^6 + q^7 + O(q^8),
q^3 + q^6 + O(q^8),
q^4 + 2*q^6 - q^7 + O(q^8),
q^5 + 2*q^6 + q^7 + O(q^8),
4*q^6 + q^7 + O(q^8)
]
> Relations;
Intrinsic 'Relations'

Signatures:

(<GrpFP> G) -> SeqEnum
(<SgpFP> G) -> SeqEnum
(<AlgFP> G) -> SeqEnum
(<GrpAb> G) -> SeqEnum
(<GrpAut> G) -> SeqEnum

The defining relations for G

(<MonRWS> M) -> SeqEnum

The defining relations for M

(<RngOrd> O) -> ModMatRngElt

The relations used in the last class group computation in O

(<SeqEnum> L, <Rng> R, <RngIntElt> m) -> ModTupRng

The module of R-linear relations between the elements of L (together with some simplifications)

(<RngInvarON> R) -> SeqEnum
[
UseGroebner
]

Algebraic relations for the invariant ring R

(<SeqEnum> L, <Rng> R) -> ModTupRng

The module of R-linear relations between the elements of L 

(<ModFrm> M, <RngIntElt> d, <RngIntElt> prec) -> SeqEnum

All relations of degree d satisfied by the q-expansions of Basis(M), computed to precision prec.


> Relations(S,2,30);
[
a*c - b^2 + b*f - 5*c*d + 4*c*f + 3*d^2 - 2*d*f - 10*e^2 + 17*e*f - 8*f^2,
a*d - b*c - 6*c*d + c*e + 5*c*f + 4*d^2 + d*e - 4*d*f - 13*e^2 + 21*e*f - 9*f^2,
a*e - b*f - c^2 - 6*c*d + 2*c*e + 5*c*f + 4*d^2 - 3*d*f - 12*e^2 + 19*e*f - 8*f^2,
a*f - b*f - 8*c*d + c*e + 6*c*f + 5*d^2 + d*e - 4*d*f - 14*e^2 + 23*e*f - 10*f^2,
b*d - b*f - c^2 + 2*c*e - d*f - e^2 + f^2,
b*e - b*f - c*d + c*e + d^2 - d*f - 2*e^2 + 2*e*f
]
> Relations(S,3,30);
[
a^2*c - a*b^2 - 5*b*c^2 + 11*c^3 + 4*c^2*d + 38*c*d^2 - 762*c*d*e + 128*c*d*f + 6896*c*e^2 - 11637*c*e*f + 5312*c*f^2 + 621*d^3 - 3934*d^2*e + 2618*d^2*f + 7822*d*e^2 - 6022*d*e*f - 299*d*f^2 - 9071*e^3 + 8405*e^2*f + 2704*e*f^2 - 2829*f^3,
a^2*d - b^3 - 6*b*c^2 + 22*c^2*d + 55*c*d^2 - 795*c*d*e + 45*c*d*f + 8100*c*e^2 - 13745*c*e*f + 6315*c*f^2 + 705*d^3 - 4663*d^2*e + 3146*d^2*f + 9150*d*e^2 - 7023*d*e*f - 384*d*f^2 - 10376*e^3 + 9218*e^2*f + 3714*e*f^2 - 3478*f^3,
a^2*e - b^2*c - 6*b*c^2 - 2*c^3 + 9*c^2*d + 72*c*d^2 - 567*c*d*e - 61*c*d*f + 6917*c*e^2 - 11834*c*e*f + 5478*c*f^2 + 591*d^3 - 4074*d^2*e + 2761*d^2*f + 7862*d*e^2 - 6012*d*e*f - 344*d*f^2 - 8685*e^3 + 7387*e^2*f + 3622*e*f^2 - 3114*f^3,
a^2*f - 8*b*c^2 - 2*c^3 + 5*c^2*d + 79*c*d^2 - 515*c*d*e - 102*c*d*f + 6898*c*e^2 - 11846*c*e*f + 5501*c*f^2 + 589*d^3 - 4106*d^2*e + 2782*d^2*f + 7863*d*e^2 - 5998*d*e*f - 351*d*f^2 - 8596*e^3 + 7178*e^2*f + 3793*e*f^2 - 3165*f^3,
a*b*c - b^3 - 5*c^3 + 11*c^2*d + 4*c*d^2 - 100*c*d*e - 9*c*d*f + 1187*c*e^2 - 2023*c*e*f + 935*c*f^2 + 97*d^3 - 680*d^2*e + 472*d^2*f + 1307*d*e^2 - 994*d*e*f - 71*d*f^2 - 1442*e^3 + 1187*e^2*f + 663*e*f^2 - 539*f^3,
a*b*d - b^2*c - 6*c^3 + 5*c^2*d + 11*c*d^2 + 63*c*d*e - 68*c*d*f + 19*c*e^2 - 83*c*e*f + 66*c*f^2 - 12*d^3 - 47*d^2*e + 55*d^2*f + 16*d*e^2 - 19*d*f^2 + 131*e^3 - 364*e^2*f + 341*e*f^2 - 108*f^3,
a*b*e - b*c^2 - 6*c^3 - 2*c^2*d + 14*c*d^2 + 220*c*d*e - 116*c*d*f - 1154*c*e^2 + 1871*c*e*f - 814*c*f^2 - 117*d^3 + 592*d^2*e - 373*d^2*f - 1282*d*e^2 + 1000*d*e*f + 36*d*f^2 + 1686*e^3 - 1859*e^2*f - 37*e*f^2 + 341*f^3,
a*b*f - 8*c^3 - 2*c^2*d + 5*c*d^2 + 350*c*d*e - 137*c*d*f - 2304*c*e^2 + 3808*c*e*f - 1698*c*f^2 - 219*d^3 + 1246*d^2*e - 810*d^2*f - 2591*d*e^2 + 2014*d*e*f + 82*d*f^2 + 3202*e^3 - 3266*e^2*f - 485*e*f^2 + 812*f^3,
a*c^2 - b^2*c - 5*c^2*d + 11*c*d^2 - 67*c*d*e - 20*c*d*f + 1139*c*e^2 - 1971*c*e*f + 918*c*f^2 + 101*d^3 - 696*d^2*e + 466*d^2*f + 1299*d*e^2 - 975*d*e*f - 69*d*f^2 - 1399*e^3 + 1126*e^2*f + 681*e*f^2 - 539*f^3,
a*c*d - b*c^2 - 6*c^2*d + 5*c*d^2 + 48*c*d*e - 35*c*d*f - 17*c*e^2 - 10*c*e*f + 21*c*f^2 - d^3 - 30*d^2*e + 20*d^2*f - 4*d*e^2 + 21*d*e*f - 12*d*f^2 + 83*e^3 - 199*e^2*f + 165*e*f^2 - 49*f^3,
a*c*e - c^3 - 6*c^2*d - 2*c*d^2 + 153*c*d*e - 42*c*d*f - 1168*c*e^2 + 1950*c*e*f - 879*c*f^2 - 103*d^3 + 641*d^2*e - 429*d^2*f - 1306*d*e^2 + 1013*d*e*f + 47*d*f^2 + 1551*e^3 - 1491*e^2*f - 378*e*f^2 + 449*f^3,
a*c*f - 8*c^2*d - 2*c*d^2 + 155*c*d*e - 42*c*d*f - 1172*c*e^2 + 1955*c*e*f - 881*c*f^2 - 102*d^3 + 641*d^2*e - 431*d^2*f - 1308*d*e^2 + 1016*d*e*f + 47*d*f^2 + 1552*e^3 - 1490*e^2*f - 381*e*f^2 + 450*f^3,
a*d^2 - c^3 - 12*c*d^2 + 114*c*d*e - 10*c*d*f - 1152*c*e^2 + 1956*c*e*f - 895*c*f^2 - 99*d^3 + 667*d^2*e - 448*d^2*f - 1314*d*e^2 + 1014*d*e*f + 48*d*f^2 + 1481*e^3 - 1326*e^2*f - 513*e*f^2 + 489*f^3,
a*d*e - c^2*d - 6*c*d^2 + 100*c*d*e - 9*c*d*f - 1153*c*e^2 + 1969*c*e*f - 901*c*f^2 - 102*d^3 + 675*d^2*e - 449*d^2*f - 1301*d*e^2 + 988*d*e*f + 59*d*f^2 + 1455*e^3 - 1271*e^2*f - 552*e*f^2 + 498*f^3,
a*d*f - 8*c*d^2 + 99*c*d*e - 8*c*d*f - 1153*c*e^2 + 1969*c*e*f - 901*c*f^2 - 101*d^3 + 676*d^2*e - 450*d^2*f - 1303*d*e^2 + 992*d*e*f + 57*d*f^2 + 1455*e^3 - 1271*e^2*f - 552*e*f^2 + 498*f^3,
a*e^2 - c*d^2 + 93*c*d*e - 14*c*d*f - 1153*c*e^2 + 1974*c*e*f - 901*c*f^2 - 105*d^3 + 679*d^2*e - 447*d^2*f - 1291*d*e^2 + 969*d*e*f + 67*d*f^2 + 1444*e^3 - 1252*e^2*f - 561*e*f^2 + 498*f^3,
a*e*f + 98*c*d*e - 20*c*d*f - 1153*c*e^2 + 1969*c*e*f - 896*c*f^2 - 106*d^3 + 675*d^2*e - 442*d^2*f - 1289*d*e^2 + 969*d*e*f + 65*d*f^2 + 1455*e^3 - 1282*e^2*f - 533*e*f^2 + 489*f^3,
a*f^2 + 106*c*d*e - 27*c*d*f - 1154*c*e^2 + 1963*c*e*f - 890*c*f^2 - 106*d^3 + 670*d^2*e - 438*d^2*f - 1290*d*e^2 + 974*d*e*f + 62*d*f^2 + 1469*e^3 - 1317*e^2*f - 502*e*f^2 + 479*f^3,
b^2*d - b*c^2 - 6*c^2*d + 10*c*d^2 + 146*c*d*e - 53*c*d*f - 1170*c*e^2 + 1959*c*e*f - 880*c*f^2 - 110*d^3 + 645*d^2*e - 424*d^2*f - 1283*d*e^2 + 973*d*e*f + 63*d*f^2 + 1538*e^3 - 1470*e^2*f - 387*e*f^2 + 449*f^3,
b^2*e - c^3 - 6*c^2*d - 2*c*d^2 + 264*c*d*e - 62*c*d*f - 2322*c*e^2 + 3909*c*e*f - 1775*c*f^2 - 209*d^3 + 1308*d^2*e - 871*d^2*f - 2596*d*e^2 + 1988*d*e*f + 112*d*f^2 + 3030*e^3 - 2813*e^2*f - 893*e*f^2 + 938*f^3,
b^2*f - 8*c^2*d - 2*c*d^2 + 261*c*d*e - 56*c*d*f - 2326*c*e^2 + 3917*c*e*f - 1781*c*f^2 - 208*d^3 + 1311*d^2*e - 877*d^2*f - 2598*d*e^2 + 1989*d*e*f + 115*d*f^2 + 3021*e^3 - 2783*e^2*f - 923*e*f^2 + 947*f^3,
b*c*d - c^3 - 6*c*d^2 + 113*c*d*e - 15*c*d*f - 1152*c*e^2 + 1956*c*e*f - 895*c*f^2 - 103*d^3 + 666*d^2*e - 444*d^2*f - 1301*d*e^2 + 993*d*e*f + 57*d*f^2 + 1481*e^3 - 1326*e^2*f - 513*e*f^2 + 489*f^3,
b*c*e - c^2*d - 6*c*d^2 + 106*c*d*e - 9*c*d*f - 1154*c*e^2 + 1964*c*e*f - 901*c*f^2 - 102*d^3 + 671*d^2*e - 449*d^2*f - 1302*d*e^2 + 992*d*e*f + 59*d*f^2 + 1468*e^3 - 1292*e^2*f - 543*e*f^2 + 498*f^3,
b*c*f - 8*c*d^2 + 99*c*d*e - 2*c*d*f - 1153*c*e^2 + 1968*c*e*f - 906*c*f^2 - 101*d^3 + 676*d^2*e - 454*d^2*f - 1303*d*e^2 + 991*d*e*f + 61*d*f^2 + 1455*e^3 - 1258*e^2*f - 573*e*f^2 + 507*f^3,
b*d^2 - c^2*d + 100*c*d*e - 14*c*d*f - 1153*c*e^2 + 1969*c*e*f - 901*c*f^2 - 106*d^3 + 675*d^2*e - 447*d^2*f - 1290*d*e^2 + 969*d*e*f + 68*d*f^2 + 1455*e^3 - 1271*e^2*f - 552*e*f^2 + 498*f^3,
b*d*e - c*d^2 + 99*c*d*e - 14*c*d*f - 1153*c*e^2 + 1969*c*e*f - 901*c*f^2 - 105*d^3 + 675*d^2*e - 447*d^2*f - 1291*d*e^2 + 971*d*e*f + 67*d*f^2 + 1455*e^3 - 1271*e^2*f - 552*e*f^2 + 498*f^3,
b*d*f + 98*c*d*e - 14*c*d*f - 1153*c*e^2 + 1969*c*e*f - 901*c*f^2 - 106*d^3 + 675*d^2*e - 446*d^2*f - 1289*d*e^2 + 969*d*e*f + 67*d*f^2 + 1455*e^3 - 1271*e^2*f - 552*e*f^2 + 498*f^3,
b*e^2 + 105*c*d*e - 20*c*d*f - 1153*c*e^2 + 1963*c*e*f - 896*c*f^2 - 106*d^3 + 671*d^2*e - 442*d^2*f - 1290*d*e^2 + 972*d*e*f + 65*d*f^2 + 1467*e^3 - 1303*e^2*f - 523*e*f^2 + 489*f^3,
b*e*f + 106*c*d*e - 20*c*d*f - 1154*c*e^2 + 1963*c*e*f - 896*c*f^2 - 106*d^3 + 670*d^2*e - 442*d^2*f - 1290*d*e^2 + 973*d*e*f + 65*d*f^2 + 1469*e^3 - 1305*e^2*f - 523*e*f^2 + 489*f^3,
b*f^2 + 106*c*d*e - 19*c*d*f - 1154*c*e^2 + 1962*c*e*f - 896*c*f^2 - 106*d^3 + 670*d^2*e - 443*d^2*f - 1290*d*e^2 + 973*d*e*f + 66*d*f^2 + 1469*e^3 - 1303*e^2*f - 525*e*f^2 + 489*f^3,
c^2*e - c*d^2 - 7*c*d*e + 6*c*d*f - c*e^2 + 6*c*e*f - 5*c*f^2 + d^3 + 5*d^2*e - 5*d^2*f - d*e^2 - d*e*f + 2*d*f^2 - 13*e^3 + 34*e^2*f - 30*e*f^2 + 9*f^3,
c^2*f - 8*c*d*e + 5*c*d*f + c*e^2 + 5*c*e*f - 5*c*f^2 + 5*d^2*e - 3*d^2*f + d*e^2 - 4*d*e*f + 2*d*f^2 - 14*e^3 + 33*e^2*f - 27*e*f^2 + 8*f^3
]
> #$1;
32
> R2 := Relations(S,2,100);
> R3 := Relations(S,3,100);
> #R2;
6
> #R3;
31
> R3 := Relations(S,3,200);
> #R3;
31
> R<a,b,c,d,e,f> := Parent(R2[1]);
> R;
Polynomial ring of rank 6 over Integer Ring
Lexicographical Order
Variables: a, b, c, d, e, f
> MonomialCoefficient;
Intrinsic 'MonomialCoefficient'

Signatures:

(<RngUPolElt> f, <RngUPolElt> m) -> RngElt
(<RngUPolResElt> f, <RngUPolResElt> m) -> RngElt
(<RngMPolEltOld> f, <RngMPolEltOld> m) -> RngElt
(<CNCMPolGElt> f, <CNCMPolGElt> m) -> RngElt

The coefficient of the monomial m in f

(<AlgFPElt> a, <SgpFPElt> t) -> RngElt
(<AlgFPElt> a, <GrpFPElt> t) -> RngElt

The coefficient of t in a


> R2 := Relations(S,2,100);
> R2;
[
a*c - b^2 + b*f - 5*c*d + 4*c*f + 3*d^2 - 2*d*f - 10*e^2 + 17*e*f - 8*f^2,
a*d - b*c - 6*c*d + c*e + 5*c*f + 4*d^2 + d*e - 4*d*f - 13*e^2 + 21*e*f - 9*f^2,
a*e - b*f - c^2 - 6*c*d + 2*c*e + 5*c*f + 4*d^2 - 3*d*f - 12*e^2 + 19*e*f - 8*f^2,
a*f - b*f - 8*c*d + c*e + 6*c*f + 5*d^2 + d*e - 4*d*f - 14*e^2 + 23*e*f - 10*f^2,
b*d - b*f - c^2 + 2*c*e - d*f - e^2 + f^2,
b*e - b*f - c*d + c*e + d^2 - d*f - 2*e^2 + 2*e*f
]
> R2, v2 := Relations(S,2,100);
> v2;
[
(0 0 1 0 0 0 -1 0 0 0 1 0 -5 0 4 3 0 -2 -10 17 -8),
(0 0 0 1 0 0 0 -1 0 0 0 0 -6 1 5 4 1 -4 -13 21 -9),
(0 0 0 0 1 0 0 0 0 0 -1 -1 -6 2 5 4 0 -3 -12 19 -8),
(0 0 0 0 0 1 0 0 0 0 -1 0 -8 1 6 5 1 -4 -14 23 -10),
( 0  0  0  0  0  0  0  0  1  0 -1 -1  0  2  0  0  0 -1 -1  0  1),
( 0  0  0  0  0  0  0  0  0  1 -1  0 -1  1  0  1  0 -1 -2  2  0)
]
> ;
> R3, v3 := Relations(S,2,100);
> #v3;
6
> R3, v3 := Relations(S,3,100);
> #v3;
31
> v3;
[
(0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 0 0 0 6 11 4 0 0 38 -126 14 -28 135 -64 -15 86 -40 82 -184 97 -257 587 -446 105),
(0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -6 0 0 0 0 0 0 0 0 7 0 22 0 0 55 -53 -88 22 -11 43 -37 27 45 120 -212 78 -93 97 39 -55),
(0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -6 0 0 0 0 0 0 0 0 6 -2 9 0 0 72 69 -175 -7 -62 102 -45 -54 103 122 -174 52 129 -431 472 -180),
(0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -8 0 0 0 0 0 0 0 0 6 -2 5 0 0 79 121 -216 -26 -74 125 -47 -86 124 123 -160 45 218 -640 643 -231),
(0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -5 11 0 0 4 6 -28 33 -61 39 -9 -10 29 17 -21 -5 27 -116 138 -50),
(0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -6 5 0 0 11 63 -68 19 -83 66 -12 -47 55 16 0 -19 131 -364 341 -108),
(0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 -6 -2 0 0 14 114 -97 0 -91 82 -11 -78 70 8 27 -30 217 -556 488 -148),
(0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -8 -2 0 0 5 138 -99 4 -116 94 -7 -94 76 -11 68 -50 264 -660 565 -166),
(0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -5 0 0 11 39 -39 -15 -9 22 -5 -26 23 9 -2 -3 70 -177 156 -50),
(0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -6 0 0 5 48 -35 -17 -10 21 -1 -30 20 -4 21 -12 83 -199 165 -49),
(0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -6 0 0 -2 47 -23 -14 -12 17 3 -29 14 -16 40 -19 82 -188 147 -40),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -8 0 0 -2 49 -23 -18 -7 15 4 -29 12 -18 43 -19 83 -187 144 -39),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 -12 8 9 2 -6 1 7 -3 -5 -24 41 -18 12 -23 12 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 -6 -6 10 1 7 -5 4 5 -6 -11 15 -7 -14 32 -27 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -8 -7 11 1 7 -5 5 6 -7 -13 19 -9 -14 32 -27 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -13 5 1 12 -5 1 9 -4 -1 -4 1 -25 51 -36 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -8 -1 1 7 0 0 5 1 1 -4 -1 -14 21 -8 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -8 0 1 6 0 0 5 0 1 -4 0 -14 23 -10),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 -1 0 -6 0 0 10 40 -34 -16 -3 16 -4 -25 19 7 0 -3 69 -167 138 -40),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -2 -1 -6 0 0 -2 52 -24 -14 -15 17 3 -32 15 -16 42 -20 92 -207 157 -40),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -2 0 -8 0 0 -2 49 -18 -18 -7 11 4 -29 9 -18 43 -17 83 -177 127 -31),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 -6 7 4 2 -6 1 3 -4 -1 -11 20 -9 12 -23 12 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 -1 0 0 -6 0 10 0 2 -5 4 1 -6 -12 19 -7 -1 11 -18 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 -8 -7 17 1 6 -10 5 6 -11 -13 18 -5 -14 45 -48 18),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1 0 0 0 -6 5 1 7 -5 0 5 -4 0 -4 2 -14 32 -27 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 -1 -7 5 1 7 -5 1 5 -4 -1 -2 1 -14 32 -27 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 -8 5 1 7 -5 0 5 -3 1 -4 1 -14 32 -27 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 -1 -1 1 1 0 0 1 1 0 -1 -1 -2 0 2 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 -1 0 -2 2 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -7 6 -1 6 -5 1 5 -5 -1 -1 2 -13 34 -30 9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -8 5 1 5 -5 0 5 -3 1 -4 2 -14 33 -27 8)
]
> monoms := MonomialsOfDegree(R,3);
> monoms;
{@
a^3,
a^2*b,
a^2*c,
a^2*d,
a^2*e,
a^2*f,
a*b^2,
a*b*c,
a*b*d,
a*b*e,
a*b*f,
a*c^2,
a*c*d,
a*c*e,
a*c*f,
a*d^2,
a*d*e,
a*d*f,
a*e^2,
a*e*f,
a*f^2,
b^3,
b^2*c,
b^2*d,
b^2*e,
b^2*f,
b*c^2,
b*c*d,
b*c*e,
b*c*f,
b*d^2,
b*d*e,
b*d*f,
b*e^2,
b*e*f,
b*f^2,
c^3,
c^2*d,
c^2*e,
c^2*f,
c*d^2,
c*d*e,
c*d*f,
c*e^2,
c*e*f,
c*f^2,
d^3,
d^2*e,
d^2*f,
d*e^2,
d*e*f,
d*f^2,
e^3,
e^2*f,
e*f^2,
f^3
@}
> monoms[2];
a^2*b
> MonomialCoefficient(a*R2[1],monoms[2]);

>> MonomialCoefficient(a*R2[1],monoms[2]);
                        ^
Runtime error in '*': Arguments are not compatible
Argument types given: RngMPolElt, RngMPolElt
> R<a,b,c,d,e,f> := Parent(R2[1]);
> > MonomialCoefficient(a*R2[1],monoms[2]);

>>   MonomialCoefficient(a*R2[1],monoms[2]);
                        ^
Runtime error in 'MonomialCoefficient': Arguments are not compatible
> R<a,b,c,d,e,f> := Parent(R2[1]);
> a*R2[1];
a^2*c - a*b^2 + a*b*f - 5*a*c*d + 4*a*c*f + 3*a*d^2 - 2*a*d*f - 10*a*e^2 + 17*a*e*f - 8*a*f^2
> monoms := MonomialsOfDegree(R,3);
> > MonomialCoefficient(a*R2[1],monoms[2]);
0
> w := [MonomialCoefficient(a*R2[1],m) : m in monoms];
> w;
[ 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -5, 0, 4, 3, 0, -2, -10, 17, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
> W := [[MonomialCoefficient(R.j*R2[i],m) : m in monoms] : i in [1..#R2], j in [1..6]];
> V := Parent(v3[1]);
> W := [V|w : w in W];
> W;
[
(0 0 1 0 0 0 -1 0 0 0 1 0 -5 0 4 3 0 -2 -10 17 -8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 1 0 0 0 -1 0 0 0 0 -6 1 5 4 1 -4 -13 21 -9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 1 0 0 0 0 0 -1 -1 -6 2 5 4 0 -3 -12 19 -8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 1 0 0 0 0 -1 0 -8 1 6 5 1 -4 -14 23 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 1 0 -1 -1 0 2 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 1 -1 0 -1 1 0 1 0 -1 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 -5 0 4 3 0 -2 -10 17 -8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -6 1 5 4 1 -4 -13 21 -9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -6 2 5 4 0 -3 -12 19 -8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -8 1 6 5 1 -4 -14 23 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 2 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 -1 1 0 1 0 -1 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -5 0 4 3 0 -2 -10 17 -8 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -6 1 5 4 1 -4 -13 21 -9 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 -6 2 5 4 0 -3 -12 19 -8 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -8 1 6 5 1 -4 -14 23 -10 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 -1 0 2 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 -1 1 0 1 0 -1 -2 2 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -5 0 4 0 0 0 3 0 -2 -10 17 -8 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -6 1 5 0 0 0 4 1 -4 -13 21 -9 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 -6 2 5 0 0 0 4 0 -3 -12 19 -8 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -8 1 6 0 0 0 5 1 -4 -14 23 -10 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 -1 0 0 0 2 0 0 0 0 0 0 -1 -1 0 1 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 -1 1 0 0 0 0 1 0 -1 -2 2 0 0 0 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -5 0 0 4 0 0 3 0 0 -2 0 -10 17 -8 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -6 0 1 5 0 0 4 0 1 -4 0 -13 21 -9 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 -6 0 2 5 0 0 4 0 0 -3 0 -12 19 -8 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -8 0 1 6 0 0 5 0 1 -4 0 -14 23 -10 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 -1 0 0 0 0 2 0 0 0 0 0 0 -1 0 -1 0 1 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 -1 0 -2 2 0 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -5 0 0 4 0 0 3 0 0 -2 0 -10 17 -8),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -6 0 1 5 0 0 4 0 1 -4 0 -13 21 -9),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 -6 0 2 5 0 0 4 0 0 -3 0 -12 19 -8),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -8 0 1 6 0 0 5 0 1 -4 0 -14 23 -10),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 -1 0 0 0 0 2 0 0 0 0 0 0 -1 0 -1 0 1),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 -1 0 -2 2 0)
]
> #W;
36
> #v3;
31
> vec := sub<V | v3>;
> vecW := sub<V | W>;
> vec subset vecW;
true
> vecW subset vec;
true
> quit;

Total time: 5.450 seconds
[was@modular modelsX0N]$