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D.15.1.2 autGradAlg
Procedure from library autgradalg.lib (see autgradalg_lib).
- Usage:
- autGradAlg(I, TOR); I is an ideal, TOR is an optional list of integers representing the torsion part of the grading group.
- Assume:
- minimally presented, degrees of the generators of I
are the minimal degrees, basering multigraded pointedly, I_w = 0
for all w = deg(var(i))
- Return:
- a ring. Also exports an ideal Jexported and a list stabExported.
Example:
| | LIB "autgradalg.lib";
intmat Q[1][3] =
1,1,1;
ring R = 0,T(1..3), dp;
setBaseMultigrading(Q);
ideal I = 0; //T(1)*T(2) + T(3)*T(4);
def RR = autGradAlg(I);
==> // coefficients: QQ
==> // number of vars : 12
==> // block 1 : ordering dp
==> // : names T(1) T(2) T(3) Y(1) Y(2) Y(3) Y(4) Y(5) Y(\
6) Y(7) Y(8) Y(9)
==> // block 2 : ordering C
==> // ** redefining adMons ( list adMons;)
setring RR;
"resulting ideal:";
==> resulting ideal:
Jexported;
==> Jexported[1]=-Y(3)*Y(5)*Y(7)*Z+Y(2)*Y(6)*Y(7)*Z+Y(3)*Y(4)*Y(8)*Z-Y(1)*Y(6\
)*Y(8)*Z-Y(2)*Y(4)*Y(9)*Z+Y(1)*Y(5)*Y(9)*Z-1
"dimension:";
==> dimension:
dim(std(Jexported));
==> 9
"as a detailed list:";
==> as a detailed list:
stabExported;
==> [1]:
==> [1]:
==> _[1,1]=Y(1)
==> _[1,2]=Y(2)
==> _[1,3]=Y(3)
==> _[2,1]=Y(4)
==> _[2,2]=Y(5)
==> _[2,3]=Y(6)
==> _[3,1]=Y(7)
==> _[3,2]=Y(8)
==> _[3,3]=Y(9)
==> [2]:
==> 1
==> [3]:
==> _[1]=-Y(3)*Y(5)*Y(7)*Z+Y(2)*Y(6)*Y(7)*Z+Y(3)*Y(4)*Y(8)*Z-Y(1)*Y(6)*\
Y(8)*Z-Y(2)*Y(4)*Y(9)*Z+Y(1)*Y(5)*Y(9)*Z-1
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