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D.15.2.2 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