Singular Manual: autGradAlg

| #### 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;) autgradalg.lib::autKS:2324
    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

User manual for Singular version 4.3.2, 2023, generated by texi2html.