Singular Manual: intersectionValRingIdeals

| #### D.4.24.14 intersectionValRingIdeals Procedure from library `normaliz.lib` (see normaliz_lib). Usage: intersectionValRingIdeals(intmat V); intersectionValRingIdeals(intmat V, intvec grading); Return: The function returns two ideals, both to be considered as lists of monomials. The first is the system of monomial generators of 247#247, the second the system of generators of 13#13. The function returns a list consisting of the ideal given by the blocking the computation of Hilbert bases has been activated. However, in this case some numerical invariants are computed, and some other data may be contained in files that you can read into Singular (see showNuminvs, exportNuminvs). Background: A discrete monomial valuation 331#331 on 1028#1028 is determined by the values 1052#1052 of the indeterminates. This function computes the subalgebra 1053#1053 for several such valuations 530#530, 1030#1030. It needs the matrix 1054#1054 as its input. This function simultaneously determines the 247#247-submodule 1055#1055 for integers 1056#1056. (If 1057#1057 for all 57#57, 13#13 is an ideal of 247#247.) The numbers 1058#1058 form the 1059#1059th column of the input matrix. Note: The function also gives an error message if the matrix V has the wrong number of columns. Example:
    LIB "normaliz.lib";
    ring R=0,(x,y,z,w),dp;
    intmat V[2][5]=0,1,2,3,4, -1,1,2,1,3;
    intersectionValRingIdeals(V);
    ==> [1]:
    ==>    _[1]=w
    ==>    _[2]=z
    ==>    _[3]=y
    ==>    _[4]=xw
    ==>    _[5]=xz
    ==>    _[6]=xy
    ==>    _[7]=x2z
    ==> [2]:
    ==>    _[1]=w3
    ==>    _[2]=zw
    ==>    _[3]=z2
    ==>    _[4]=yw2
    ==>    _[5]=y2w
    ==>    _[6]=y2z
    ==>    _[7]=y4
    ==>    _[8]=xz2
    ==>    _[9]=xy2z
    ==>    _[10]=xy4
See also: diagInvariants; finiteDiagInvariants; intersectionValRings; torusInvariants.

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