Singular Manual: intersectionValRingIdeals

| #### D.4.25.14 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 249#249, 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 333#333 on 1030#1030 is determined by the values 1054#1054 of the indeterminates. This function computes the subalgebra 1055#1055 for several such valuations 532#532, 1032#1032. It needs the matrix 1056#1056 as its input. This function simultaneously determines the 249#249-submodule 1057#1057 for integers 1058#1058. (If 1059#1059 for all 57#57, 13#13 is an ideal of 249#249.) The numbers 1060#1060 form the 1061#1061th 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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