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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
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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