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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
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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