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D.4.16.9 intersectionValRings
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- intersectionValRings(intmat V);
- Return:
- The function returns a monomial ideal, to be considered as the list
of monomials generating
 as an algebra over the coefficient
field.
- Background:
- @tex
A discrete monomial valuation $v$ on $R = K[X_1 ,\ldots,X_n]$ is determined by
the values $v(X_j)$ of the indeterminates. This function computes the
subalgebra $S = \{ f \in R : v_i ( f ) \geq 0,\ i = 1,\ldots,r\}$ for several
such valuations $v_i$, $i=1,\ldots,r$. It needs the matrix $V = (v_i(X_j))$ as
its input.
@end tex
The function returns the ideal given by the input matrix V if one of
the options supp, triang, or hvect 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.
Example:
| | LIB "normaliz.lib";
ring R=0,(x,y,z,w),dp;
intmat V0[2][4]=0,1,2,3, -1,1,2,1;
intersectionValRings(V0);
==> _[1]=w
==> _[2]=xw
==> _[3]=z
==> _[4]=xz
==> _[5]=x2z
==> _[6]=y
==> _[7]=xy
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See also:
diagInvariants;
exportNuminvs;
finiteDiagInvariants;
intersectionValRingIdeals;
showNuminvs;
torusInvariants.
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