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D.4.16.10 intersectionValRingIdeals
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- intersectionValRingIdeals(intmat V);
- Return:
- The function returns two ideals, both to be considered as lists of
monomials which generate an algebra over the coefficient field. The
first is the system of monomial generators of
, the second
the system of generators of
.
The function returns a list consisting of the ideal given by the
input matrix T 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 (see showNuminvs, exportNuminvs).
- 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.
This function simultaneously determines the $S$-submodule
$M = \{ f \in R : v_i(f) \geq w_i ,\ i = 1,\ldots,r\}$ for integers
$w_1,\ldots\,w_r$. (If $w_i \geq 0$ for all $i$, $M$ is an ideal of $S$.)
The numbers $w_i$ form the $(n+1)$th column of the input matrix.
@end tex
- Note:
- The function also gives an error message if the matrix V has the
wrong number of columns.
Example:
See also:
diagInvariants;
finiteDiagInvariants;
intersectionValRings;
torusInvariants.
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