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D.4.19.9 intersectionValRings

Procedure from library normaliz.lib (see normaliz_lib).

Usage:
intersectionValRings(intmat V, intvec grading);

Return:
The function returns a monomial ideal, to be considered as the list of monomials generating $S$ as an algebra over the coefficient field.

Background:
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.


The function returns the ideal given by the input matrix V if one of the options supp, triang, volume, or hseries 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).

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]=z
==> _[3]=y
==> _[4]=xw
==> _[5]=xz
==> _[6]=xy
==> _[7]=x2z
See also: diagInvariants; finiteDiagInvariants; intersectionValRingIdeals; torusInvariants.