Singular

D.4.16.9 intersectionValRings

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.

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