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D.4.15.6 valRing

Procedure from library normaliz.lib (see normaliz_lib).

Usage:
valRing(intmat V);

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, 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).

Note:
It is of course possible that $S=K$. At present, Normaliz cannot deal with the zero cone and will issue the (wrong) error message that the cone is not pointed. 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 V0[2][4]=0,1,2,3, -1,1,2,1;
valRing(V0);
==> _[1]=y
==> _[2]=xy
==> _[3]=w
==> _[4]=xw
==> _[5]=z
==> _[6]=xz
==> _[7]=x2z
See also: torusInvariants; valRingIdeal.


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