Top
Back: diagInvariants
Forward: intersectionValRingIdeals
FastBack: normal_lib
FastForward: pointid_lib
Up: normaliz_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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 $S$ 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
See also: diagInvariants; exportNuminvs; finiteDiagInvariants; intersectionValRingIdeals; showNuminvs; torusInvariants.


Top Back: diagInvariants Forward: intersectionValRingIdeals FastBack: normal_lib FastForward: pointid_lib Up: normaliz_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.