|
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
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.
|