|  |  D.4.20.9 intersectionValRings Procedure from librarynormaliz.lib(see  normaliz_lib).
 
Example:Usage:
intersectionValRings(intmat V, intvec grading);
Return:
The function returns a monomial ideal, to be considered as the list
of monomials generating 
 as an algebra over the coefficient
field. 
Background:
A discrete monomial valuation  on ![$R = K[X_1 ,\ldots,X_n]$](sing_960.png) is determined by
the values  of the indeterminates. This function computes the
subalgebra  for several
such valuations  ,  . It needs the matrix  as
its input. 
The function returns the ideal given by the input matrix V if one of
the options
 supp,triang,volume, orhserieshas 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). 
 See also:
 diagInvariants;
 finiteDiagInvariants;
 intersectionValRingIdeals;
 torusInvariants.|  | 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
 | 
 
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