|  |  D.4.20.10 intersectionValRingIdeals Procedure from librarynormaliz.lib(see  normaliz_lib).
 
Example:Usage:
intersectionValRingIdeals(intmat V);
intersectionValRingIdeals(intmat V, intvec grading);
 
Return:
The function returns two ideals, both to be considered as lists of
monomials. The
first is the system of monomial generators of 
 , the second
the system of generators of  . The function returns a list consisting of the ideal given by the
input matrix T if one of the options
 supp,triang, orhvecthas 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).
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. 
This function simultaneously determines the  -submodule  for integers  . (If  for all  ,  is an ideal of  .)
The numbers  form the  th column of the input matrix. 
Note:
The function also gives an error message if the matrix V has the
wrong number of columns.
 See also:
 diagInvariants;
 finiteDiagInvariants;
 intersectionValRings;
 torusInvariants.|  | LIB "normaliz.lib";
ring R=0,(x,y,z,w),dp;
intmat V[2][5]=0,1,2,3,4, -1,1,2,1,3;
intersectionValRingIdeals(V);
==> [1]:
==>    _[1]=w
==>    _[2]=z
==>    _[3]=y
==>    _[4]=xw
==>    _[5]=xz
==>    _[6]=xy
==>    _[7]=x2z
==> [2]:
==>    _[1]=w3
==>    _[2]=zw
==>    _[3]=z2
==>    _[4]=yw2
==>    _[5]=y2w
==>    _[6]=y2z
==>    _[7]=y4
==>    _[8]=xz2
==>    _[9]=xy2z
==>    _[10]=xy4
 | 
 
 |