|
D.4.24.4 toricRingFromBinomials
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- toricRingFromBinomials(ideal I);
toricRingFromBinomials(ideal I, intvec grading);
- Return:
- The ideal is generated by binomials of type (multiindex notation)
in the surrounding polynomial ring
. The binomials
represent a congruence on the monoid with residue monoid .
Let be the image of in gp()/torsion. Then is universal in the
sense that every homomorphism from to an affine monoid factors through .
If is a prime ideal, then . In general, where
is the unique minimal prime ideal of generated by binomials of type
.
The function computes and returns a newly created
polynomial ring of the same Krull dimension, whose variables are
, where is the rank of the matrix with rows .
(In general there is no canonical choice for such an embedding.)
The function returns the input ideal I if an option blocking
the computation of Hilbert bases 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).
Example:
| LIB "normaliz.lib";
ring R = 37,(u,v,w,x,y,z),dp;
ideal I = u2v-xyz, ux2-wyz, uvw-y2z;
def S = toricRingFromBinomials(I);
setring S;
I;
==> I[1]=x(3)
==> I[2]=x(1)
==> I[3]=x(2)*x(3)^3
==> I[4]=x(1)*x(2)*x(3)^2
==> I[5]=x(1)^3*x(2)
==> I[6]=x(1)^2*x(2)^3*x(3)^5
| See also:
normalToricRingFromBinomials;
toricRingFromBinomials.
|