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D.4.24.2 normalToricRing
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- normalToricRing(ideal I);
normalToricRing(ideal I, intvec grading);
- Return:
- The toric ring S is the subalgebra of the basering generated by the
leading monomials of the elements of I (considered as a list of
polynomials). The function computes the
normalisation T of S and returns an ideal listing the algebra
generators of T over the coefficient field.
The function returns the input ideal I if one of the options
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).
- Note:
- A mathematical remark: the toric ring depends on the list of
monomials given, and not only on the ideal they generate!
Example:
| | LIB "normaliz.lib";
ring R = 37,(x,y,t),dp;
ideal I = x3,x2y,y3;
normalToricRing(I);
==> _[1]=y3
==> _[2]=xy2
==> _[3]=x2y
==> _[4]=x3
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See also:
ehrhartRing;
intclMonIdeal;
intclToricRing;
normalToricRingFromBinomials;
toricRingFromBinomials.
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