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D.4.24.7 definingBinomialIdeal
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- definingBinomialIdeal(ideal I);
- 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 computes the definig binomial
ideal J of S with respect to the generators and returns it, together with
J. DSee eample.
- Note:
- A mathematical remark: the toric ring depends on the list of
monomials given, and not only on the ideal they generate!
This function requires the previous setting of an NmzFilename.
The function does not delete the written files.
Example:
| | LIB "normaliz.lib";
ring R = 37,(x,y,z,w),dp;
ideal I = x4,x3y,x2y2,xy3,y4;
setNmzFilename("binomials");
def S = definingBinomialIdeal(I);
==> 1
==> 1
setring S;
J;
==> J[1]=-x(3)*x(4)+x(2)*x(5)
==> J[2]=-x(2)*x(4)+x(1)*x(5)
==> J[3]=x(2)*x(3)-x(1)*x(4)
==> J[4]=-x(2)^2+x(1)*x(3)
==> J[5]=-x(4)^2+x(3)*x(5)
==> J[6]=x(3)^2-x(2)*x(4)
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See also:
normalToricRingFromBinomials.
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