next | previous | forward | backward | up | top | index | toc | home

hilbertFunct -- return the Hilbert function of a quotient by a homogeneous ideal as a list

Synopsis

Description

Let I be a homogeneous ideal in a ring R that is either a polynomial ring or a quotient of a polynomial ring, and suppose that R has the standard grading. hilbertFunct returns the Hilbert function of R/I as a list.

If R/I is Artinian, then the default is for hilbertFunct to return the entire Hilbert function (i.e., until the Hilbert function is zero) of R/I as a list. The user can override this by using the Degree option to bound the highest degree considered.

If R/I is not Artinian, then hilbertFunct returns the Hilbert function of R/I through degree 20. Again, the user can select a different upper bound for the degree by using the Degree option.

We require the standard grading on R in order to compute with the Hilbert series, which is much faster than repeatedly computing the Hilbert function.

R=ZZ/32003[a..c];
hilbertFunct ideal(a^3,b^3,c^3)
hilbertFunct ideal(a^3,a*b^2)
hilbertFunct(ideal(a^3,a*b^2),Degree=>4)
M=ideal(a^3,b^4,a*c);
Q=R/M;
hilbertFunct ideal(c^4)
hilbertFunct ideal(b*c,a*b)

See also

Ways to use hilbertFunct :