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

degree(ProjectiveHilbertPolynomial)

Synopsis

Description

This degree is obtained from the Hilbert polynomial f as follows: if f = d z^e/e! + lower terms in z, then d is returned. This is the lead coefficient of the highestP^e in the ProjectiveHilbertPolynomial display.
R = QQ[a..d];
I = ideal(a^3, b^2, a*b*c);
F = hilbertPolynomial I
degree F
The degree of this polynomial may be recovered using dim:
dim F
The dimension as a projective variety is also one less that the Krull dimension of R/I
(dim I - 1, degree I)

See also