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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.
i1 : R = QQ[a..d];
i2 : I = ideal(a^3, b^2, a*b*c);

o2 : Ideal of R
i3 : F = hilbertPolynomial I

o3 = - 2*P  + 4*P
          0      1

o3 : ProjectiveHilbertPolynomial
i4 : degree F

o4 = 4
The degree of this polynomial may be recovered using dim:
i5 : dim F

o5 = 1
The dimension as a projective variety is also one less that the Krull dimension of R/I
i6 : (dim I - 1, degree I)

o6 = (1, 4)

o6 : Sequence

See also

Ways to use this method: