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the affine Hilbert function

AffHilbert(R:RING or TAGGED("Quotient")):TAGGED("$hp.Hilbert")
AffHilbert(R:RING or TAGGED("Quotient"), N:INT):INT

The first form of this function computes the affine Hilbert function for R. The second form computes the N-th value of the affine Hilbert function. The weights of the indeterminates of R must all be 1. For repeated evaluations of the Hilbert function, use EvalHilbertFn instead of Hilbert(R, N) in order to speed up execution.

This function is the same as AffHilbertFn .

The coefficient ring must be a field.

  Use R ::= QQ[x,y,z];
  AffHilbert(R/Ideal(z^4-1, xz^4-y-3));
H(0) = 1
H(1) = 3
H(t) = 4t - 2   for t >= 2

See Also