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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
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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
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