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the affine Hilbert function

AffHilbertFn(R: RING): TAGGED("$hp.Hilbert")
AffHilbertFn(R: RING, 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 AffHilbertFn(R, N) in order to speed up execution.

The coefficient ring must be a field.

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

See Also