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the Hilbert polynomial
HilbertPoly(R: RING or TAGGED("Quotient")): RINGELEM in the ring QQt.
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This function returns the Hilbert polynomial for R as a polynomial in
the standard CoCoA ring
QQt
(= QQ[t]).
The weights of the indeterminates of
R
must all be 1, and the
coefficient ring must be a field.
If the input is not homogeneous, the Hilbert polynomial of the
corresponding leading term (initial) ideal or module is calculated.
For the Hilbert *function*, see
HilbertFn
.
/**/ Use R ::= QQ[w,x,y,z];
/**/ I := ideal(z^2-x*y, x*z^2+w^3);
/**/ HilbertFn(R/I);
H(0) = 1
H(1) = 4
H(t) = 6*t-3 for t >= 2
/**/ F := HilbertPoly(R/I);
/**/ F; -- a polynomial in the ring Qt
6*t-3
/**/ T := indet(RingOf(F), 1);
/**/ subst(F, T, 3);
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