up previous next
HilbertPoly

the Hilbert polynomial
Syntax 

HilbertPoly(R:RING or TAGGED("Quotient")):POLY in the ring Qt.

Description
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 Hilbert .

Example 
  Use R ::= QQ[w,x,y,z];
  I := Ideal(z^2-xy,xz^2+w^3);
  Hilbert(R/I);
H(0) = 1
H(1) = 4
H(t) = 6t-3   for t >= 2
-------------------------------
  F := HilbertPoly(R/I);
  F;  -- a polynomial in the ring Qt
Qt :: 6t-3
-------------------------------
  Subst(F, Qt::t,3);
Qt :: 15
-------------------------------


See Also