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the h-vector of a module or quotient object

HVector(R: RING or TAGGED("Quotient")): LIST

This function returns the h-vector of M, i.e., the coefficients of the numerator of the simplified Poincare series for M. M can be a module or a quotient.

The weights of the indeterminates of the polynomial ring of M must all be 1, and the coefficient ring must be a field.

If the input is not homogeneous, the Hilbert function of the corresponding leading term (initial) ideal or module is calculated.

/**/  Use R ::= QQ[t,x,y,z];
/**/  HVector(R/ideal(x,y,z)^5);
[1, 3, 6, 10, 15]

/**/  HilbertSeries(R/ideal(x,y,z)^5);
(1 + 3t + 6t^2 + 10t^3 + 15t^4) / (1-t)

See Also