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HVector

Syntax

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

Summary

the h-vector of a ring or quotient object

Description

This function returns the h-vector of the ring R, i.e., the coefficients of the numerator of the simplified Poincare series for R.

The weights of the indeterminates of the current ring 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.

example

    
Use R ::= Q[t,x,y,z];
HVector(R/Ideal(x,y,z)^5);
[1, 3, 6, 10, 15]
-------------------------------
Poincare(R/Ideal(x,y,z)^5);
(1 + 3t + 6t^2 + 10t^3 + 15t^4) / (1-t)
-------------------------------
        
    

See Also