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HilbertSeriesMultiDeg

the Hilbert-Poincare series wrt a multigrading

Syntax
HilbertSeriesMultiDeg(RmodI: RING, WM: MAT): TAGGED("$hp.PSeries")

Description
This function computes the multigraded Hilbert-Poincare series of RmodI wrt the multigrading WM . The I must be homogeneous wrt the multigrading WM .

This function is only a handy shortcut to avoid creating the proper polynomial ring multi-graded with WM .

Example
/**/  use R ::= QQ[x,y];
/**/  HilbertSeriesMultiDeg(R/ideal(Indets(R))^2, mat([[1,1]]));
(1 + 2*t) / (1-t)^0

/**/  HilbertSeriesMultiDeg(R/ideal(Indets(R))^2, mat([[1,0],[0,1]]));
---  Non-simplified HilbertPoincare' Series  ---
(1 - t[2]^2 - t[1]*t[2] - t[1]^2 + t[1]*t[2]^2 + t[1]^2*t[2])
/ ( (1-t[1])*(1-t[2]) )

See Also