hilbertSequence M
Given an $\NN^p$-graded module M, this function computes the coefficients of the pth sum transform of the $\NN^p$-graded Hilbert function of M in its Macaulay expansion. If the input is an ideal I, then the Hilbert sequence of comodule I is returned.
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For singly-graded modules, one can read off the Hilbert polynomial from the Hilbert sequence:
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A convenient expression for the Hilbert sequence is provided via printHilbertSequence.
In general, to retain a connection to the Hilbert polynomial (as opposed to the pth sum transform) it is necessary to saturate with respect to the irrelevant ideal, cf. page 235 of Conca-De Negri-Gorla, "Cartwright–Sturmfels ideals associated to graphs and linear spaces", 2018. This is handled by the optional argument DoSaturate.
The object hilbertSequence is a method function with options.