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hilbertSeries -- compute the Hilbert series

Synopsis

Optional inputs:
- Order => ..., -- display the truncated power series expansion

Description

The Hilbert series is the formal power series in the variables of the degrees ring whose coefficients are the dimensions of the corresponding graded component.

Note that the series is provided as a type of expression called a Divide.

See also

degreesRing -- the ring of degrees
reduceHilbert -- reduce a Hilbert series expression
poincare -- assemble degrees into polynomial
poincareN -- assemble degrees into polynomial
hilbertPolynomial -- compute the Hilbert polynomial
hilbertFunction -- compute the Hilbert function

Ways to use `hilbertSeries` :

hilbertSeries(Ideal) -- compute the Hilbert series of the quotient of the ambient ring by the ideal
hilbertSeries(Module) -- compute the Hilbert series of the module
hilbertSeries(ProjectiveHilbertPolynomial) -- compute the Hilbert series of a projective Hilbert polynomial
hilbertSeries(ProjectiveVariety) -- compute the Hilbert series of a projective variety
hilbertSeries(Ring) -- compute the Hilbert series of the ring