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

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.

- 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 -- the Hilbert function

- hilbertSeries(ZZ,BettiTally), see BettiTally -- the class of all Betti tallies
- 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(MonomialIdeal)`(missing documentation)- hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring
- hilbertSeries(QuotientRing), see hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring
- hilbertSeries(ProjectiveHilbertPolynomial) -- compute the Hilbert series of a projective Hilbert polynomial
- hilbertSeries(ProjectiveVariety) -- compute the Hilbert series of a projective variety