- degreesRing -- the ring or monoid of degrees
- reduceHilbert -- reduce a Hilbert series expression
- poincare -- assemble degrees of a ring, module, or ideal into a 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(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

The object hilbertSeries is a method function with options.