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::
hilbertSeries
hilbertSeries  compute the Hilbert series
Synopsis
Optional inputs
:
Order => ...
,  display the truncated power series expansion
Reduce => ...
,  reduce the Hilbert series
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
 the Hilbert function
Ways to use
hilbertSeries
:
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