24.4 Commands

The commands and algorithms were done by Eric Rowell with help from Dell Kronewitter and Bill Helton.

24.4.1 NCHilbertCoefficient[integer1, aListOfExpressions, integer2, anOption]

Aliases: none
Description: NCHilbertCoefficient[integer1,aListOfExpressions,integer2, anOption] attempts to compute the first integer1 coefficients of the Hilbert series for the algebra generated by the relations in aListOfExpressions. There are four possible calls to this function, here expressed in order of longest time used to least.
Arguments: integer1, aListOfExpressions, integer2, anOption
Comments / Limitations: The order is alway the ambient order. Make certain that your order is only length lexicographic as this will save time. There is no reason to use any order other than length lexicographic for Hilbert series computations that the author of this code can think of. Currently the with the default version of this function the ambient order will be cleared during the computation, as there is a new variable introduced that is later removed. For now, just remember to reset the order before proceding.

24.4.2 NCX1VectorDimension[alist]

Aliases: none
Description: NCX1VectorDimension computes the dimension of the span of a set of polynomials as a vector space over the ground field.
Arguments: alist
Comments / Limitations: none