hilbertBergman -- Calls Bergman to compute the Hilbert series of an NCQuotientRing

Synopsis

Usage:

hseries = hilbertBergman(A)
Inputs:
- A, an instance of the type NCQuotientRing,
Optional inputs:
- DegreeLimit => an integer, default value 10
Outputs:
- hseries, a ring element,

Description

This method calls the Bergman function ncpbhgroebner to compute the Hilbert series of an NCQuotientRing. The input ring must be a ring over QQ or ZZ/p. At this time, the output is correct only for NCRings with a standard grading - all generators have degree 1. The output is returned as a polynomial in ZZ[T].

i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z})
--Calling Bergman for NCGB calculation.
Complete!

o1 = B

o1 : NCQuotientRing

i2 : hilbertBergman(B,DegreeLimit=>12)
--Calling bergman for HS computation.
Complete!

                2      3      4      5      6      7      8      9      10  
o2 = 1 + 3T + 6T  + 10T  + 15T  + 21T  + 28T  + 36T  + 45T  + 55T  + 66T   +
     ------------------------------------------------------------------------
        11      12
     78T   + 91T

o2 : ZZ[T]

Ways to use hilbertBergman :

hilbertBergman(NCQuotientRing)

For the programmer

The object hilbertBergman is a method function with options.