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NCAlgebra :: hilbertBergman

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

Synopsis

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.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12506-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12506-0/3.ter ... Complete!

o1 = B

o1 : NCQuotientRing
i2 : hilbertBergman(B,DegreeLimit=>12)
--Calling bergman for HS computation.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12506-0/5.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12506-0/10.ter ... 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 :