Software for Hilbert series of quotients of exterior algebras

Question

Is there some software which computes Hilbert series of quotients of exterior algebras? In commutative case, Maple can compute Hilbert series. Thank you very much.

Answer 1

Macaulay2 (M2) is good for Hilbert series computations and can do exterior algebras. You can see the documentation for exterior algebras in M2 for more info. Below is a quick example of a Hilbert series computation.

i1 : R = QQ[a..d,SkewCommutative=>true];

i2 : I = ideal(a+b+c+d);

o2 : Ideal of R

i3 : M = R/I;

i4 : reduceHilbert hilbertSeries M

                2    3
     1 + 3T + 3T  + T
o4 = -----------------
             1

o4 : Expression of class Divide