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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.

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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
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