sage koszul

# parameter
for r in range(100):
    R = IntegerModRing(r^3)

    a = r
    b = r^2

    #koszul complex on (a, b) (shifted by 2)
    d0 = matrix(ZZ, 2, 1, [b, -a])
    d1 = matrix(ZZ, 1, 2, [a, b])
    K = ChainComplex({ -2: d0, -1: d1 }, base_ring=R)
    Kdual = ChainComplex({ 0: d1.transpose(), 1: d0.transpose() }, base_ring=R)
    # K is perfect so Hom(K, K) is K^* (x) K
    hom_complex = Kdual.tensor(K)
    ident = vector([1, 1, 0, 0, 1, -1])
    mult_r = r * ident
    d = hom_complex.differential(-1)
    d.solve_right(mult_r)