Given a complex of modules in homological degrees $-1, 0$, and $1$, with the differentials being identical, this method produces the corresponding DifferentialModule.
i1 : S = QQ[x,y]
o1 = S
o1 : PolynomialRing
i2 : del = map(S^{-1,0,0,1},S^{-1,0,0,1},matrix{{0,y,x,-1},{0,0,0,x},{0,0,0,-y},{0,0,0,0}}, Degree=>2)
o2 = {1} | 0 y x -1 |
{0} | 0 0 0 x |
{0} | 0 0 0 -y |
{-1} | 0 0 0 0 |
4 4
o2 : Matrix S <-- S
i3 : C = complex{-del, -del}[1]
4 4 4
o3 = S <-- S <-- S
-1 0 1
o3 : Complex
i4 : D = differentialModule C
4 4 4
o4 = S <-- S <-- S
-1 0 1
o4 : DifferentialModule
i5 : D.dd
4 4
o5 = -1 : S <--------------------- S : 0
{1} | 0 y x -1 |
{0} | 0 0 0 x |
{0} | 0 0 0 -y |
{-1} | 0 0 0 0 |
4 4
0 : S <--------------------- S : 1
{1} | 0 y x -1 |
{0} | 0 0 0 x |
{0} | 0 0 0 -y |
{-1} | 0 0 0 0 |
o5 : ComplexMap