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# differentialModule(Complex) -- converts a complex into a differential module

## Synopsis

• Function: differentialModule
• Usage:
differentialModule C
• Inputs:
• C, , a complex concentrated in homological degrees -1, 0, 1
• Outputs:

## Description

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