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differentialModule -- converts a square zero matrix into a differential module

Synopsis

Description

Given a module map $f: M \rightarrow M$ of degree $a$ this creates a degree $a$ differential module from $f$ represented as a 3-term chain complex in homological degrees $-1, 0$, and $1$. If $a \neq 0$, then since the source and target of $f$ are required to be equal, we must specify the degree of the differential to be $a$ in order for the differential to be homogeneous.

i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing
 
i2 : phi = map(R^1/(x^2),R^1/(x^2), x, Degree=>1)

o2 = | x |

o2 : Matrix
 
i3 : differentialModule(phi)

o3 = cokernel | x2 | <-- cokernel | x2 | <-- cokernel | x2 |
                                              
     -1                  0                   1

o3 : DifferentialModule

See also

Ways to use differentialModule:

For the programmer

The object differentialModule is a method function.