# ChainComplexMap _ ZZ = Thing -- install component of chain complex map

## Synopsis

• Usage:
f_i = g
• Operator: _
• Inputs:
• Outputs:
• install g as the i-th module of the chain complex map f

## Description

 ```i1 : R = ZZ[x..z] o1 = R o1 : PolynomialRing``` ```i2 : C = chainComplex R o2 = 0 o2 : ChainComplex``` ```i3 : C.dd o3 = 0 o3 : ChainComplexMap``` ```i4 : C.dd_1 = vars R o4 = | x y z | 1 3 o4 : Matrix R <--- R``` ```i5 : C.dd_3 = transpose vars R o5 = {-1} | x | {-1} | y | {-1} | z | 3 1 o5 : Matrix R <--- R``` ```i6 : C.dd 1 3 o6 = 0 : R <------------- R : 1 | x y z | 3 3 1 : R <----- R : 2 0 3 1 2 : R <-------------- R : 3 {-1} | x | {-1} | y | {-1} | z | o6 : ChainComplexMap``` ```i7 : C 1 3 3 1 o7 = R <-- R <-- R <-- R 0 1 2 3 o7 : ChainComplex``` ```i8 : HH C o8 = 0 : cokernel | x y z | 1 : image {1} | -y 0 -z | {1} | x -z 0 | {1} | 0 y x | 2 : cokernel {-1} | x | {-1} | y | {-1} | z | 3 : image 0 o8 : GradedModule``` ```i9 : prune HH C o9 = 0 : cokernel | z y x | 1 : cokernel | z | | x | | -y | 2 : cokernel | x | | y | | z | 3 : 0 o9 : GradedModule```