# chainComplexMap -- Defines a ChainComplexMap via a list of matrices.

## Synopsis

• Usage:
chainComplexMap(D,C,mapList)
• Inputs:
• D, , target of ChainComplexMap
• C, , source of ChainComplexMap
• mapList, a list, list of maps defining the new ChainComplexMap
• Optional inputs:
• InitialDegree => ..., default value -infinity, Specify initial degree.
• Outputs:
• , The desired ChainComplexMap.

## Description

 i1 : R = ZZ/101[a,b,c] o1 = R o1 : PolynomialRing i2 : kRes = res coker vars R 1 3 3 1 o2 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o2 : ChainComplex i3 : multBya = extend(kRes,kRes,matrix{{a}}) 1 1 o3 = 0 : R <--------- R : 0 | a | 3 3 1 : R <----------------- R : 1 {1} | a b c | {1} | 0 0 0 | {1} | 0 0 0 | 3 3 2 : R <----- R : 2 0 1 1 3 : R <----- R : 3 0 4 : 0 <----- 0 : 4 0 o3 : ChainComplexMap i4 : mapList = apply((min kRes..max kRes), i -> multBya_i) o4 = (| a |, {1} | a b c |, 0, 0, 0) {1} | 0 0 0 | {1} | 0 0 0 | o4 : Sequence i5 : multBya2 = chainComplexMap(kRes,kRes,toList mapList) 1 1 o5 = 0 : R <--------- R : 0 | a | 3 3 1 : R <----------------- R : 1 {1} | a b c | {1} | 0 0 0 | {1} | 0 0 0 | 3 3 2 : R <----- R : 2 0 1 1 3 : R <----- R : 3 0 4 : 0 <----- 0 : 4 0 o5 : ChainComplexMap i6 : multBya2 == multBya o6 = true

## Ways to use chainComplexMap :

• "chainComplexMap(ChainComplex,ChainComplex,List)"

## For the programmer

The object chainComplexMap is .