source(ChainComplexMap) -- find the source of a map of chain complexes

Synopsis

Function: source
Usage:

source f
Inputs:
- f, a chain complex map
Outputs:
- the source chain complex of f

Description

In the example below, we have a map between two modules and extend it to a map between projective resolutions of the two modules. Then source gives the source of the map of chain complexes.

i1 : R = ZZ[x,y,z];

i2 : M = R^1/(x,y,z);

i3 : N = R^1/(x^2,y^2,x*y*z,z^2);

i4 : g = map(N,M,x*y);

o4 : Matrix

i5 : f = res g;

i6 : source f

      1      3      3      1
o6 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o6 : ChainComplex

(That was an expensive way of resolving M.)