Hom(Matrix,Module) -- induced map on Hom modules

Synopsis

Usage:
Hom(f,M)
Hom(M,f)
Function: Hom
Inputs:
- f, a matrix, a map N1 --> N2 of modules or a chain complex
- M, a module, over the same ring R as f
Outputs:
- a matrix, either the map Hom_R(N2,M) --> Hom_R(N1,M) in the first case, or the map Hom_R(M,N1) --> Hom_R(M,N2) in the second case

Description

If f is a map of chain complexes, then the result is a a chain complex map.

i1 : R = QQ[a..d];

i2 : I = ideal(a*b,c*d);

o2 : Ideal of R

i3 : J = I + ideal(a*d);

o3 : Ideal of R

i4 : f = inducedMap(module J,module I)

o4 = {2} | 1 0 |
     {2} | 0 1 |
     {2} | 0 0 |

o4 : Matrix

i5 : g = Hom(R^3,f)

o5 = {2} | 1 0 0 0 0 0 |
     {2} | 0 1 0 0 0 0 |
     {2} | 0 0 0 0 0 0 |
     {2} | 0 0 1 0 0 0 |
     {2} | 0 0 0 1 0 0 |
     {2} | 0 0 0 0 0 0 |
     {2} | 0 0 0 0 1 0 |
     {2} | 0 0 0 0 0 1 |
     {2} | 0 0 0 0 0 0 |

o5 : Matrix

i6 : ker g

o6 = image 0

                             3
o6 : R-module, submodule of R

i7 : image g

o7 = image | ab cd 0  0  0  0  |
           | 0  0  ab cd 0  0  |
           | 0  0  0  0  ab cd |

                             3
o7 : R-module, submodule of R

Caveat

Not all possible combinations are implemented yet