factor(Module) -- factor a ZZ-module

Synopsis

Usage:
factor M
Function: factor
Inputs:
- M, a module
Outputs:
- a symbolic expression describing the decomposition of M into a direct sum of principal modules

Description

The ring of M must be ZZ.

In the following example we construct a module with a known (but disguised) factorization.

i1 : f = random(ZZ^6, ZZ^4)

o1 = | 7 4 3 0 |
     | 2 8 4 3 |
     | 0 2 2 2 |
     | 8 5 9 9 |
     | 5 1 4 7 |
     | 1 8 7 3 |

              6        4
o1 : Matrix ZZ  <--- ZZ

i2 : M = subquotient ( f * diagonalMatrix{2,3,8,21}, f * diagonalMatrix{2*11,3*5*13,0,21*5} )

o2 = image 0

                               6
o2 : ZZ-module, submodule of ZZ

i3 : factor M

o3 = 0

o3 : Expression of class Sum