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

              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 = subquotient (| 14 3  64 0   |, | 154 195  0 0   |)
                  | 14 0  16 21  |  | 154 0    0 105 |
                  | 2  27 8  189 |  | 22  1755 0 945 |
                  | 10 15 40 168 |  | 110 975  0 840 |
                  | 8  6  24 84  |  | 88  390  0 420 |
                  | 6  9  56 168 |  | 66  585  0 840 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

          ZZ   ZZ    ZZ
o3 = ZZ + -- + -- + ----
           5   11   5*13

o3 : Expression of class Sum