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

              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 (| 8  3  0  105 |, | 88  195  0 525 |)
                  | 14 24 64 42  |  | 154 1560 0 210 |
                  | 18 3  72 168 |  | 198 195  0 840 |
                  | 0  12 56 21  |  | 0   780  0 105 |
                  | 14 24 16 147 |  | 154 1560 0 735 |
                  | 6  3  24 105 |  | 66  195  0 525 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum