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 = | 1 0 4 4 |
     | 5 8 1 0 |
     | 4 1 2 3 |
     | 6 4 0 9 |
     | 6 0 0 2 |
     | 9 7 0 0 |

              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 (| 2  0  32 84  |, | 22  0    0 420 |)
                  | 10 24 8  0   |  | 110 1560 0 0   |
                  | 8  3  16 63  |  | 88  195  0 315 |
                  | 12 12 0  189 |  | 132 780  0 945 |
                  | 12 0  0  42  |  | 132 0    0 210 |
                  | 18 21 0  0   |  | 198 1365 0 0   |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum