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

              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 (| 0  18 56 63  |, | 0   1170 0 315 |)
                  | 14 3  56 189 |  | 154 195  0 945 |
                  | 12 18 40 189 |  | 132 1170 0 945 |
                  | 14 15 24 168 |  | 154 975  0 840 |
                  | 4  12 0  0   |  | 44  780  0 0   |
                  | 4  3  0  42  |  | 44  195  0 210 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum