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

              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 (| 6  0  72 189 |, | 66  0    0 945 |)
                  | 18 18 72 0   |  | 198 1170 0 0   |
                  | 14 9  32 126 |  | 154 585  0 630 |
                  | 14 0  40 63  |  | 154 0    0 315 |
                  | 12 3  24 0   |  | 132 195  0 0   |
                  | 12 15 24 147 |  | 132 975  0 735 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum