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

              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  15 0  84  |, | 88  975  0 420 |)
                  | 4  3  16 42  |  | 44  195  0 210 |
                  | 2  18 8  63  |  | 22  1170 0 315 |
                  | 16 3  48 42  |  | 176 195  0 210 |
                  | 0  21 72 105 |  | 0   1365 0 525 |
                  | 12 9  56 189 |  | 132 585  0 945 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum