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

              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  21 48 189 |, | 88  1365 0 945 |)
                  | 10 15 0  84  |  | 110 975  0 420 |
                  | 8  3  32 168 |  | 88  195  0 840 |
                  | 2  0  8  42  |  | 22  0    0 210 |
                  | 4  27 32 126 |  | 44  1755 0 630 |
                  | 10 24 48 84  |  | 110 1560 0 420 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum