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

              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 (| 18 9  64 84  |, | 198 585  0 420 |)
                  | 12 0  32 21  |  | 132 0    0 105 |
                  | 2  15 0  189 |  | 22  975  0 945 |
                  | 0  9  32 63  |  | 0   585  0 315 |
                  | 10 27 24 63  |  | 110 1755 0 315 |
                  | 0  9  48 21  |  | 0   585  0 105 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum