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 = | 1 0 8 4 |
     | 6 9 3 8 |
     | 3 2 0 7 |
     | 9 9 3 7 |
     | 6 1 3 6 |
     | 1 9 4 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 (| 2  0  64 84  |, | 22  0    0 420 |)
                  | 12 27 24 168 |  | 132 1755 0 840 |
                  | 6  6  0  147 |  | 66  390  0 735 |
                  | 18 27 24 147 |  | 198 1755 0 735 |
                  | 12 3  24 126 |  | 132 195  0 630 |
                  | 2  27 32 21  |  | 22  1755 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