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

              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  18 40 126 |, | 88  1170 0 630 |)
                  | 6  15 56 63  |  | 66  975  0 315 |
                  | 16 18 0  84  |  | 176 1170 0 420 |
                  | 2  15 24 105 |  | 22  975  0 525 |
                  | 6  15 72 147 |  | 66  975  0 735 |
                  | 18 12 16 0   |  | 198 780  0 0   |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum