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 = | 2 0 5 7 |
     | 9 8 7 2 |
     | 6 6 2 7 |
     | 0 0 0 1 |
     | 1 5 5 3 |
     | 4 6 1 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 (| 4  0  40 147 |, | 44  0    0 735 |)
                  | 18 24 56 42  |  | 198 1560 0 210 |
                  | 12 18 16 147 |  | 132 1170 0 735 |
                  | 0  0  0  21  |  | 0   0    0 105 |
                  | 2  15 40 63  |  | 22  975  0 315 |
                  | 8  18 8  84  |  | 88  1170 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