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

              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 (| 14 3  64 63  |, | 154 195 0 315 |)
                  | 8  9  56 105 |  | 88  585 0 525 |
                  | 10 9  32 168 |  | 110 585 0 840 |
                  | 6  6  0  126 |  | 66  390 0 630 |
                  | 14 15 64 147 |  | 154 975 0 735 |
                  | 4  3  24 42  |  | 44  195 0 210 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum