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

              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 (| 0  6  0  105 |, | 0   390  0 525 |)
                  | 16 21 16 84  |  | 176 1365 0 420 |
                  | 14 18 24 84  |  | 154 1170 0 420 |
                  | 14 24 0  42  |  | 154 1560 0 210 |
                  | 16 27 56 42  |  | 176 1755 0 210 |
                  | 4  0  56 147 |  | 44  0    0 735 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum