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

              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  27 56 147 |, | 44  1755 0 735 |)
                  | 14 15 0  168 |  | 154 975  0 840 |
                  | 16 15 24 42  |  | 176 975  0 210 |
                  | 18 12 16 21  |  | 198 780  0 105 |
                  | 10 0  56 0   |  | 110 0    0 0   |
                  | 16 15 56 63  |  | 176 975  0 315 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum