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 = | 3 6 3 2 |
     | 1 2 1 7 |
     | 1 3 3 0 |
     | 2 2 6 5 |
     | 1 9 3 6 |
     | 0 7 6 5 |

              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 (| 6 18 24 42  |, | 66 1170 0 210 |)
                  | 2 6  8  147 |  | 22 390  0 735 |
                  | 2 9  24 0   |  | 22 585  0 0   |
                  | 4 6  48 105 |  | 44 390  0 525 |
                  | 2 27 24 126 |  | 22 1755 0 630 |
                  | 0 21 48 105 |  | 0  1365 0 525 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum