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 3 0 2 |
     | 7 7 3 9 |
     | 2 0 0 9 |
     | 1 9 0 5 |
     | 2 7 9 8 |
     | 6 1 4 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 (| 6  9  0  42  |, | 66  585  0 210 |)
                  | 14 21 24 189 |  | 154 1365 0 945 |
                  | 4  0  0  189 |  | 44  0    0 945 |
                  | 2  27 0  105 |  | 22  1755 0 525 |
                  | 4  21 72 168 |  | 44  1365 0 840 |
                  | 12 3  32 147 |  | 132 195  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