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 = | 8 9 0 2 |
     | 6 0 0 1 |
     | 0 8 9 1 |
     | 4 4 8 1 |
     | 5 6 1 4 |
     | 1 6 1 1 |

              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 (| 16 27 0  42 |, | 176 1755 0 210 |)
                  | 12 0  0  21 |  | 132 0    0 105 |
                  | 0  24 72 21 |  | 0   1560 0 105 |
                  | 8  12 64 21 |  | 88  780  0 105 |
                  | 10 18 8  84 |  | 110 1170 0 420 |
                  | 2  18 8  21 |  | 22  1170 0 105 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum