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  0   -4 -6 |
     | 1  7   6  4  |
     | 5  8   0  -4 |
     | 2  -9  -2 3  |
     | -9 4   9  -7 |
     | -9 -10 -5 4  |

              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   0   -32 -126 |, | 0    0     0 -630 |)
                  | 2   21  48  84   |  | 22   1365  0 420  |
                  | 10  24  0   -84  |  | 110  1560  0 -420 |
                  | 4   -27 -16 63   |  | 44   -1755 0 315  |
                  | -18 12  72  -147 |  | -198 780   0 -735 |
                  | -18 -30 -40 84   |  | -198 -1950 0 420  |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

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

o3 : Expression of class Sum