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factor(Module) -- factor a ZZ-module

Synopsis

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 0 8 4 |
     | 8 5 0 5 |
     | 8 5 9 9 |
     | 8 0 7 1 |
     | 5 7 4 8 |
     | 9 4 3 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 (| 4  0  64 84  |, | 44  0    0 420 |)
                  | 16 15 0  105 |  | 176 975  0 525 |
                  | 16 15 72 189 |  | 176 975  0 945 |
                  | 16 0  56 21  |  | 176 0    0 105 |
                  | 10 21 32 168 |  | 110 1365 0 840 |
                  | 18 12 24 84  |  | 198 780  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