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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 = | 4 5 9 2 |
     | 4 0 2 5 |
     | 5 7 6 6 |
     | 6 7 2 8 |
     | 9 8 2 4 |
     | 4 4 8 6 |

              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 (| 8  15 72 42  |, | 88  975  0 210 |)
                  | 8  0  16 105 |  | 88  0    0 525 |
                  | 10 21 48 126 |  | 110 1365 0 630 |
                  | 12 21 16 168 |  | 132 1365 0 840 |
                  | 18 24 16 84  |  | 198 1560 0 420 |
                  | 8  12 64 126 |  | 88  780  0 630 |

                                 6
o2 : ZZ-module, subquotient of ZZ
i3 : factor M

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

o3 : Expression of class Sum