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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 = | 3 0 5 8 |
     | 8 9 6 1 |
     | 8 8 4 4 |
     | 0 6 6 9 |
     | 8 4 4 2 |
     | 9 8 7 8 |

              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  0  40 168 |, | 66  0    0 840 |)
                  | 16 27 48 21  |  | 176 1755 0 105 |
                  | 16 24 32 84  |  | 176 1560 0 420 |
                  | 0  18 48 189 |  | 0   1170 0 945 |
                  | 16 12 32 42  |  | 176 780  0 210 |
                  | 18 24 56 168 |  | 198 1560 0 840 |

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

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

o3 : Expression of class Sum