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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 = | 9 4 3 9 |
     | 5 3 4 0 |
     | 5 7 4 1 |
     | 7 5 7 5 |
     | 7 2 9 7 |
     | 5 6 3 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 (| 18 12 24 189 |, | 198 780  0 945 |)
                  | 10 9  32 0   |  | 110 585  0 0   |
                  | 10 21 32 21  |  | 110 1365 0 105 |
                  | 14 15 56 105 |  | 154 975  0 525 |
                  | 14 6  72 147 |  | 154 390  0 735 |
                  | 10 18 24 168 |  | 110 1170 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