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

              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  24 48 21  |, | 0   1560 0 105 |)
                  | 16 15 16 42  |  | 176 975  0 210 |
                  | 4  21 64 105 |  | 44  1365 0 525 |
                  | 14 12 0  0   |  | 154 780  0 0   |
                  | 2  9  72 189 |  | 22  585  0 945 |
                  | 4  0  32 189 |  | 44  0    0 945 |

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

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

o3 : Expression of class Sum