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

              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 (| 16 21 24 189 |, | 176 1365 0 945 |)
                  | 6  3  56 0   |  | 66  195  0 0   |
                  | 6  21 8  63  |  | 66  1365 0 315 |
                  | 16 9  0  147 |  | 176 585  0 735 |
                  | 10 15 56 147 |  | 110 975  0 735 |
                  | 12 0  72 21  |  | 132 0    0 105 |

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

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

o3 : Expression of class Sum