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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 9 5 3 |
     | 6 4 6 0 |
     | 9 9 3 2 |
     | 8 2 3 3 |
     | 5 5 1 3 |
     | 0 8 6 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  27 40 63  |, | 88  1755 0 315 |)
                  | 12 12 48 0   |  | 132 780  0 0   |
                  | 18 27 24 42  |  | 198 1755 0 210 |
                  | 16 6  24 63  |  | 176 390  0 315 |
                  | 10 15 8  63  |  | 110 975  0 315 |
                  | 0  24 48 126 |  | 0   1560 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