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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 = | 5 1 5 6 |
     | 7 0 4 8 |
     | 0 7 5 6 |
     | 2 0 2 2 |
     | 6 6 6 3 |
     | 1 9 9 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 (| 10 3  40 126 |, | 110 195  0 630 |)
                  | 14 0  32 168 |  | 154 0    0 840 |
                  | 0  21 40 126 |  | 0   1365 0 630 |
                  | 4  0  16 42  |  | 44  0    0 210 |
                  | 12 18 48 63  |  | 132 1170 0 315 |
                  | 2  27 72 168 |  | 22  1755 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