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

              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  12 0  168 |, | 88  780  0 840 |)
                  | 4  15 40 21  |  | 44  975  0 105 |
                  | 0  24 24 63  |  | 0   1560 0 315 |
                  | 8  15 72 63  |  | 88  975  0 315 |
                  | 18 18 56 168 |  | 198 1170 0 840 |
                  | 0  3  32 147 |  | 0   195  0 735 |

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

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

o3 : Expression of class Sum