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

              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 18 24 21  |, | 176 1170 0 105 |)
                  | 10 3  48 189 |  | 110 195  0 945 |
                  | 0  6  0  21  |  | 0   390  0 105 |
                  | 16 0  40 42  |  | 176 0    0 210 |
                  | 2  27 64 189 |  | 22  1755 0 945 |
                  | 14 0  64 42  |  | 154 0    0 210 |

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

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

o3 : Expression of class Sum