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Macaulay2Doc :: factor(Module)

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

              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 (| 12 18 24 168 |, | 132 1170 0 840 |)
                  | 10 21 24 84  |  | 110 1365 0 420 |
                  | 2  3  32 42  |  | 22  195  0 210 |
                  | 2  21 48 84  |  | 22  1365 0 420 |
                  | 8  3  32 105 |  | 88  195  0 525 |
                  | 2  0  24 63  |  | 22  0    0 315 |

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

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

o3 : Expression of class Sum