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

              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 (| 14 21 72 105 |, | 154 1365 0 525 |)
                  | 6  0  24 0   |  | 66  0    0 0   |
                  | 16 27 0  126 |  | 176 1755 0 630 |
                  | 12 15 24 63  |  | 132 975  0 315 |
                  | 0  3  56 63  |  | 0   195  0 315 |
                  | 6  3  40 84  |  | 66  195  0 420 |

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

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

o3 : Expression of class Sum