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

              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 (| 18 9  64 105 |, | 198 585  0 525 |)
                  | 10 27 64 84  |  | 110 1755 0 420 |
                  | 14 27 72 0   |  | 154 1755 0 0   |
                  | 0  12 16 84  |  | 0   780  0 420 |
                  | 4  3  64 126 |  | 44  195  0 630 |
                  | 4  3  64 21  |  | 44  195  0 105 |

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

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

o3 : Expression of class Sum