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

              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 12 8  147 |, | 132 780  0 735 |)
                  | 16 27 64 105 |  | 176 1755 0 525 |
                  | 12 27 64 147 |  | 132 1755 0 735 |
                  | 8  3  16 147 |  | 88  195  0 735 |
                  | 2  27 72 0   |  | 22  1755 0 0   |
                  | 10 24 72 189 |  | 110 1560 0 945 |

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

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

o3 : Expression of class Sum