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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 = | 2 8 4 5 |
     | 9 4 9 8 |
     | 0 6 2 1 |
     | 2 5 4 8 |
     | 3 6 1 1 |
     | 5 9 1 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 (| 4  24 32 105 |, | 44  1560 0 525 |)
                  | 18 12 72 168 |  | 198 780  0 840 |
                  | 0  18 16 21  |  | 0   1170 0 105 |
                  | 4  15 32 168 |  | 44  975  0 840 |
                  | 6  18 8  21  |  | 66  1170 0 105 |
                  | 10 27 8  42  |  | 110 1755 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