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

              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 (| 16 12 8  84  |, | 176 780  0 420 |)
                  | 18 0  8  42  |  | 198 0    0 210 |
                  | 14 27 24 147 |  | 154 1755 0 735 |
                  | 10 0  16 168 |  | 110 0    0 840 |
                  | 12 24 8  42  |  | 132 1560 0 210 |
                  | 12 6  24 105 |  | 132 390  0 525 |

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

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

o3 : Expression of class Sum