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

              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 6  64 63  |, | 154 390  0 315 |)
                  | 10 12 32 84  |  | 110 780  0 420 |
                  | 0  0  64 105 |  | 0   0    0 525 |
                  | 8  27 72 63  |  | 88  1755 0 315 |
                  | 8  18 32 105 |  | 88  1170 0 525 |
                  | 4  18 48 147 |  | 44  1170 0 735 |

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

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

o3 : Expression of class Sum