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

              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 (| 6  27 0  63  |, | 66  1755 0 315 |)
                  | 6  21 16 21  |  | 66  1365 0 105 |
                  | 8  0  72 63  |  | 88  0    0 315 |
                  | 10 27 32 42  |  | 110 1755 0 210 |
                  | 2  21 40 63  |  | 22  1365 0 315 |
                  | 0  6  64 126 |  | 0   390  0 630 |

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

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

o3 : Expression of class Sum