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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 1 1 3 |
     | 8 3 3 5 |
     | 1 3 0 0 |
     | 5 2 9 1 |
     | 3 7 6 7 |
     | 1 9 5 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 (| 12 3  8  63  |, | 132 195  0 315 |)
                  | 16 9  24 105 |  | 176 585  0 525 |
                  | 2  9  0  0   |  | 22  585  0 0   |
                  | 10 6  72 21  |  | 110 390  0 105 |
                  | 6  21 48 147 |  | 66  1365 0 735 |
                  | 2  27 40 105 |  | 22  1755 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