next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 = | 1 0 6 2 |
     | 1 7 0 2 |
     | 4 1 5 1 |
     | 4 9 7 4 |
     | 2 9 6 6 |
     | 6 1 7 4 |

              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 (| 2  0  48 42  |, | 22  0    0 210 |)
                  | 2  21 0  42  |  | 22  1365 0 210 |
                  | 8  3  40 21  |  | 88  195  0 105 |
                  | 8  27 56 84  |  | 88  1755 0 420 |
                  | 4  27 48 126 |  | 44  1755 0 630 |
                  | 12 3  56 84  |  | 132 195  0 420 |

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

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

o3 : Expression of class Sum