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

              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 (| 8  27 8  168 |, | 88  1755 0 840 |)
                  | 18 0  0  42  |  | 198 0    0 210 |
                  | 0  0  16 105 |  | 0   0    0 525 |
                  | 0  21 16 168 |  | 0   1365 0 840 |
                  | 0  18 8  147 |  | 0   1170 0 735 |
                  | 16 3  48 0   |  | 176 195  0 0   |

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

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

o3 : Expression of class Sum