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Macaulay2Doc :: directSum

directSum -- direct sum of modules or maps

Description

directSum(M,N,...) -- forms the direct sum of matrices or modules.

The components can be recovered later with components.

Projection and inclusion maps for direct sums:

It sometimes happens that the user has indices for the components of a direct sum preferable to the usual consecutive small integers. In this case the preferred indices can be specified with code like directSum(a=>M,b=>N,...), as in the following example.

i1 : F = directSum(a=>ZZ^1, b=>ZZ^2, c=>ZZ^3)

       6
o1 = ZZ

o1 : ZZ-module, free
i2 : F_[b]

o2 = | 0 0 |
     | 1 0 |
     | 0 1 |
     | 0 0 |
     | 0 0 |
     | 0 0 |

              6        2
o2 : Matrix ZZ  <--- ZZ
i3 : F^[c]

o3 = | 0 0 0 1 0 0 |
     | 0 0 0 0 1 0 |
     | 0 0 0 0 0 1 |

              3        6
o3 : Matrix ZZ  <--- ZZ
Similar syntax works with ++.
i4 : F = (a => ZZ^1) ++ (b => ZZ^2)

       3
o4 = ZZ

o4 : ZZ-module, free
i5 : F_[b]

o5 = | 0 0 |
     | 1 0 |
     | 0 1 |

              3        2
o5 : Matrix ZZ  <--- ZZ

See also

Ways to use directSum :