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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 or with formation.

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

Menu

Ways to use directSum:

  • directSum(List)
  • directSum(Matrix)
  • directSum(Module)
  • directSum(Option)
  • directSum(Sequence)

For the programmer

The object directSum is a method function with a single argument.

The source of this document is in Macaulay2Doc/functions/directSum-doc.m2:117:0.