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# Module ++ Module -- direct sum of modules

- Operator: ++

## Description

M++N -- computes the direct sum of two modules (or coherent sheaves).

    i1 : R = ZZ/101[a..c];

    i2 : image vars R ++ kernel vars R

    o2 = image {0} | a b c 0  0  0  |
               {1} | 0 0 0 -b 0  -c |
               {1} | 0 0 0 a  -c 0  |
               {1} | 0 0 0 0  b  a  |

                                 4
    o2 : R-module, submodule of R

The projection and inclusion maps for direct sums can be obtained with the following methods.

- Module ^ Array -- projection onto summand
- Module _ Array -- inclusion from summand

The components can be recovered later with components or with formation.

## See also

- directSum -- direct sum of modules or maps

## Ways to use this method:

- Module ++ Module -- direct sum of modules

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/directSum-doc.m2:48:0.