Module ++ Module -- direct sum of modules

Module ++ Module -- direct sum of modules

Synopsis:

Operator: ++ -- a binary operator, usually used for direct sum

Input:

an instance of class Module.

Output:

an instance of class Module.

M++N -- computes the direct sum of two modules.

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 0  -b -c |

           {1} | 0 0 0 -c a  0  |

           {1} | 0 0 0 b  0  a  |



                             4

o2 : R-module, submodule of R

Projection and inclusion maps for direct sums:

Module ^ [...] -- projection onto some factors of a direct sum module

Module _ [...] -- get inclusion map into direct sum

See also:

directSum -- direct sum of modules or maps