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<head><title>Module ++ Module -- direct sum of modules</title>
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<div><h1>Module ++ Module -- direct sum of modules</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><span>Operator: <a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</a></span></li>
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<div class="single"><h2>Description</h2>
<div><tt>M++N</tt> -- computes the direct sum of two modules (or coherent sheaves).<p/>
<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..c];</pre>
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<tr><td><pre>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</pre>
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Projection and inclusion maps for direct sums:<ul><li><span><a href="___Module_sp^_sp__Array.html" title="projection onto summand">Module ^ Array</a> -- projection onto summand</span></li>
<li><span><a href="___Module_sp_us_sp__Array.html" title="inclusion from summand">Module _ Array</a> -- inclusion from summand</span></li>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></li>
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