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<head><title>directSum -- direct sum of modules or maps</title>
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<div><h1>directSum -- direct sum of modules or maps</h1>
<div class="single"><h2>Description</h2>
<div><tt>directSum(M,N,...)</tt> -- forms the direct sum of matrices or modules.<p/>
The components can be recovered later with <a href="_components.html" title="list the components of a direct sum">components</a>.<p/>
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>
<li><span><a href="___Matrix_sp^_sp__List.html" title="select rows">Matrix ^ List</a> -- select rows</span></li>
<li><span><a href="___Matrix_sp_us_sp__List.html" title="select columns">Matrix _ List</a> -- select columns</span></li>
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<p/>
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 <tt>directSum(a=>M,b=>N,...)</tt>, as in the following example.<table class="examples"><tr><td><pre>i1 : F = directSum(a=>ZZ^1, b=>ZZ^2, c=>ZZ^3)
6
o1 = ZZ
o1 : ZZ-module, free</pre>
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<tr><td><pre>i2 : F_[b]
o2 = | 0 0 |
| 1 0 |
| 0 1 |
| 0 0 |
| 0 0 |
| 0 0 |
6 2
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>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</pre>
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Similar syntax works with <a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</a>.<table class="examples"><tr><td><pre>i4 : F = (a => ZZ^1) ++ (b => ZZ^2)
3
o4 = ZZ
o4 : ZZ-module, free</pre>
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<tr><td><pre>i5 : F_[b]
o5 = | 0 0 |
| 1 0 |
| 0 1 |
3 2
o5 : Matrix ZZ <--- ZZ</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</a> -- a binary operator, usually used for direct sum</span></li>
<li><span><a href="_components.html" title="list the components of a direct sum">components</a> -- list the components of a direct sum</span></li>
<li><span><a href="_index__Components.html" title="specify keys for components of a direct sum">indexComponents</a> -- specify keys for components of a direct sum</span></li>
<li><span><a href="_indices.html" title="indices of a polynomial; also components for a direct sum">indices</a> -- indices of a polynomial; also components for a direct sum</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>directSum</tt> :</h2>
<ul><li>directSum(ChainComplex)</li>
<li>directSum(GradedModule)</li>
<li>directSum(List)</li>
<li>directSum(Matrix)</li>
<li>directSum(Module)</li>
<li>directSum(Option)</li>
<li>directSum(Sequence)</li>
</ul>
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