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<head><title>Matrix ^ Array -- component of map corresponding to summand of target</title>
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<div><h1>Matrix ^ Array -- component of map corresponding to summand of target</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>F^[i,j,...,k]</tt></div>
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<li><span>Operator: <a href="_^.html" title="a binary operator, usually used for powers">^</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, or <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span> or <span>a <a href="___Graded__Module__Map.html">graded module map</a></span></span></li>
<li><span><tt>[i,j,...,k]</tt>, an array of indices</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, or <span>a <a href="___Graded__Module__Map.html">graded module map</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>The target of the module or chain complex <tt>F</tt> should be a direct sum, and the result is the component of this map corresponding to the sum of the components numbered or named <tt>i, j, ..., k</tt>. Free modules are regarded as direct sums of modules. In otherwords, this routine returns the map given by certain blocks of columns.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..d];</pre>
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<tr><td><pre>i2 : F = (vars R) ++ ((vars R) ++ matrix{{a-1,b-3},{c,d}})
o2 = | a b c d 0 0 0 0 0 0 |
| 0 0 0 0 a b c d 0 0 |
| 0 0 0 0 0 0 0 0 a-1 b-3 |
| 0 0 0 0 0 0 0 0 c d |
4 10
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : F^[1]
o3 = | 0 0 0 0 a b c d 0 0 |
| 0 0 0 0 0 0 0 0 a-1 b-3 |
| 0 0 0 0 0 0 0 0 c d |
3 10
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : F_[1]^[1]
o4 = | a b c d 0 0 |
| 0 0 0 0 a-1 b-3 |
| 0 0 0 0 c d |
3 6
o4 : Matrix R <--- R</pre>
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<p>If the components have been given names (see <a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a>), use those instead.</p>
<table class="examples"><tr><td><pre>i5 : G = (a=>R^2) ++ (b=>R^1)
3
o5 = R
o5 : R-module, free</pre>
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<tr><td><pre>i6 : N = map(G,R^2, (i,j) -> (i+37*j)_R)
o6 = | 0 37 |
| 1 38 |
| 2 39 |
3 2
o6 : Matrix R <--- R</pre>
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<tr><td><pre>i7 : N^[a]
o7 = | 0 37 |
| 1 38 |
2 2
o7 : Matrix R <--- R</pre>
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<tr><td><pre>i8 : N^[b]
o8 = | 2 39 |
1 2
o8 : Matrix R <--- R</pre>
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<tr><td><pre>i9 : N = directSum(x1 => matrix{{a,b-1}}, x2 => matrix{{a-3,b-17,c-35}}, x3 => vars R)
o9 = | a b-1 0 0 0 0 0 0 0 |
| 0 0 a-3 b-17 c-35 0 0 0 0 |
| 0 0 0 0 0 a b c d |
3 9
o9 : Matrix R <--- R</pre>
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<tr><td><pre>i10 : N^[x1,x3]
o10 = | a b-1 0 0 0 0 0 0 0 |
| 0 0 0 0 0 a b c d |
2 9
o10 : Matrix R <--- R</pre>
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<p>This works the same way for maps between chain complexes.</p>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Matrix_sp^_sp__Array.html" title="component of map corresponding to summand of target">Matrix ^ Array</a> -- component of map corresponding to summand of target</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="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></li>
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