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<head><title>extend(ChainComplex,ChainComplex,Matrix) -- extend a module map to a chain map, if possible</title>
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<div><h1>extend(ChainComplex,ChainComplex,Matrix) -- extend a module map to a chain map, if possible</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>extend(D,C,f0)</tt></div>
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<li><span>Function: <a href="_extend.html" title="extend a module map to a chain map, if possible">extend</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>D</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
<li><span><tt>f0</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map from <tt>C_0</tt> to <tt>D_0</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, a chain complex map <tt>f: D <--- C</tt> of degree 0 extending <tt>f0</tt> in the sense that <tt>f_0==f0</tt></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>Verify => </tt><span><span>a <a href="___Boolean.html">Boolean value</a></span>, <span>default value true</span>, whether to check that the map extends</span></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..c]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = image vars R
o2 = image | a b c |
1
o2 : R-module, submodule of R</pre>
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<tr><td><pre>i3 : J = image symmetricPower (2,vars R)
o3 = image | a2 ab ac b2 bc c2 |
1
o3 : R-module, submodule of R</pre>
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<tr><td><pre>i4 : g = extend( resolution (R^1/I), resolution (R^1/J), id_(R^1))
1 1
o4 = 0 : R <--------- R : 0
| 1 |
3 6
1 : R <----------------------- R : 1
{1} | a b 0 0 0 0 |
{1} | 0 0 b 0 0 0 |
{1} | 0 0 0 a b c |
3 8
2 : R <--------------------------- R : 2
{2} | 0 b 0 0 0 0 0 0 |
{2} | 0 0 a b 0 0 0 0 |
{2} | 0 0 0 0 0 b 0 0 |
1 3
3 : R <----------------- R : 3
{3} | 0 b 0 |
4 : 0 <----- 0 : 4
0
o4 : ChainComplexMap</pre>
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<tr><td><pre>i5 : g_1
o5 = {1} | a b 0 0 0 0 |
{1} | 0 0 b 0 0 0 |
{1} | 0 0 0 a b c |
3 6
o5 : Matrix R <--- R</pre>
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<tr><td><pre>i6 : g_2
o6 = {2} | 0 b 0 0 0 0 0 0 |
{2} | 0 0 a b 0 0 0 0 |
{2} | 0 0 0 0 0 b 0 0 |
3 8
o6 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Chain__Complex_sp_us_sp__Z__Z.html" title="component">ChainComplex _ ZZ</a> -- component</span></li>
<li><span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z.html" title="component map">ChainComplexMap _ ZZ</a> -- component map</span></li>
<li><span><a href="_cone_lp__Chain__Complex__Map_rp.html" title="mapping cone of a chain map">cone(ChainComplexMap)</a> -- mapping cone of a chain map</span></li>
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