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<head><title>Ext^ZZ(Module,Matrix) -- map between Ext modules</title>
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<div><h1>Ext^ZZ(Module,Matrix) -- map between Ext modules</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>Ext^i(M,f)</tt></div>
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<li><span>Scripted functor: <a href="___Ext.html" title="compute an Ext module">Ext</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
<li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, N1 --> N2</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the induced map <i>Ext<sup>i</sup>(M,N1) → Ext<sup>i</sup>(M,N2)</i></span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>M</tt> is an ideal, it is regarded as a module in the evident way.<p/>
<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[a..d];</pre>
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<tr><td><pre>i2 : I = monomialCurveIdeal(R,{1,3,4})
3 2 2 2 3 2
o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : M = R^1/I
o3 = cokernel | bc-ad c3-bd2 ac2-b2d b3-a2c |
1
o3 : R-module, quotient of R</pre>
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<tr><td><pre>i4 : f = inducedMap(R^1,module I)
o4 = | bc-ad c3-bd2 ac2-b2d b3-a2c |
o4 : Matrix</pre>
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<tr><td><pre>i5 : Ext^1(M,f)
o5 = 0
o5 : Matrix</pre>
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<tr><td><pre>i6 : g = Ext^2(M,f)
o6 = 0
o6 : Matrix</pre>
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<tr><td><pre>i7 : source g == Ext^2(M,source f)
o7 = true</pre>
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<tr><td><pre>i8 : target g == Ext^2(M,target f)
o8 = true</pre>
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<tr><td><pre>i9 : Ext^3(f,R)
o9 = 0
o9 : Matrix 0 <--- 0</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_resolution.html" title="projective resolution">resolution</a> -- projective resolution</span></li>
<li><span><a href="___Tor.html" title="Tor module">Tor</a> -- Tor module</span></li>
<li><span><a href="___Hom.html" title="module of homomorphisms">Hom</a> -- module of homomorphisms</span></li>
<li><span><a href="___Ext^__Z__Z_lp__Module_cm__Module_rp.html" title="Ext module">Ext^ZZ(Module,Module)</a> -- Ext module</span></li>
<li><span><a href="___Ext^__Z__Z_lp__Matrix_cm__Module_rp.html" title="map between Ext modules">Ext^ZZ(Matrix,Module)</a> -- map between Ext modules</span></li>
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