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<head><title>isQuotientModule -- whether something is evidently a quotient of a free module</title>
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<div><h1>isQuotientModule -- whether something is evidently a quotient of a free module</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>isQuotientModule M</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Thing.html">thing</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Boolean.html">Boolean value</a></span>, <a href="_true.html" title="">true</a> if the given representation of <tt>M</tt> a quotient of a free module.</span></li>
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<div class="single"><h2>Description</h2>
<div>This function checks if the module <tt>M</tt> is a quotient of its <a href="_ambient.html" title="ambient free module of a subquotient, or ambient ring">ambient</a> free module by examining its matrix of <a href="_generators_lp__Module_rp.html">generators</a>.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b,c];</pre>
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<tr><td><pre>i2 : M = R^1/(a^2,b^2,c^2)
o2 = cokernel | a2 b2 c2 |
1
o2 : R-module, quotient of R</pre>
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<tr><td><pre>i3 : isQuotientModule M
o3 = true</pre>
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The image of a map from a free module to the first generator of <tt>M</tt> yields an equivalent module that is <em>not</em> presented as a quotient.<table class="examples"><tr><td><pre>i4 : f = M_{0}
o4 = | 1 |
o4 : Matrix</pre>
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<tr><td><pre>i5 : N = image f
o5 = subquotient (| 1 |, | a2 b2 c2 |)
1
o5 : R-module, subquotient of R</pre>
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<tr><td><pre>i6 : M == N
o6 = true</pre>
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<tr><td><pre>i7 : isQuotientModule N
o7 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Module_sp_us_sp__List.html" title="map from free module to some generators">Module _ List</a> -- map from free module to some generators</span></li>
<li><span><a href="_ambient.html" title="ambient free module of a subquotient, or ambient ring">ambient</a> -- ambient free module of a subquotient, or ambient ring</span></li>
<li><span><a href="_is__Free__Module.html" title="whether something is a free module">isFreeModule</a> -- whether something is a free module</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isQuotientModule</tt> :</h2>
<ul><li>isQuotientModule(Module)</li>
<li>isQuotientModule(Thing)</li>
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