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<head><title>isFreeModule -- whether something is a free module</title>
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<div><h1>isFreeModule -- whether something is 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>isFreeModule 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> is a free module and <a href="_false.html" title="">false</a> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div>This function checks if the module <tt>M</tt> is equal to 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> and its matrix of <a href="_relations.html">relations</a>.<p/>
To determine whether <tt>M</tt> is isomorphic to a free module, use <a href="_prune.html" title="prune, e.g., compute a minimal presentation">prune</a> <tt>M</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ/7[x,y];</pre>
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<tr><td><pre>i2 : M = kernel vars R
o2 = image {1} | -y |
{1} | x |
2
o2 : R-module, submodule of R</pre>
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<tr><td><pre>i3 : isFreeModule M
o3 = false</pre>
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<tr><td><pre>i4 : isFreeModule prune M
o4 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><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="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">prune(Module)</a> -- minimal presentation of a module</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isFreeModule</tt> :</h2>
<ul><li>isFreeModule(Module)</li>
<li>isFreeModule(Thing)</li>
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