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<head><title>ideal(Module) -- converts a module to an ideal</title>
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<div><h1>ideal(Module) -- converts a module to an ideal</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>ideal M</tt></div>
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<li><span>Function: <a href="_ideal.html" title="make an ideal">ideal</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span>, which is a submodule of a free module of rank 1</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, given by the generators of <tt>M</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[w,x,y,z];</pre>
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<tr><td><pre>i2 : f = map(R^1,R^3, matrix{{x^2-w*y, x*y-w*z, x*z-y^2}})
o2 = | x2-wy xy-wz -y2+xz |
1 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : image f
o3 = image | x2-wy xy-wz -y2+xz |
1
o3 : R-module, submodule of R</pre>
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<tr><td><pre>i4 : ideal image f
2 2
o4 = ideal (x - w*y, x*y - w*z, - y + x*z)
o4 : Ideal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_generators_lp__Module_rp.html" title="the generator matrix of a module">generators(Module)</a> -- the generator matrix of a module</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__Submodule.html" title="whether a module is evidently a submodule of a free module">isSubmodule</a> -- whether a module is evidently a submodule of a free module</span></li>
<li><span><a href="_is__Ideal.html" title="whether something is an ideal">isIdeal</a> -- whether something is an ideal</span></li>
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