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<head><title>quotient(..., MinimalGenerators => ...) -- Decides whether quotient computes and outputs a trimmed set of generators; default is true</title>
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<div><h1>quotient(..., MinimalGenerators => ...) -- Decides whether quotient computes and outputs a trimmed set of generators; default is true</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>quotient(I,J,MinimalGenerators => b)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>b</tt>, <span>a <a href="___Boolean.html">Boolean value</a></span>, <tt>true</tt> forces trimmed output.</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : S=ZZ/101[a,b]
o1 = S
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : i=ideal(a^4,b^4)
4 4
o2 = ideal (a , b )
o2 : Ideal of S</pre>
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The following returns 2 minimal generators (Serre's Theorem: a codim 2 Gorenstein ideal is a complete intersection.)<table class="examples"><tr><td><pre>i3 : quotient(i, a^3+b^3)
3 3
o3 = ideal (a*b, a - b )
o3 : Ideal of S</pre>
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Without trimming we'd get 4 generators instead.<table class="examples"><tr><td><pre>i4 : quotient(i, a^3+b^3, MinimalGenerators=>false)
3 3
o4 = ideal (a*b, a - b )
o4 : Ideal of S</pre>
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<h2>Further information</h2>
<ul><li><span>Default value: <a href="_true.html" title="">true</a></span></li>
<li><span>Function: <span><a href="_quotient.html" title="quotient or division">quotient</a> -- quotient or division</span></span></li>
<li><span>Option name: <span><a href="___Minimal__Generators.html" title="">MinimalGenerators</a></span></span></li>
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