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<head><title>isField -- whether something is a field</title>
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<div><h1>isField -- whether something is a field</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>isField R</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</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 <tt>R</tt> was explicitly constructed as a field (no computation is done) and <a href="_false.html" title="">false</a> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div>This function recognizes basic fields, <a href="___Galois__Field.html">Galois fields</a> and <a href="___Fraction__Field.html">fraction fields</a>.<table class="examples"><tr><td><pre>i1 : isField QQ
o1 = true</pre>
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<tr><td><pre>i2 : isField CC_53
o2 = true</pre>
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<tr><td><pre>i3 : isField GF(2,3)
o3 = true</pre>
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<tr><td><pre>i4 : isField(frac(QQ[x,y]))
o4 = true</pre>
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This function will not recognize other rings as fields.<table class="examples"><tr><td><pre>i5 : R = QQ[x]/(x^2+1)
o5 = R
o5 : QuotientRing</pre>
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<tr><td><pre>i6 : isUnit x
o6 = true</pre>
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<tr><td><pre>i7 : isField R
o7 = false</pre>
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<tr><td><pre>i8 : F = toField R
o8 = F
o8 : PolynomialRing</pre>
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<tr><td><pre>i9 : isField F
o9 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_to__Field_lp__Ring_rp.html" title="declare that a ring is a field">toField</a> -- declare that a ring is a field</span></li>
<li><span><a href="___Fraction__Field.html" title="the class of all fraction fields">FractionField</a> -- the class of all fraction fields</span></li>
<li><span><a href="___Galois__Field.html" title="the class of all Galois fields">GaloisField</a> -- the class of all Galois fields</span></li>
<li><span><a href="___Quotient__Ring.html" title="the class of all quotient rings">QuotientRing</a> -- the class of all quotient rings</span></li>
<li><span><a href="_is__Unit.html" title="whether a ring element is a unit">isUnit</a> -- whether a ring element is a unit</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isField</tt> :</h2>
<ul><li>isField(EngineRing)</li>
<li>isField(Ring)</li>
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