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<head><title>FractionField -- the class of all fraction fields</title>
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<div><h1>FractionField -- the class of all fraction fields</h1>
<div class="single"><h2>Description</h2>
<div>Macaulay2 provides for fraction fields of integral domains.<p/>
In some cases, normal forms of fractions makes sense, but in general for fraction fieldss of quotient rings, there is no notion of normal form for a fraction. In other words, fractions may be equal without displaying the same numerator and denominator.<p/>
Computations over fraction fields, or polynomial rings over fraction fields, especially Gröbner basis computations, are much slower than over prime fields. Still, an attempt is made to speed up these computations as much as possible, and more is planned in the future.<p/>
For an overview, see <a href="_fraction_spfields.html" title="">fraction fields</a> and <a href="_frac.html" title="construct a fraction field">frac</a>.<h4>Useful functions for use with fractions and fraction fields include:</h4>
<ul><li><span><a href="_frac.html" title="construct a fraction field">frac</a> -- construct a fraction field</span></li>
<li><span><a href="_numerator.html" title="numerator of a fraction">numerator</a> -- numerator of a fraction</span></li>
<li><span><a href="_denominator.html" title="denominator of a fraction">denominator</a> -- denominator of a fraction</span></li>
<li><span><a href="_liftable.html" title="whether lifting to another ring is possible">liftable</a> -- whether lifting to another ring is possible</span></li>
<li><span><a href="_lift.html" title="lift to another ring">lift</a> -- lift to another ring</span></li>
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<div class="waystouse"><h2>Functions and methods returning a fraction field :</h2>
<ul><li><span><a href="_frac.html" title="construct a fraction field">frac</a> -- construct a fraction field</span></li>
</ul>
<h2>Methods that use a fraction field :</h2>
<ul><li><span><tt>degrees(FractionField)</tt> (missing documentation<!-- tag: (degrees,FractionField) -->)</span></li>
<li><span>describe(FractionField), see <span><a href="_describe.html" title="real description">describe</a> -- real description</span></span></li>
<li><span>dim(FractionField), see <span><a href="_dim_lp__Ring_rp.html" title="compute the Krull dimension">dim(Ring)</a> -- compute the Krull dimension</span></span></li>
<li><span>frac(FractionField), see <span><a href="_frac.html" title="construct a fraction field">frac</a> -- construct a fraction field</span></span></li>
<li><span>numgens(FractionField), see <span><a href="_numgens_lp__Ring_rp.html" title="number of generators of a polynomial ring">numgens(Ring)</a> -- number of generators of a polynomial ring</span></span></li>
<li><span><tt>precision(FractionField)</tt> (missing documentation<!-- tag: (precision,FractionField) -->)</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Fraction__Field.html" title="the class of all fraction fields">FractionField</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Engine__Ring.html" title="the class of rings handled by the engine">EngineRing</a> < <a href="___Ring.html" title="the class of all rings">Ring</a> < <a href="___Type.html" title="the class of all types">Type</a> < <a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> < <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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