/usr/share/doc/axiom-doc/hypertex/numquotientfields.xhtml

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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Quotient Fields</div>
  <hr/>
The <a href="db.xhtml?Fraction">Fraction</a> domain implements quotients.
The elements must belong to a domain of category 
<a href="db.xhtml?IntegralDomain">IntegralDomain</a>: multiplication 
must be commutative and the product of two non-zero elements must not be
zero. This allows you to make fractions of most things you would think of,
but don't expect to create a fraction of two matrices. The abbreviation for
<a href="db.xhtml?Fraction">Fraction</a> is
<a href="db.xhtml?Fraction">FRAC</a>.

Use <a href="dbopdivide.xhtml">/</a> to create a fraction.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="a:=11/12" />
  <div id="ansp1"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="makeRequest('p2');"
    value="b:=23/24" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
The standard arithmetic operations are available.
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" 
    onclick="handleFree(['p1','p2','p3']);"
    value="3-a*b^2+a+b/a" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
Extract the numerator and denominator by using 
<a href="dbopnumer.xhtml">numer</a> and <a href="dbopdenom.xhtml">denom</a>,
respectively.
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" 
    onclick="handleFree(['p1','p4']);"
    value="numer(a)" />
  <div id="ansp4"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p5" class="subbut" 
    onclick="handleFree(['p2','p5']);"
    value="denom(b)" />
  <div id="ansp5"><div></div></div>
 </li>
</ul>
Operations like 
<a href="dbopmax.xhtml">max</a>, <a href="dbopmin.xhtml">min</a>,
<a href="dbopnegativeq.xhtml">negative?</a>,
<a href="dboppositiveq.xhtml">positive?</a>, and
<a href="dbopzeroq.xhtml">zero?</a> are all available if they are
provided for the numerators and denominators. See
<a href="numintegers.xhtml?Integer">Integer</a> for examples.

Don't expect a useful answer from 
<a href="dbopfactor.xhtml">factor</a>,
<a href="dbopgcd.xhtml">gcd</a>, or
<a href="dboplcm.xhtml">lcm</a> if you apply them to fractions.
<ul>
 <li>
  <input type="submit" id="p6" class="subbut" 
    onclick="makeRequest('p6');"
    value="r:=(x^2+2*x+1)/(x^2-2*x+1)" />
  <div id="ansp6"><div></div></div>
 </li>
</ul>
Since all non-zero fractions are invertible, these operations have
trivial definitions.
<ul>
 <li>
  <input type="submit" id="p7" class="subbut" 
    onclick="handleFree(['p6','p7']);"
    value="factor(r)" />
  <div id="ansp7"><div></div></div>
 </li>
</ul>
Use <a href="dbopmap.xhtml">map</a> to apply 
<a href="dbopfactor.xhtml">factor</a> to the numerator and denominator,
which is probably what you mean.
<ul>
 <li>
  <input type="submit" id="p8" class="subbut" 
    onclick="handleFree(['p6','p8']);"
    value="map(factor,r)" />
  <div id="ansp8"><div></div></div>
 </li>
</ul>

Other forms of fractions are available, Use
<a href="dbopcontinuedfraction.xhtml">continuedFraction</a>
to create a continued fraction.
<ul>
 <li>
  <input type="submit" id="p9" class="subbut" 
    onclick="makeRequest('p9');"
    value="continuedFraction(7/12)" />
  <div id="ansp9"><div></div></div>
 </li>
</ul>
Use <a href="dboppartialfraction.xhtml">partialFraction</a> to create a
partial fraction. 
See <a href="numcontinuedfractions.xhtml">continuedFraction</a>
and <a href="numpartialfractions.xhtml">PartialFraction</a> for
additional information and examples.
<ul>
 <li>
  <input type="submit" id="p10" class="subbut" 
    onclick="makeRequest('p10');"
    value="partialFraction(7,12)" />
  <div id="ansp10"><div></div></div>
 </li>
</ul>
Use conversion to create alternative views of fractions with objects
moved in and out of the numerator and denominator.
<ul>
 <li>
  <input type="submit" id="p11" class="subbut" 
    onclick="makeRequest('p11');"
    value="g:=2/3+4/5*%i" />
  <div id="ansp11"><div></div></div>
 </li>
</ul>
Conversion is discussed in detail in 
<a href="axbook/section-2.7.xhtml">Conversion</a>.
<ul>
 <li>
  <input type="submit" id="p12" class="subbut" 
    onclick="handleFree(['p11','p12']);"
    value="g::FRAC COMPLEX INT" />
  <div id="ansp12"><div></div></div>
 </li>
</ul>
 </body>
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / numquotientfields.xhtml
