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

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  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Simplification</div>
  <hr/>
Simplifying an expression often means different things at different times.
Axiom offers a large number of "simplification" functions. The most common
one, which performs the usual trigonometric simplifications is
<a href="dbopsimplify.xhtml">simplify</a>.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="f:=cos(x)/sin(x)*log(sin(x)^2/(cos(x)^2+sin(x)^2))" />
  <div id="ansp1"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="handleFree(['p1','p2']);"
    value="g:=simplify f" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
If the result of <a href="dbopsimplify.xhtml">simplify</a> is not 
satisfactory, specific transformations are available. For example, to
rewrite g in terms of secants and cosecants instead of sines and cosines,
issues:
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" 
    onclick="handleFree(['p1','p2','p3']);"
    value="h:=sin2csc cos2sec g" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
To apply the logarithm simplification rules to h, issue:
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" 
    onclick="handleFree(['p1','p2','p3','p4']);"
    value="h:=expandLog h" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
Since the square root of x^2 is the absolute value of x and not x itself,
algebraic radicals are not automatically simplified, but you can 
specifically request it by calling 
<a href="dboprootsimp.xhtml">rootSimp</a>:
<ul>
 <li>
  <input type="submit" id="p5" class="subbut" 
    onclick="makeRequest('p5');"
    value="f1:=sqrt((x+1)^3)" />
  <div id="ansp5"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p6" class="subbut" 
    onclick="makeRequest('p6');"
    value="rootSimp f1" />
  <div id="ansp6"><div></div></div>
 </li>
</ul>
There are other transformations which are sometimes useful. Use the 
functions 
<a href="dbopcomplexelementary.xhtml">complexElementary</a> and
<a href="dboptrigs.xhtml">trigs</a> to go back and forth between
the complex exponential and trigonometric forms of an elementary function.
<ul>
 <li>
  <input type="submit" id="p7" class="subbut" 
    onclick="makeRequest('p7');"
    value="g1:=sin(x+cos x)" />
  <div id="ansp7"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p8" class="subbut" 
    onclick="handleFree(['p7','p8']);"
    value="g2:=complexElementary g1" />
  <div id="ansp8"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p9" class="subbut" 
    onclick="handleFree(['p7','p8','p9']);"
    value="trigs g2" />
  <div id="ansp9"><div></div></div>
 </li>
</ul>
Similarly, the functions
<a href="dboprealelementary.xhtml">realElementary</a> and
<a href="dbophtrigs.xhtml">htrigs</a> convert hyperbolic functions in
and out of their exponential form.
<ul>
 <li>
  <input type="submit" id="p10" class="subbut" 
    onclick="makeRequest('p10');"
    value="h1:=sinh(x+cosh x)" />
  <div id="ansp10"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p11" class="subbut" 
    onclick="handleFree(['p10','p11']);"
    value="h2:=realElementary h1" />
  <div id="ansp11"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p12" class="subbut" 
    onclick="handleFree(['p10','p11','p12']);"
    value="htrigs h2" />
  <div id="ansp12"><div></div></div>
 </li>
</ul>
Axiom has other transformations, most of which are in the packages
<a href="db.xhtml?ElementaryFunctionStructurePackage">
ElementaryFunctionStructurePackage</a>,
<a href="db.xhtml?TrigonometricManipulations">
TrigonometricManipulations</a>,
<a href="db.xhtml?AlgebraicManipulations">AlgebraicManipulations</a>, and
<a href="db.xhtml?TranscendentalManipulations">
TranscendentalManipulations</a>. If you need to apply a simplification
rule not built into the system you can use Axiom's 
<a href="funpatternmatching.xhtml">pattern matcher</a>.
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / funsimplification.xhtml
