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

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  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Algebraic Functions</div>
  <hr/>
Algebraic functions are functions defined by algebraic equations. There are
two ways of constructing them, either by using rational powers or implicitly.
For rational powers, use <a href="dbopstarstar.xhtml">**</a> or the system
functions <a href="dbopsqrt.xhtml">sqrt</a> and 
<a href="dbopnthroot.xhtml">nthRoot</a> for square and nth roots.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="f:=sqrt(1+x^(1/3))" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
To define an algebraic function implicitly use 
<a href="dboprootof.xhtml">rootOf</a>. The following line defines a function
y of x satisfying the equation 
<pre>
  y^3 = x*y-y^2-x^3+1
</pre>
<ul>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="makeRequest('p2');"
    value="y:=rootOf(y^3+y^2-x*y+x^3-1,y)" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
You can manipulate, differentiate or integrate an implicitly defined
algebraic function like any other Axiom function.
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" 
    onclick="handleFree(['p2','p3']);"
    value="differentiate(y,x)" />
  <div id="ansp3"><div></div></div>
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</ul>
Higher powers of algebraic functions are automatically reduced during
calculations.
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 <li>
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    onclick="handleFree(['p2','p4']);"
    value="(y+1)^3" />
  <div id="ansp4"><div></div></div>
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</ul>
But denominators are not automatically rationalized.
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 <li>
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    onclick="handleFree(['p1','p5']);"
    value="g:=inv f" />
  <div id="ansp5"><div></div></div>
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</ul>
Use <a href="dbopratdenom.xhtml">ratDenom</a> to remove the algebraic
quantities from the denominator.
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 <li>
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    onclick="handleFree(['p1','p5','p6']);"
    value="ratDenom g" />
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / funalgebraicfunctions.xhtml
