/usr/share/doc/axiom-doc/hypertex/calseries2.xhtml

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  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Coefficients of Power Series</div>
  <hr/>
You can extract any coefficient from a power series -- even on that
hasn't been computed yet. This is possible because in Axiom, infinite
series are represented by a list of the coefficients that have already
been determined, together with a function for computing additional 
coefficients. (This is known as lazy evaluation.) When you ask for a
coefficient that hasn't yet been computed, Axiom computes whatever
additional coefficients it needs and then stores them in the representation
of the power series.

Here's an example of how to extract the coefficients of a power series.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="x:=series('x)" />
  <div id="ansp1"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="handleFree(['p1','p2']);"
    value="y:=exp(x)*sin(x)" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
This coefficient is readily available
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" 
    onclick="handleFree(['p1','p2','p3']);"
    value="coefficient(y,6)" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
But let's get the fifteenth coefficient of y
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" 
    onclick="handleFree(['p1','p2','p4']);"
    value="coefficient(y,15)" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
If you look at y then you see that the coefficients up to order 15 have 
all been computed.
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 <li>
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    onclick="handleFree(['p1','p2','p4','p5']);"
    value="y" />
  <div id="ansp5"><div></div></div>
 </li>
</ul>
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / calseries2.xhtml
