File r37/lisp/csl/html/r37_0170.html artifact 47296cdf53 part of check-in 9992369dd3

<A NAME=PF>

<TITLE>PF</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>PF</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
 <P>
<P>
 <P> <H3> 
syntax: </H3>
pf(&lt;expression&gt;,&lt;variable&gt;) 
<P>
<P>
<P>
<em>pf</em>transforms &lt;expression&gt; into a 
<A HREF=r37_0053.html>list</A> of partial fraction 
s 
with respect to the main variable, &lt;variable&gt;. <em>pf</em> does a 
complete partial fraction decomposition, and as the algorithms used are 
fairly unsophisticated (factorization and the extended Euclidean 
algorithm), the code may be unacceptably slow in complicated cases. 
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
pf(2/((x+1)^2*(x+2)),x); 

      2    -2        2
  	{-----,-----,------------} 
    X + 2 X + 1  2
                X  + 2*X + 1


off exp; 

pf(2/((x+1)^2*(x+2)),x);
 

     2    - 2     2
  {-----,-----,--------} 
   X + 2 X + 1        2
               (X + 1)


for each j in ws sum j; 

         2
  ----------------
                2
  ( + 2)*(X + 1)

</TT></PRE><P><P>
<P>
If you want the denominators in factored form, turn 
<A HREF=r37_0284.html>exp</A> off, as 
shown in the second example above. As shown in the final example, the 

<A HREF=r37_0047.html>for</A> <em>each</em> construct can be used to recombine t
he terms. 
Alternatively, one can use the operations on lists to extract any desired 
term. 
<P>
<P>
<P>