Program:	PARFRAC	
Author:	Dave Gaebler
February 17, 1999

Variables used:A,B,C,D,E,F,G,[A],L1,L2,L3,listL,listN,listLPROD,listQPROD,listLP,listQP,
listQX,listQC (I know, too many lists)
This program breaks up a rational function into partial fractions (if you don't know what 
they are, consult a calculus textbook).  It assumes that the numerator is of lesser degree 
than the denominator (if not, use my POLYDIV program!) and that the denominator has already 
been factored into linear and irreducible (i.e. no real roots) quadratic factors.  It uses 
the method of comparing coefficients, in case you care.  You are asked to enter the 
numerator as a list of coefficients (e.g. x^3-3x+5 would be {1,0,-3,5}).  Then enter the 
constant terms of all the linear factors in the denominator.  (It assumes that the linear 
factors are in the form x-a.  If not, factor the x coefficient out of your entire rational 
function.)  If your linear factors are x-2 and x+3, enter {-2,3}.  Then list the power of 
each linear factor.  For example, if the (x-2) was squared but the (x+3) wasn't, enter 
{2,1}.  Then enter a list of the x terms of the quadratic factors (again, assumes a unity 
lead coefficient.)  Then a list of the constant terms of the quadratic factors.  For 
example, if (x^2+1) was a factor, you would enter {0} for the x coefficients and {1} for 
the constant terms.  Finally you are asked for the power list for the quadratic factors.  
After thinking a while, the decomposition will be displayed.  Our example, 
(x^3-3x+5)/((x-2)^2*(x+3)*(x^2+1)) decomposes into 
7/25(x-2)^2+2/25(x-2)-13/250(x+3)+(101-7x)/250(x^2+1).  Although big rational functions 
take a while (a 13th degree numerator over a 20th degree denominator took three minutes 
and 40 seconds), it should be able to do anything in your calculus textbook in 
ten seconds or less.

