Same as the "prtlfrac.rav" program currently on archive except 
this version includes PRTLFRAC,PDERIV,PMUL,PDIV,PROOT in 1 PROGRAM.


You must first run the uudecode "UUD20" program which will create the
"POLYNOML.85P" file and then you must run the "LINK85" program to load
the file to your TI85.  The reason for sending this version 
which is basically the same as the earlier prtlfrac.rav 
program is because in the earlier version, you needed to run 
the pmul, pdiv, and execute the poly command to get the roots 
etc.  Since I am using these routines in the prtlfrac.rav 
program to begin with, I figured why not put it as a menu 
option so you have to run other programs alos.  This also 
frees up some additional memory.  I AM PLANNING ON WRITING 
OTHER POLYNOMIAL HANDLING ROUTINES THAT I WILL PROBABLY ADD TO 
THE EXISTING "POLYNOML.RAV" PROGRAM.  If I do, I will post a 
note for all.


                          Running the program.

Simply execute the "POLYNOML" program by selecting it from the PROG
menu.  Select the "Pmul" of "Pdiv" etc. for polynomial 
multiplication.  The "Pder" menu will let you take the n'th 
derivative of a function.  The polynomial must be entered in 
list form as usual.  The "Proot" option will give you the 
roots of a polynomial entered in list form.  If you select 
the "Prtl" menu, you will be prompted to enter N(x) and the roots 
to D(x).  N(x) is the numerator of the function to be worked on.  
Accordingly, D(x) is the denominator of the same function.  Due 
to accuracy problems, I was forced to write a routine
where you must enter the roots of the denominator versus entering the
denominator polynomial itselt.  Anyway, I latter emply the multiply 
routine and build the needed denominator.  It is a good idea to 
enter duplicated roots of D(x) at the same time, although not 
necessary.  After a while, the partial fraction decomposition is 
done and the necessary information presented in matrix form.  
The matrix is also saved under the variable "x" for your future review.  Again, due to accuracy problems on the TI, I have employed
a routine which randomly selects a number and checks the value 
of this number in the original function, and then in the newly 
decomposed fraction form.  If a difference between the two 
exist by more than the "tol" value setup in you TI-85, the 
matrix presented is displayed with question marks. I have 
found that in most cases, the difference is trivial and can be 
ignored.  The difference between the two versions are held in 
the greek character "omega" for your further review.

                                          2  
Example:                                 x
                           F(x) = -------------------
                                        2
                                   (x+1)   (x+2)

                                                           2
enter in LIST form N(x): {1,0,0}        which represents 1x  + 0x + 0
enter in LIST form Roots of D(x): {-1,-1,-2}  which shows -1 as a double root

the solution presented in matrix form says that the fuction F(x) can also
be represented as:

        -3             1              4
     --------  +  -----------  +  ----------
            1            2               1
       (x+1)         (x+1)          (x+2)

The numerator values (-3,1,4) are presented in row 1 of the matrix
The values (x+n) where n is 1,1,2 are presented in row 2 of the matrix
The powers on the denominator (1,2,1) appear in row 3.

The matrix has been organixed such that each column corresponds to each term.

Again, as previously mentioned, if the computational difference greater
than the internal "tol" value exist between the original function and
the decomposed form, the screen has question marks displed next to the
sample matrix.  In most cases this is not anything significant.
One last note,  as always, I have made common practice to start all 
program variables with the greek letter omega.  This makes deletion 
of the variables much easier since they appear all together in the
memory management screen.

