Polfatt5  Copyright (C) 2012  Marco Spadini
    
This program comes with ABSOLUTELY NO WARRANTY. 
This is free software, and you are welcome to redistribute it under certain 
conditions.  
See the GNU General Public License for more details.


About the author:
Marco Spadini                         
Dipartimento di Matematica e Informatica,
Via S. Marta 3, 50139 Firenze,       
ITALY 

web: http:\\\www.dma.unifi.it\~spadini
e-mail: marco.spadini@math.unifi.it

Description:

   This is a port to GNU Pascal, with slight modifications, of a program I  
wrote in 1993 in TurboPascal as a test. Its purpose is to factorize in Q[X] 
(actually in Z[X]), polynomials with integer (small) coefficients.          
   Unlike serious and powerful program based on commutative alebra tools,   
This program is based on the Schubert-Kronecker algorithm which is not very 
efficient, actually, I think it has an exponential complexity... not good   
at all for serious factoring. However, for polynomials with rather small    
coefficients and low degree (let us say smaller than 7 or 8) I find it is   
fast and reliable. (One should also beware of factors that have rational    
cofficients with large numerators or denominators.)                         
  In fact, there is a limitation built in this program (not in the          
underlying algorithm, only in the implementation): it cannot correctly      
treat irreducible factors of degree higher than 5; so, for instance, if a   
polynomial P of degree 12 has two irreducible factors of degree 6, the      
program will incorrectly state that P is irreducible (it would also take a  
_long_ time to say so). For this reason, NEVER use this program to          
factorize anything of degree larger than 11 (although it might be able to   
factorize it: an answer with factors of degree at most five is certainly    
correct). This strange limitation is due to the  nasty nested cycle in      
function calnodi. I could have used some cleverer way  to allow for         
arbitrary degree but, as I said, this was meant to be a test and  neither   
then I felt, nor now I feel, inclined to waste time on a test (one  should  
bear in mind the exponential complexity of the algorithm which make  rather 
pointless to implement a mechanism for arbitrarily large degree). What      
is more, now (for me) this is merely legacy code (but fun to look at!).     
                                                                            
One more caveat. Beware that the program wants integer coefficients for the 
input polynomial but quietly accepts other stuff. If you feed unexpected    
data you may get what you deserve: unpredictable behaviour!                 
 
                                                                           
RUNNING the program:                                                      
                                                                            
 This is source code written in GNU Pascal. To run the program obtain   
 the compiler (gpc under Linux) compile the source file and launch the  
 object according to the rules of your system. For instance, in my      
 Linux box I run:                                                       

    gpc POLFATT5.pas -o polfatt                                            
    ./polfatt                                                              
                                                                            
                                                                            

For any issues concerning this program please contact the author
Have fun!