25. POLYSOLV Command                                                            
                                                                                
     The POLYSOLV command will solve for the roots on an equation with          
either real or complex coefficients. If desired an estimate of the error        
in the root can be calculated.  The POLYDIVIDE sentence can be used for         
polynomial division.  If the POLYDIVIDE sentence is present, only               
polynomial division is performed and NO options or parameters are               
passed on the POLYSOLV sentence. The POLYDIVIDE sentence lists the roots        
of the polynomial. It is useful in testing models for stationarity.             
                                                                                
     Form of command.                                                           
                                                                                
     B34SEXEC POLYSOLV options parameters$                                      
       POLYDIVIDE  parameters$                                                  
       PGMCARDS$                                                                
            coefficients here  free format                                      
       B34SRETURN$                                                              
       B34SEEND$                                                                
                                                                                
Solving polynomials.                                                            
                                                                                
Options for POLYSOLV sentence.                                                  
                                                                                
       REAL     -  Coefficients will be real.  This is default.                 
                                                                                
       COMPLEX  -  Coefficients will be complex.                                
                                                                                
Parameters for POLYSOLV sentence.                                               
                                                                                
       IORDER = n1  Sets maximum order of the polynomial. Required.             
                                                                                
       IN = n2      Sets number of coefficients supplied.                       
                        Default = IORDER + 1. IN is only needed if INPU         
                        set NE 0. If IN = 0, program counts cards after         
                        PGMCARDS$ and before B34SRETURN$                        
                                                                                
       IFMT = n3    =0  Coefficients read in free format (see below).           
                    =1  Coefficients read in DP unformatted from unit           
                        INPU.                                                   
                    =2  Coefficients read from unit INPU following              
                        format (I5,3E16.8).                                     
                                                                                
       INPU = n4    Sets coefficient input unit. Defaults to 5 where            
                    coefficients are read after PGMCARDS$ and before            
                    B34SRETURN$. If INPU NE 5, then PGMCARDS$ and               
                    B34SRETURN$ sentences not used.                             
                                                                                
Method to input coefficients.                                                   
                                                                                
     Coefficients are inputted with PGMCARDS$ and B34SRETURN$ sentences         
in free format. For real case on each line put:                                 
                                                                                
           COEF order,  Real part of coef                                       
                                                                                
For the complex case, put the imaginary part of the coeffient after the         
real part.                                                                      
                                                                                
Sample problem.                                                                 
                                                                                
     Solve the equation 0 = 1 -3X + 4X**2 - 2X**3                               
                                                                                
   b34sexec polysolv real iorder=3$                                             
       pgmcards$                                                                
       0 1.0                                                                    
       1 -3.                                                                    
       2 4.                                                                     
       3 -2.                                                                    
       b34sreturn$                                                              
       b34seend$                                                                
                                                                                
                                                                                
Dividing Polynomials.                                                           
                                                                                
Parameters for POLYDIVIDE sentence.                                             
                                                                                
       TOP(r1,r2,..)  Specify terms for numerator.                              
                                                                                
       BOT(rk,rj,..)  Specify terms for denominator.                            
                                                                                
       NTERMS=n1      Sets number of terms for answer. Default = 12.            
Sample problem.                                                                 
                                                                                
  Solve the problem (1.0 - .4B -.3B**3)/(1.0 - .5B) for 40 terms.               
                                                                                
b34sexec polysolv$                                                              
 polydivide top(1.0, -.4 0.0 -.3) bot(1.0, -.5)  nterms=40$                     
 b34seend$                                                                      
                                                                                
Example that shows that sum will converge                                       
                                                                                
             if sqrt(real*2 + imag*2) > 1                                       
                                                                                
         b34sexec polysolv$ polydivide top(1.0) bot(1.0 -.5) $ b34seend$        
         b34sexec polysolv$ polydivide top(1.0) bot(1.0 -1.01)                  
                  nterms=60 $ b34seend$                                         
         b34sexec polysolv$ polydivide top(1.0 -.4 0.0, -.3)                    
                  bot(1.0 -.5) nterms=40$ b34srun;