> I am really excited to tell you that I implemented the algorithm for > solving generalized Pell equation. For the past week or so I was working > on the case B**2 - 4*A*C > 0 in quadratic DEs. Now, since the pell > equation is solved, I can solve the above case by transforming it to a > Pell equation. I looked a bit at the transformation and it's not that hard. > I will be able to code it and finish implementing quadratic DEs at the > end of this week.
Excellent, great job! > > Currently, solutions returned for the Pell equations are the basic solutions > of the particular equation passed to the Pell equation solver. We can > represent > other solutions by a recurrence. Both you and Aaron had answered on how > to represent the recurrence in the solution. If I am not mistaken rsolve() > currently > solves the recurrences in one variable. But recurrences we are talking here > involves two variables. So returning the recurrence itself won't be a good > idea. > What Wolfram alpha currently does is, it solves the recurrence and returns > the general solution without returning any other specific solutions. Would > that > be a bad idea since I am implementing lower level API's? Do you know how to solve the recurrence of two variables? Do you have some examples for Wolfram Alpha that you tried? Let me see some examples and think about the best way. > I coded the algorithms mostly looking at these two papers. > > [1] Solving the generalized Pell equation x**2 - D*y**2 = N, John P. > Robertson, > July 31, 2004, Pages 16 - 17 and 4 - 8. http://www.jpr2718.org/pell.pdf > > [2] Solving the equation ax**2 + bxy + cx**2 + dx + ey + f = 0, by John P. > Robertson. http://www.jpr2718.org/ax2p.pdf > > I added a commit. I would love to have your feedback on that. Please take > a look at that when you are free. I left some small comments. Ondrej > > Regards, > Thilina > > > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
