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On Wed, Jul 3, 2013 at 7:30 PM, Thilina Rathnayake <[email protected]>wrote: > > > > Hi Ondrej, > > I don't know much about solving recurrence relations on two variables, but > the sources > I am referencing provides the solutions for the recurrences involved with > Pell equation. > So, I think that would be enough. > > Concerning the solutions of x**2 - 13*y**2 = 27, solutions returned by > diop_pell > are: > >>> diop_pell(13, 27) > [(220, 61), (40, 11), (768, 213), (12, 3)] > > Here is how wolfram alpha represents it: > http://www.wolframalpha.com/input/?i=x**2+-+13*y^2+%3D+27 > > They provide general solutions for each class. > (Look in the box named "Integer solutions") > > Regards, > Thilina > > > > > On Wed, Jul 3, 2013 at 2:55 AM, Ondřej Čertík <[email protected]>wrote: > >> > 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. >> >> >> > -- 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.
