I see, it's the Chapter IV. Are you going to implement the "Sieving method" (IV.3.1)? Or the "descent method"?
So, if I take the Pythagorean formula a^2 + b^2 = c^2, your new solver will be able to give me all integer solutions to this? That would be really cool. As far as a solver, I found this one (http://www.alpertron.com.ar/QUAD.HTM). But it can only do equations for "x" an "y". You need equations for "x", "y" and "z". I would suggest that you implement the solver, and then we just check the solutions numerically, that should be quite easy. We will not know for sure that you got all the solutions, but just cite the algorithm reference in the docstring, so that users know what it does. That would be good start. If somebody later finds some other software that can do this, or some other reference with examples and results, we can make sure that it returns all the solutions. Ondrej On Sun, Jul 14, 2013 at 11:21 PM, Thilina Rathnayake <[email protected]> wrote: > This is what I use. > > “The Algorithmic resolution of Diophantine Equations”, Nigel P. Smart, > Chapter IV, Quadratic ternary forms. > > Here is the book: > > > > On Mon, Jul 15, 2013 at 2:20 AM, Aaron Meurer <[email protected]> wrote: >> >> On Sun, Jul 14, 2013 at 12:09 AM, Thilina Rathnayake >> <[email protected]> wrote: >> > Hi All, >> > >> > I am planning to implement ternary quadratic forms, i.e equations of the >> > form, >> > a*x**2 + by**2 + cz**2 + fxy + gyz + hzx = 0. It would be better If I >> > can >> > find >> > a system which currently implement this so I can validate my results. If >> > you >> > know >> > of any system which solves this or a source which have good literature >> > on >> > the problem, >> > please let me know. >> >> What is the literature that you plan to use to get the algorithm in >> the first place? >> >> Aaron Meurer >> >> > >> > Also I have to solve the quadratic congruence x**2 = D (mod m) as a sub >> > problem to implement the algorithm I found. I found a few algorithms on >> > this >> > but >> > none of them explain precisely how to solve the general equation, all >> > they >> > do is >> > solve the equation for m prime and gcd(D, m) = 1 and just ask to use >> > Chinese >> > remainder theorem to combine the results to solve for the general case >> > where >> > m >> > is not prime and gcd(D, m) not necessarily equal to 1. Any help on this >> > would >> > be highly appreciated. >> > >> > 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. > > -- 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.
