It would certainly be nice to have Maxima solve specific families of
Diophantine equations, even if the general case is unsolvable. Perhaps you
could implement Alpern's method for Maxima? If you prefer to start from
code rather than English, you could ask Alpern for permission to translate
his code.
-s
On Fri, Dec 7, 2012 at 4:24 PM, Benito van der Zander <benito at benibela.de>wrote:
> Hi,
> is there any way to get all solution of a Diophantine equation
> symbolically?
> I.e. all solutions of Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
> where x,y are unknown integers, and A,B,C,D,E,F are constant terms (mostly
> numbers, even 0, but some might contain other variables)
>
> There is an long, universal solution algorithm:
> http://www.alpertron.com.ar/**METHODS.HTM<http://www.alpertron.com.ar/METHODS.HTM>;
> And you can solve them, by looking up the corresponding case there, and
> putting the terms in the expressions given there,
> but that is boring. And tedious.
>
> Of course the solutions can become quite complex, like (di - E) / B for
> any di \in divisors(DE - BF).
> But Maxima could calculate DE - BF, and print it, or if it becomes a term
> without other variables, even directly calculate the divisors.
> (and that DE - BF is actually an easy case)
>
> Benito
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