This is an application written in Common Lisp, which attempts to find solutions for diophantine equations.
Currently, not all equations are supported (you can only enter equations with integer coefficients and exponents). The program also attempts to find integer values for the variables.
I expect you to have Quicklisp installed. Simply clone this repository
(directly, or create a symlink) on your local-projects directory. Then load the
system and run the REPL:
(ql:quickload :diophantine)
(diophantine:ask-for-equation)The REPL asks you to input an equation to perform the checking. The equation
should have a single = sign, and each side of the equations can have any number
of different variables.
Each variable should be written in the form cx^e, where c is a numeric
coefficient, and e is a numeric exponent. Both of these numbers can be negative
as well, though it is preferable that you leave the negative symbol between two
factors.
Below are some valid examples of equations.
x^2 + y^2 = c^2 w^3 + x^3 = y^3 + z^3 12x^3 + 3y^2 - 4z = 0
While the program attempts to find a solution, it will debrief the user periodically on the current state of the program. If the program takes too long, it will interrupt its work and ask the user if it should proceed.
- Currently does not determine whether a solution is trivial;
- Only positive values are being tested;
- Parser doesn’t check variable usage, pretending each factor is just a different variable (not that the program should work if any variable is repeated, though);
- Range evolution still makes possible to attempt redundant solutions.
This project is distributed under a 2-clause BSD License. See LICENSE for details.
Copyright (c) 2018 Lucas Vieira