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Indeed, there is no code in Sage to solve the quadratic Diophantine in two variables like Alpern's program does. You are welcome to contribute, and I'm willing to help. Contact me through my G+ page if you are interested.

Indeed, there is no code in Sage to solve the quadratic Diophantine in two variables like Alpern's program does. You are welcome to contribute, and I'm willing to help. Contact me through my G+ page if you are interested.

Indeed, there is no code in Sage to solve the quadratic Diophantine in two variables like Alpern's program does. You are welcome to contribute, and I'm willing to help. Contact me through my G+ page if you are interested.

The most immediate task would be to integrate the sympy stuff. I have opened this ticket:

http://trac.sagemath.org/ticket/16590

sage: from sympy.solvers.diophantine import *
sage: from sympy import sympify
sage: var('x,y,m')
(x, y, m)
sage: diop_solve(sympify(x**2 + y**2 - 5))
{(-2, -1), (-2, 1), (2, -1), (2, 1)}
sage: diop_solve(sympify(x**2 - 3*y**2 - 1))
{(-sqrt(3)*(-sqrt(3) + 2)**t/2 + (-sqrt(3) + 2)**t + sqrt(3)*(sqrt(3) + 2)**t/2 + (sqrt(3) + 2)**t,
  -sqrt(3)*(-sqrt(3) + 2)**t/3 + (-sqrt(3) + 2)**t/2 + (sqrt(3) + 2)**t/2 + sqrt(3)*(sqrt(3) + 2)**t/3)}