id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
16590,interface sympy Diophantine function(s),Ralf Stephan,Ralf Stephan,"In sympy the solution of Diophantine equations is available for several types of equations (http://docs.sympy.org/latest/modules/solvers/diophantine.html). This meta-ticket aims at
* implementing a global `solve_diophantine()` function that wraps the sympy functionality and takes
1. symbolic expressions (up to order 2)
2. univariate polynomials (up to order 2)
3. multivariate polynomials (up to order 2)
4. quadratic forms
* where useful implementing member functions `solve_diophantine()`
It is however not possible to directly make the resp. sympy functions fully usable with Sage, from within Sage. If desired that must be done in sympy.
Until then there is the following workaround:
{{{
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)}
}}}",enhancement,closed,major,sage-6.7,number theory,fixed,"pellian, integers, solution",John Cremona,,Ralf Stephan,"Kannappan Sampath, Travis Scrimshaw",N/A,,9a8c2f3b419b5f199a7f2b1d61ac507924f559b1,9a8c2f3b419b5f199a7f2b1d61ac507924f559b1,,