diophantine_nd

diophantine_nd, a MATLAB code which is given a Diophantine equation in N variables, and returns all strictly positive solutions or all nonnegative solutions.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

diophantine_nd is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

diophantine, a MATLAB code which finds one solution of a diophantine equation in any number of variables.

diophantine_2d, a MATLAB code which is given a Diophantine equation in 2 variables, and can characterize all solutions, all strictly positive solutions, or all nonnegative solutions.

diophantine_3d, a MATLAB code which is given a Diophantine equation in 3 variables, and can return all strictly positive solutions, or all nonnegative solutions.

diophantine_4d, a MATLAB code which is given a Diophantine equation in 4 variables, and can return all strictly positive solutions, or all nonnegative solutions.

diophantine_5d, a MATLAB code which is given a Diophantine equation in 5 variables, and can return all strictly positive solutions, or all nonnegative solutions.

diophantine_nd_doc

diophantine_nd_test

Reference:

• William Gilbert, Ann Pathria,
  Linear Diophantine Equations,
  https://www.math.uwaterloo.ca/~wgilbert/Research/GilbertPathria.pdf
• Aaron Greicius,
  Linear Diophantine Equations,
  https://gauss.math.luc.edu/greicius/Math201/Fall2012/Lectures/linear-diophantine.article.pdf

Source Code:

• diophantine_nd_check.m, checks that a given Diophantine problem is well posed.
• diophantine_nd_nonnegative.m, returns all nonnegative solutions of a Diophantine equation in N variables.
• diophantine_nd_nonnegative_bounded.m, returns all solutions of a Diophantine equation in N variables for which each component is nonnegative and less than a given bound.
• diophantine_nd_positive.m, returns all strictly positive solutions of a Diophantine equation in N variables.
• diophantine_bounds_print.m, prints the upper and lower bounds imposed on solutions of a Diophantine equation.
• diophantine_equation_print.m, prints the data associated with a Diophantine equation.
• diophantine_solution_print.m, prints the solutions associated with a Diophantine equation.