diophantine

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

Licensing:

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

Languages:

diophantine is available in a MATLAB version.

Related Data and Programs:

diophantine_test

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 returns all strictly positive solutions, or all nonnegative solutions.

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

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

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

i4mat_rref2, a MATLAB code which computes a version of the reduced row echelon form of an integer matrix.

row_echelon_integer, a MATLAB code which carries out the exact computation of the integer row echelon form (IREF) and integer reduced row echelon form (IRREF) of an integer matrix.

subset, a MATLAB code which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems. Some routines for continued fractions are included.

Reference:

• William Gilbert, Ann Pathria,
  Linear Diophantine Equations,
  https://www.math.uwaterloo.ca/~wgilbert/Research/GilbertPathria.pdf

Source Code:

• diophantine_basis.m, returns a basis for the solution space of a Diophantine equation.
• diophantine_basis2.m, returns a basis for the solution space of a Diophantine equation.
• diophantine_basis_print.m, prints a basis for the solution space of a Diophantine equation.
• diophantine_equation_print.m, prints the data associated with a Diophantine equation.
• diophantine_nonnegative.m, finds nonnegative diophantine solutions.
• diophantine_residual.m, returns the residual b-a'x for a proposed solution.
• diophantine_solution_print.m, prints the solution of a diophantine equation.
• i4_is_integer.m, checks that a value is actually an integer.
• i4vec_gcd.m, finds the greatest common divisor of the elements of an integer vector.
• i4vec_is_integer.m, checks that all entries in a vector are integers.