diophantine_2d

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.

Licensing:

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

Languages:

diophantine_2d is available in a MATLAB version.

Related Data and Programs:

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

diophantine_2d_test

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_2d_basis.m, returns a basis for the solution space of a Diophantine equation in two variables.
• diophantine_2d_nonnegative.m, returns all nonnegative solutions of a Diophantine equation in two variables.
• diophantine_2d_positive.m, returns all strictly positive solutions of a Diophantine equation in two variables.
• diophantine_basis_print.m, prints solution space basis for a Diophantine equation.
• diophantine_equation_print.m, prints the data associated with a Diophantine equation.
• diophantine_residual.m, returns the residual b-a'x for a proposed solution.
• i4_is_integer.m, is true if an I4 stores an integer value.
• i4vec_gcd.m, returns the greatest common divisor (GCD) of the entries in an I4VEC.
• i4vec_is_integer.m, is true if an I4VEC stores an integer value.