MATLAB: Solving Diophantine Equations in MATLAB

Question

How do I solve Diophantine Equations in MATLAB?

Answer 1

Use the “solve” function. Before using “solve”, assume that the variables in the Diophantine equation are integers to ensure “solve” returns integer solutions. For example, solve the linear Diophantine equation 1027*x + 712*y = 1;

For MATLAB R2015a and later:

syms x y integer                % assume ‘x’ and ‘y’ are integers

eqn = 1027*x + 712*y == 1;       % declare the equation

[xSol, ySol] = solve(eqn,[x y])  % solve for ‘x’ and ‘y’

xSol =
-165
ySol =
238

For MATLAB R2014b or before:

syms x y
assume([x y], 'integer')        % assume ‘x’ and ‘y’ are integers
eqn = 1027*x + 712*y == 1;       % declare the equation
[xSol, ySol] = solve(eqn,[x y])  % solve for ‘x’ and ‘y’
xSol =
-165
ySol =
238

For details on “solve”, see: https://www.mathworks.com/help/symbolic/solve.html

For more information on assumptions, see: https://www.mathworks.com/help/symbolic/assumptions-for-symbolic-objects.html