Using sympy to solve an inequality with two variables

June 1, 2024

I’m trying to use Sympy to solve 0 < x + y <= 4 in the case where both x and y are positive integers or 0, in the hopes to have it return a list of tuples that solves the inequality.

import sympy as sp

# Assign variables
x, y = sp.symbols('x y', natural0 = True)

# Define the inequalities
ineq1 = sp.And(0 < x + y, x + y <= 4)
ineq2 = x >= 0
ineq3 = y >= 0

# Solve the inequality
result = sp.solve([ineq1, ineq2, ineq3], [x,y])

Expected result:
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (4, 0)]

>Solution :

Solve() can not do that. You can just do it manually:

import sympy as sp

x, y = sp.symbols('x y')

ineq1 = sp.And(0 < x + y, x + y <= 4)
ineq2 = x >= 0
ineq3 = y >= 0

result = []
for xi in range(5):
    for yi in range(5):
        A = ineq1.subs({x: xi, y: yi})
        B = ineq2.subs({x: xi, y: yi})
        C = ineq3.subs({x: xi, y: yi})
        if A and B and C:
            result.append((xi, yi))

print(result)