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import pytest
import sympy as sp
from pystencils.utils import LinearEquationSystem
def test_linear_equation_system():
unknowns = sp.symbols("x_:3")
x, y, z = unknowns
m = LinearEquationSystem(unknowns)
m.add_equation(x + y - 2)
m.add_equation(x - y - 1)
assert m.solution_structure() == 'multiple'
m.set_unknown_zero(2)
assert m.solution_structure() == 'single'
solution = m.solution()
assert solution[unknowns[2]] == 0
assert solution[unknowns[1]] == sp.Rational(1, 2)
assert solution[unknowns[0]] == sp.Rational(3, 2)
m.set_unknown_zero(0)
assert m.solution_structure() == 'none'
# special case where less rows than unknowns, but no solution
m = LinearEquationSystem(unknowns)
m.add_equation(x - 3)
m.add_equation(x - 4)
assert m.solution_structure() == 'none'
m.add_equation(y - 4)
assert m.solution_structure() == 'none'
with pytest.raises(ValueError) as e:
m.add_equation(x**2 - 1)
assert 'Not a linear equation' in str(e.value)