def test_solve_system_of_3x3(self):
system = symbolic.System([
-x1 + 2*x2 - 3*x3 == 4,
5*x1 - 6*x2 + 7*x3 == -8,
9*x1 + 10*x2 - 11*x3 == 12]
for (x1, x2, x3) in symbolic.Any)
r = solvers.solve(system)
self.assertAlmostEqual(r[0].right, 0.0)
self.assertAlmostEqual(r[1].right, -1.0)
self.assertAlmostEqual(r[2].right, -2.0)
def test_expanded_coefficients_matrix(self):
system = symbolic.System([
-x1 + 2*x2 - 3*x3 == 4,
5*x1 - 6*x2 + 7*x3 == -8,
9*x1 + 10*x2 - 11*x3 == 12]
for (x1, x2, x3) in symbolic.Any)
matrix = [[-1, 2, -3, 4],
[ 5, -6, 7, -8],
[ 9, 10, -11, 12]]
expected = matrix, [core.Eq]*3
obtained = solvers.expanded_coefficients_matrix(system)
self.assertEqual(obtained, expected)
def test_unsorted_expanded_coefficients_matrix(self):
"""Should extract all coefficients of an unsorted system of linear
equalities."""
system = symbolic.System([
-x1 + 2*x2 == 4 + 3*x3,
7*x3 + 5*x1 - 6*x2 == -8,
-11*x3 + 10*x2 + 9*x1 == 12]
for (x1, x2, x3) in symbolic.Any)
matrix = [[-1, 2, -3, 4],
[ 5, -6, 7, -8],
[ 9, 10, -11, 12]]
expected = matrix, [core.Eq]*3
obtained = solvers.expanded_coefficients_matrix(system)
self.assertEqual(obtained, expected)
def test_solve_inequality(self):
system = symbolic.System([b == g, -1 < g, g < r, -1 < r, r < 256]
for (r, g, b) in symbolic.Any)
obtained = solvers.solve(system)
self.assertAlmostEqual(obtained, expected)
def test_zero_equation(self):
expr = symbolic.System(
0 == x + 4 for x in symbolic.Any)
result = solvers.solve(expr)
self.assertEqual(result, core.Eq('x', -4.0))
def test_solve_single_variable_linear_equation(self):
expr = symbolic.System(
x - 2*x + 5*x - 46*(235-24) == x + 2 for x in symbolic.Any)
result = solvers.solve(expr)
self.assertEqual(result, core.Eq('x', 3236.0))