def test_diop_ternary_quadratic(): # Commented out test cases should be uncommented after # the bug with factor_list() gets merged. assert check_solutions(2*x**2 + z**2 + y**2 - 4*x*y) assert check_solutions(x**2 - y**2 - z**2 - x*y - y*z) assert check_solutions(3*x**2 - x*y - y*z - x*z) assert check_solutions(x**2 - y*z - x*z) # assert check_solutions(5*x**2 - 3*x*y - x*z) assert check_solutions(4*x**2 - 5*y**2 - x*z) assert check_solutions(3*x**2 + 2*y**2 - z**2 - 2*x*y + 5*y*z - 7*y*z) assert check_solutions(8*x**2 - 12*y*z) assert check_solutions(45*x**2 - 7*y**2 - 8*x*y - z**2) assert check_solutions(x**2 - 49*y**2 - z**2 + 13*z*y - 8*x*y) assert check_solutions(90*x**2 + 3*y**2 + 5*x*y + 2*z*y + 5*x*z) assert check_solutions(x**2 + 3*y**2 + z**2 - x*y - 17*y*z) assert check_solutions(x**2 + 3*y**2 + z**2 - x*y - 16*y*z + 12*x*z) assert check_solutions(x**2 + 3*y**2 + z**2 - 13*x*y - 16*y*z + 12*x*z) assert check_solutions(x*y - 7*y*z + 13*x*z) assert diop_ternary_quadratic_normal(x**2 + y**2 + z**2) == (None, None, None) assert diop_ternary_quadratic_normal(x**2 + y**2) is None pytest.raises(ValueError, lambda: _diop_ternary_quadratic_normal((x, y, z), {x*y: 1, x**2: 2, y**2: 3, z**2: 0})) eq = -2*x*y - 6*x*z + 7*y**2 - 3*y*z + 4*z**2 assert diop_ternary_quadratic(eq) == (7, 2, 0) assert diop_ternary_quadratic_normal(4*x**2 + 5*y**2 - z**2) == (1, 0, 2) assert diop_ternary_quadratic(x*y + 2*y*z) == (-2, 0, n1) eq = -5*x*y - 8*x*z - 3*y*z + 8*z**2 assert parametrize_ternary_quadratic(eq) == (64*p**2 - 24*p*q, -64*p*q + 64*q**2, 40*p*q) # this cannot be tested with diophantine because it will # factor into a product assert diop_solve(x*y + 2*y*z) == (-4*p*q, -2*n1*p**2 + 2*p**2, 2*p*q)
def test_diop_ternary_quadratic(): # Commented out test cases should be uncommented after # the bug with factor_list() gets merged. assert check_solutions(2 * x**2 + z**2 + y**2 - 4 * x * y) assert check_solutions(x**2 - y**2 - z**2 - x * y - y * z) assert check_solutions(3 * x**2 - x * y - y * z - x * z) assert check_solutions(x**2 - y * z - x * z) # assert check_solutions(5*x**2 - 3*x*y - x*z) assert check_solutions(4 * x**2 - 5 * y**2 - x * z) assert check_solutions(3 * x**2 + 2 * y**2 - z**2 - 2 * x * y + 5 * y * z - 7 * y * z) assert check_solutions(8 * x**2 - 12 * y * z) assert check_solutions(45 * x**2 - 7 * y**2 - 8 * x * y - z**2) assert check_solutions(x**2 - 49 * y**2 - z**2 + 13 * z * y - 8 * x * y) assert check_solutions(90 * x**2 + 3 * y**2 + 5 * x * y + 2 * z * y + 5 * x * z) assert check_solutions(x**2 + 3 * y**2 + z**2 - x * y - 17 * y * z) assert check_solutions(x**2 + 3 * y**2 + z**2 - x * y - 16 * y * z + 12 * x * z) assert check_solutions(x**2 + 3 * y**2 + z**2 - 13 * x * y - 16 * y * z + 12 * x * z) assert check_solutions(x * y - 7 * y * z + 13 * x * z) assert diop_ternary_quadratic_normal(x**2 + y**2 + z**2) == (None, None, None) assert diop_ternary_quadratic_normal(x**2 + y**2) is None pytest.raises( ValueError, lambda: _diop_ternary_quadratic_normal((x, y, z), { x * y: 1, x**2: 2, y**2: 3, z**2: 0 })) eq = -2 * x * y - 6 * x * z + 7 * y**2 - 3 * y * z + 4 * z**2 assert diop_ternary_quadratic(eq) == (7, 2, 0) assert diop_ternary_quadratic_normal(4 * x**2 + 5 * y**2 - z**2) == (1, 0, 2) assert diop_ternary_quadratic(x * y + 2 * y * z) == (-2, 0, n1) eq = -5 * x * y - 8 * x * z - 3 * y * z + 8 * z**2 assert parametrize_ternary_quadratic(eq) == (64 * p**2 - 24 * p * q, -64 * p * q + 64 * q**2, 40 * p * q) # this cannot be tested with diophantine because it will # factor into a product assert diop_solve(x * y + 2 * y * z) == (-4 * p * q, -2 * n1 * p**2 + 2 * p**2, 2 * p * q)
def test_diopcoverage(): eq = (2*x + y + 1)**2 assert diop_solve(eq) == {(t_0, -2*t_0 - 1)} eq = 2*x**2 + 6*x*y + 12*x + 4*y**2 + 18*y + 18 assert diop_solve(eq) == {(t_0, -t_0 - 3), (2*t_0 - 3, -t_0)} assert diop_quadratic(x + y**2 - 3) == {(-t**2 + 3, -t)} assert diop_quadratic(x + y) is None # wrong type assert diop_linear(x + y - 3) == (t_0, 3 - t_0) assert diop_linear(x**2 - 1) is None # wrong type assert base_solution_linear(0, 1, 2, t=None) == (0, 0) ans = (3*t - 1, -2*t + 1) assert base_solution_linear(4, 8, 12, t) == ans assert base_solution_linear(4, 8, 12, t=None) == tuple(_.subs({t: 0}) for _ in ans) assert cornacchia(1, 1, 20) is None assert cornacchia(1, 1, 5) == {(1, 2)} assert cornacchia(1, 2, 17) == {(3, 2)} assert cornacchia(2, 3, 31) == set() pytest.raises(ValueError, lambda: reconstruct(4, 20, 1)) assert gaussian_reduce(4, 1, 3) == (1, 1) eq = -w**2 - x**2 - y**2 + z**2 assert (diop_general_pythagorean(eq) == diop_general_pythagorean(-eq) == (m1**2 + m2**2 - m3**2, 2*m1*m3, 2*m2*m3, m1**2 + m2**2 + m3**2)) assert check_param(Integer(3) + x/3, Integer(4) + x/2, Integer(2), x) == (None, None) assert check_param(Rational(3, 2), Integer(4) + x, Integer(2), x) == (None, None) assert check_param(Integer(4) + x, Rational(3, 2), Integer(2), x) == (None, None) assert _nint_or_floor(16, 10) == 2 assert _odd(1) == (not _even(1)) is True assert _odd(0) == (not _even(0)) is False assert _remove_gcd(2, 4, 6) == (1, 2, 3) pytest.raises(TypeError, lambda: _remove_gcd((2, 4, 6))) assert sqf_normal(2 * 3**2 * 5, 2 * 5 * 11, 2 * 7**2 * 11) == (11, 1, 5) # it's ok if these pass some day when the solvers are implemented pytest.raises(NotImplementedError, lambda: diophantine(x**2 + y**2 + x*y + 2*y*z - 12)) pytest.raises(NotImplementedError, lambda: diophantine(x**3 + y**2)) # issue sympy/sympy#11026 pytest.raises(NotImplementedError, lambda: diophantine(x**3 + y**3 - 2)) assert transformation_to_DN(x + y) is None # wrong type assert find_DN(x + y) is None # wrong type assert diop_ternary_quadratic(x + y) is None # wrong type assert transformation_to_normal(x + y) is None # wrong type assert parametrize_ternary_quadratic(x + y) is None # wrong type assert diop_general_pythagorean(x + y) is None # wrong type assert diop_general_sum_of_squares(x + y) is None # wrong type assert diop_general_sum_of_even_powers(x + y) is None # wrong type
def test_diopcoverage(): eq = (2 * x + y + 1)**2 assert diop_solve(eq) == {(t_0, -2 * t_0 - 1)} eq = 2 * x**2 + 6 * x * y + 12 * x + 4 * y**2 + 18 * y + 18 assert diop_solve(eq) == {(t_0, -t_0 - 3), (2 * t_0 - 3, -t_0)} assert diop_quadratic(x + y**2 - 3) == {(-t**2 + 3, -t)} assert diop_quadratic(x + y) is None # wrong type assert diop_linear(x + y - 3) == (t_0, 3 - t_0) assert diop_linear(x**2 - 1) is None # wrong type assert base_solution_linear(0, 1, 2, t=None) == (0, 0) ans = (3 * t - 1, -2 * t + 1) assert base_solution_linear(4, 8, 12, t) == ans assert base_solution_linear(4, 8, 12, t=None) == tuple(_.subs({t: 0}) for _ in ans) assert cornacchia(1, 1, 20) is None assert cornacchia(1, 1, 5) == {(2, 1)} assert cornacchia(1, 2, 17) == {(3, 2)} assert cornacchia(2, 3, 31) == set() assert cornacchia(1, 4, 52) == {(4, 3)} pytest.raises(ValueError, lambda: reconstruct(4, 20, 1)) assert gaussian_reduce(4, 1, 3) == (1, 1) eq = -w**2 - x**2 - y**2 + z**2 assert (diop_general_pythagorean(eq) == diop_general_pythagorean(-eq) == (m1**2 + m2**2 - m3**2, 2 * m1 * m3, 2 * m2 * m3, m1**2 + m2**2 + m3**2)) assert check_param(Integer(3) + x / 3, Integer(4) + x / 2, Integer(2), x) == (None, None) assert check_param(Rational(3, 2), Integer(4) + x, Integer(2), x) == (None, None) assert check_param(Integer(4) + x, Rational(3, 2), Integer(2), x) == (None, None) assert _nint_or_floor(16, 10) == 2 assert _odd(1) == (not _even(1)) is True assert _odd(0) == (not _even(0)) is False assert _remove_gcd(2, 4, 6) == (1, 2, 3) assert sqf_normal(2 * 3**2 * 5, 2 * 5 * 11, 2 * 7**2 * 11) == (11, 1, 5) # it's ok if these pass some day when the solvers are implemented pytest.raises(NotImplementedError, lambda: diophantine(x**2 + y**2 + x * y + 2 * y * z - 12)) pytest.raises(NotImplementedError, lambda: diophantine(x**3 + y**2)) # issue sympy/sympy#11026 pytest.raises(NotImplementedError, lambda: diophantine(x**3 + y**3 - 2)) assert transformation_to_DN(x + y) is None # wrong type assert find_DN(x + y) is None # wrong type assert diop_ternary_quadratic(x + y) is None # wrong type assert transformation_to_normal(x + y) is None # wrong type assert parametrize_ternary_quadratic(x + y) is None # wrong type assert diop_general_pythagorean(x + y) is None # wrong type assert diop_general_sum_of_squares(x + y) is None # wrong type assert diop_general_sum_of_even_powers(x + y) is None # wrong type assert diop_quadratic(x**2 + y**2 - 1**2 - 3**4) == \ {(-9, -1), (-9, 1), (-1, -9), (-1, 9), (1, -9), (1, 9), (9, -1), (9, 1)}