def test_diop_general_sum_of_squares_quick():
for i in range(3, 10):
assert check_solutions(sum(i**2 for i in symbols(f':{i:d}')) - i)
pytest.raises(ValueError, lambda: _diop_general_sum_of_squares((x, y), 2))
assert _diop_general_sum_of_squares((x, y, z), -2) == set()
eq = x**2 + y**2 + z**2 - (1 + 4 + 9)
assert diop_general_sum_of_squares(eq) == {(1, 2, 3)}
eq = u**2 + v**2 + x**2 + y**2 + z**2 - 1313
assert len(diop_general_sum_of_squares(eq, 3)) == 3
# issue sympy/sympy#11016
var = symbols(':5') + (symbols('6', negative=True), )
eq = Add(*[i**2 for i in var]) - 112
assert diophantine(eq) == {(0, 1, 1, 5, 6, -7), (1, 1, 1, 3, 6, -8),
(2, 3, 3, 4, 5, -7), (0, 1, 1, 1, 3, -10),
(0, 0, 4, 4, 4, -8), (1, 2, 3, 3, 5, -8),
(0, 1, 2, 3, 7, -7), (2, 2, 4, 4, 6, -6),
(1, 1, 3, 4, 6, -7), (0, 2, 3, 3, 3, -9),
(0, 0, 2, 2, 2, -10), (1, 1, 2, 3, 4, -9),
(0, 1, 1, 2, 5, -9), (0, 0, 2, 6, 6, -6),
(1, 3, 4, 5, 5, -6), (0, 2, 2, 2, 6, -8),
(0, 3, 3, 3, 6, -7), (0, 2, 3, 5, 5, -7),
(0, 1, 5, 5, 5, -6)}
# handle negated squares with signsimp
assert diophantine(12 - x**2 - y**2 - z**2) == {(2, 2, 2)}
# diophantine handles simplification, so classify_diop should
# not have to look for additional patterns that are removed
# by diophantine
eq = a**2 + b**2 + c**2 + d**2 - 4
pytest.raises(NotImplementedError, lambda: classify_diop(-eq))
def test_diop_general_sum_of_squares_quick():
for i in range(3, 10):
assert check_solutions(sum(i**2 for i in symbols(':%i' % i)) - i)
pytest.raises(ValueError, lambda: _diop_general_sum_of_squares((x, y), 2))
assert _diop_general_sum_of_squares((x, y, z), -2) == set()
eq = x**2 + y**2 + z**2 - (1 + 4 + 9)
assert diop_general_sum_of_squares(eq) == {(1, 2, 3)}
eq = u**2 + v**2 + x**2 + y**2 + z**2 - 1313
assert len(diop_general_sum_of_squares(eq, 3)) == 3
# issue sympy/sympy#11016
var = symbols(':5') + (symbols('6', negative=True),)
eq = Add(*[i**2 for i in var]) - 112
assert diophantine(eq) == {
(0, 1, 1, 5, 6, -7), (1, 1, 1, 3, 6, -8), (2, 3, 3, 4, 5, -7),
(0, 1, 1, 1, 3, -10), (0, 0, 4, 4, 4, -8), (1, 2, 3, 3, 5, -8),
(0, 1, 2, 3, 7, -7), (2, 2, 4, 4, 6, -6), (1, 1, 3, 4, 6, -7),
(0, 2, 3, 3, 3, -9), (0, 0, 2, 2, 2, -10), (1, 1, 2, 3, 4, -9),
(0, 1, 1, 2, 5, -9), (0, 0, 2, 6, 6, -6), (1, 3, 4, 5, 5, -6),
(0, 2, 2, 2, 6, -8), (0, 3, 3, 3, 6, -7), (0, 2, 3, 5, 5, -7),
(0, 1, 5, 5, 5, -6)}
# handle negated squares with signsimp
assert diophantine(12 - x**2 - y**2 - z**2) == {(2, 2, 2)}
# diophantine handles simplification, so classify_diop should
# not have to look for additional patterns that are removed
# by diophantine
eq = a**2 + b**2 + c**2 + d**2 - 4
pytest.raises(NotImplementedError, lambda: classify_diop(-eq))
def test_classify_diop():
pytest.raises(TypeError, lambda: classify_diop(x**2 / 3 - 1))
pytest.raises(ValueError, lambda: classify_diop(1))
pytest.raises(NotImplementedError,
lambda: classify_diop(w * x * y * z - 1))
assert classify_diop(14 * x**2 + 15 * x - 42) == ([x], {
1: -42,
x: 15,
x**2: 14
}, 'univariate')
assert classify_diop(x * y + z) == ([x, y, z], {
x * y: 1,
z: 1
}, 'inhomogeneous_ternary_quadratic')
assert classify_diop(x * y + z + w + x**2) == ([w, x, y, z], {
x * y: 1,
w: 1,
x**2: 1,
z: 1
}, 'inhomogeneous_general_quadratic')
assert classify_diop(x * y + x * z + x**2 + 1) == ([x, y, z], {
x * y: 1,
x * z: 1,
x**2: 1,
1: 1
}, 'inhomogeneous_general_quadratic')
assert classify_diop(x * y + z + w + 42) == ([w, x, y, z], {
x * y: 1,
w: 1,
1: 42,
z: 1
}, 'inhomogeneous_general_quadratic')
assert classify_diop(x * y + z * w) == ([w, x, y, z], {
x * y: 1,
w * z: 1
}, 'homogeneous_general_quadratic')
assert classify_diop(x * y**2 + 1) == ([x, y], {
x * y**2: 1,
1: 1
}, 'cubic_thue')
# issue sympy/sympy#11418
pytest.raises(NotImplementedError,
lambda: classify_diop(x**3 + y**3 + z**4 - 90))
assert classify_diop(x**4 + y**4 + z**4 - 98) == ([x, y, z], {
1: -98,
x**4: 1,
z**4: 1,
y**4: 1
}, 'general_sum_of_even_powers')
def test_classify_diop():
pytest.raises(TypeError, lambda: classify_diop(x**2/3 - 1))
pytest.raises(ValueError, lambda: classify_diop(1))
pytest.raises(NotImplementedError, lambda: classify_diop(w*x*y*z - 1))
assert classify_diop(14*x**2 + 15*x - 42) == ([x], {1: -42, x: 15, x**2: 14}, 'univariate')
assert classify_diop(x*y + z) == ([x, y, z], {x*y: 1, z: 1}, 'inhomogeneous_ternary_quadratic')
assert classify_diop(x*y + z + w + x**2) == ([w, x, y, z], {x*y: 1, w: 1, x**2: 1, z: 1}, 'inhomogeneous_general_quadratic')
assert classify_diop(x*y + x*z + x**2 + 1) == ([x, y, z], {x*y: 1, x*z: 1, x**2: 1, 1: 1}, 'inhomogeneous_general_quadratic')
assert classify_diop(x*y + z + w + 42) == ([w, x, y, z], {x*y: 1, w: 1, 1: 42, z: 1}, 'inhomogeneous_general_quadratic')
assert classify_diop(x*y + z*w) == ([w, x, y, z], {x*y: 1, w*z: 1}, 'homogeneous_general_quadratic')
assert classify_diop(x*y**2 + 1) == ([x, y], {x*y**2: 1, 1: 1}, 'cubic_thue')
# issue sympy/sympy#11418
pytest.raises(NotImplementedError, lambda: classify_diop(x**3 + y**3 + z**4 - 90))
assert classify_diop(x**4 + y**4 + z**4 - 98) == ([x, y, z], {1: -98, x**4: 1, z**4: 1, y**4: 1}, 'general_sum_of_even_powers')