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)
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) == \
set([(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 11016
var = symbols(':5') + (symbols('6', negative=True), )
eq = Add(*[i**2 for i in var]) - 112
base_soln = set([(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)])
assert diophantine(eq) == base_soln
assert len(diophantine(eq, permute=True)) == 196800
# handle negated squares with signsimp
assert diophantine(12 - x**2 - y**2 - z**2) == set([(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
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)
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) == \
set([(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 11016
var = symbols(':5') + (symbols('6', negative=True),)
eq = Add(*[i**2 for i in var]) - 112
assert diophantine(eq) == set(
[(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) == set([(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
raises(NotImplementedError, lambda: classify_diop(-eq))
def test_classify_diop():
raises(TypeError, lambda: classify_diop(x**2/3 - 1))
raises(ValueError, lambda: classify_diop(1))
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')
def test_classify_diop():
raises(TypeError, lambda: classify_diop(x**2 / 3 - 1))
raises(ValueError, lambda: classify_diop(1))
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')
def test_classify_diop():
raises(TypeError, lambda: classify_diop(x ** 2 / 3 - 1))
raises(ValueError, lambda: classify_diop(1))
raises(NotImplementedError, lambda: classify_diop(w * x * y * z - 1))
raises(NotImplementedError, lambda: classify_diop(x ** 3 + y ** 3 + z ** 4 - 90))
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")
assert classify_diop(x ** 4 + y ** 4 + z ** 4 - (1 + 16 + 81)) == (
[x, y, z],
{1: -98, x ** 4: 1, z ** 4: 1, y ** 4: 1},
"general_sum_of_even_powers",
)
