def num_solutions(n):
ret = set()
for a, b in diop_quadratic(n * y + n * x - x * y, t):
if a <= 0 or b <= 0:
continue
ret.add(frozenset((a, b)))
return len(ret)
def test_diopcoverage():
eq = (2 * x + y + 1)**2
assert diop_solve(eq) == set([(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) == set([(t_0, -t_0 - 3), (2 * t_0 - 3, -t_0)])
assert diop_quadratic(x + y**2 - 3) == set([(-t**2 + 3, -t)])
assert diop_linear(x + y - 3) == (t_0, 3 - t_0)
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) == set([(2, 1)])
assert cornacchia(1, 2, 17) == set([(3, 2)])
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(S(3) + x / 3, S(4) + x / 2, S(2), x) == (None, None)
assert check_param(S(3) / 2, S(4) + x, S(2), x) == (None, None)
assert check_param(S(4) + x, S(3) / 2, S(2), x) == (None, None)
assert _nint_or_floor(16, 10) == 2
assert _odd(1) == (not _even(1)) == True
assert _odd(0) == (not _even(0)) == False
assert _remove_gcd(2, 4, 6) == (1, 2, 3)
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
raises(NotImplementedError,
lambda: diophantine(x**2 + y**2 + x * y + 2 * y * z - 12))
raises(NotImplementedError, lambda: diophantine(x**3 + y**2))
assert diop_quadratic(x**2 + y**2 - 1**2 - 3**4) == \
set([(-9, -1), (-9, 1), (-1, -9), (-1, 9), (1, -9), (1, 9), (9, -1), (9, 1)])
def test_diopcoverage():
eq = (2*x + y + 1)**2
assert diop_solve(eq) == set([(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) == set([(t_0, -t_0 - 3), (2*t_0 - 3, -t_0)])
assert diop_quadratic(x + y**2 - 3) == set([(-t**2 + 3, -t)])
assert diop_linear(x + y - 3) == (t_0, 3 - t_0)
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) == set([(2, 1)])
assert cornacchia(1, 2, 17) == set([(3, 2)])
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(S(3) + x/3, S(4) + x/2, S(2), x) == (None, None)
assert check_param(S(3)/2, S(4) + x, S(2), x) == (None, None)
assert check_param(S(4) + x, S(3)/2, S(2), x) == (None, None)
assert _nint_or_floor(16, 10) == 2
assert _odd(1) == (not _even(1)) == True
assert _odd(0) == (not _even(0)) == False
assert _remove_gcd(2, 4, 6) == (1, 2, 3)
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
raises(NotImplementedError, lambda: diophantine(x**2 + y**2 + x*y + 2*y*z - 12))
raises(NotImplementedError, lambda: diophantine(x**3 + y**2))
assert diop_quadratic(x**2 + y**2 - 1**2 - 3**4) == \
set([(-9, -1), (-9, 1), (-1, -9), (-1, 9), (1, -9), (1, 9), (9, -1), (9, 1)])
from sympy.abc import x, y, t
from sympy.solvers.diophantine import diop_quadratic
limit = 1001
max_x = 0
for d in range(2, limit):
s = list(diop_quadratic(x**2 - d * (y**2) - 1, 0))
if s[0][0] > max_x:
max_x, solution_d = s[0][0], d
print(solution_d)
