def test_guess_generating_function():
x = Symbol('x')
assert guess_generating_function([fibonacci(k)
for k in range(5, 15)]) == ((3*x + 5)/(-x**2 - x + 1))
assert guess_generating_function(
[1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919]) == (
(1/(x**4 + 2*x**2 - 4*x + 1))**(sympify("1/2")))
assert guess_generating_function(sympify(
"[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]")
) == (x + sympify("3/2"))/(11*x**2 - 3*x + 1)
def test_guess_generating_function():
x = Symbol('x')
assert guess_generating_function([fibonacci(k) for k in range(5, 15)
]) == ((3 * x + 5) / (-x**2 - x + 1))
assert guess_generating_function(
[1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122,
38919]) == ((1 / (x**4 + 2 * x**2 - 4 * x + 1))**(sympify("1/2")))
assert guess_generating_function(
sympify(
"[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]"
)) == (x + sympify("3/2")) / (11 * x**2 - 3 * x + 1)
def test_guess_generating_function():
x = Symbol('x')
assert guess_generating_function([fibonacci(k)
for k in range(5, 15)])['ogf'] == ((3*x + 5)/(-x**2 - x + 1))
assert guess_generating_function(
[1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf'] == (
(1/(x**4 + 2*x**2 - 4*x + 1))**Rational(1, 2))
assert guess_generating_function(sympify(
"[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]")
)['ogf'] == (x + Rational(3, 2))/(11*x**2 - 3*x + 1)
assert guess_generating_function([factorial(k) for k in range(12)],
types=['egf'])['egf'] == 1/(-x + 1)
assert guess_generating_function([k+1 for k in range(12)],
types=['egf']) == {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)}
def test_guess_generating_function():
x = Symbol('x')
assert guess_generating_function(
[fibonacci(k)
for k in range(5, 15)])['ogf'] == ((3 * x + 5) / (-x**2 - x + 1))
assert guess_generating_function(
[1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122,
38919])['ogf'] == ((1 / (x**4 + 2 * x**2 - 4 * x + 1))**S.Half)
assert guess_generating_function(
sympify(
"[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]"
))['ogf'] == (x + Rational(3, 2)) / (11 * x**2 - 3 * x + 1)
assert guess_generating_function([factorial(k) for k in range(12)],
types=['egf'])['egf'] == 1 / (-x + 1)
assert guess_generating_function([k + 1 for k in range(12)],
types=['egf']) == {
'egf': (x + 1) * exp(x),
'lgdegf': (x + 2) / (x + 1)
}