| from sympy.series import approximants | |
| from sympy.core.symbol import symbols | |
| from sympy.functions.combinatorial.factorials import binomial | |
| from sympy.functions.combinatorial.numbers import (fibonacci, lucas) | |
| def test_approximants(): | |
| x, t = symbols("x,t") | |
| g = [lucas(k) for k in range(16)] | |
| assert list(approximants(g)) == ( | |
| [2, -4/(x - 2), (5*x - 2)/(3*x - 1), (x - 2)/(x**2 + x - 1)] ) | |
| g = [lucas(k)+fibonacci(k+2) for k in range(16)] | |
| assert list(approximants(g)) == ( | |
| [3, -3/(x - 1), (3*x - 3)/(2*x - 1), -3/(x**2 + x - 1)] ) | |
| g = [lucas(k)**2 for k in range(16)] | |
| assert list(approximants(g)) == ( | |
| [4, -16/(x - 4), (35*x - 4)/(9*x - 1), (37*x - 28)/(13*x**2 + 11*x - 7), | |
| (50*x**2 + 63*x - 52)/(37*x**2 + 19*x - 13), | |
| (-x**2 - 7*x + 4)/(x**3 - 2*x**2 - 2*x + 1)] ) | |
| p = [sum(binomial(k,i)*x**i for i in range(k+1)) for k in range(16)] | |
| y = approximants(p, t, simplify=True) | |
| assert next(y) == 1 | |
| assert next(y) == -1/(t*(x + 1) - 1) | |