Server : Apache/2.4.41 (Ubuntu) System : Linux absol.cf 5.4.0-198-generic #218-Ubuntu SMP Fri Sep 27 20:18:53 UTC 2024 x86_64 User : www-data ( 33) PHP Version : 7.4.33 Disable Function : pcntl_alarm,pcntl_fork,pcntl_waitpid,pcntl_wait,pcntl_wifexited,pcntl_wifstopped,pcntl_wifsignaled,pcntl_wifcontinued,pcntl_wexitstatus,pcntl_wtermsig,pcntl_wstopsig,pcntl_signal,pcntl_signal_get_handler,pcntl_signal_dispatch,pcntl_get_last_error,pcntl_strerror,pcntl_sigprocmask,pcntl_sigwaitinfo,pcntl_sigtimedwait,pcntl_exec,pcntl_getpriority,pcntl_setpriority,pcntl_async_signals,pcntl_unshare, Directory :  /proc/self/root/usr/local/lib/python3.6/dist-packages/sympy/series/tests/

Upload File : current_dir [ Writeable ] document_root [ Writeable ]

from sympy.series import approximants
from sympy import lucas, fibonacci, symbols, binomial


def test_approximants():
    x, t = symbols("x,t")
    g = [lucas(k) for k in range(16)]
    assert [e for e in 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 [e for e in 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 [e for e in 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)