Spaces:
Sleeping
Sleeping
| from sympy.core.numbers import E | |
| from sympy.core.singleton import S | |
| from sympy.functions.elementary.exponential import exp | |
| from sympy.functions.elementary.hyperbolic import tanh | |
| from sympy.functions.elementary.trigonometric import (cos, sin) | |
| from sympy.series.order import Order | |
| from sympy.abc import x, y | |
| def test_sin(): | |
| e = sin(x).lseries(x) | |
| assert next(e) == x | |
| assert next(e) == -x**3/6 | |
| assert next(e) == x**5/120 | |
| def test_cos(): | |
| e = cos(x).lseries(x) | |
| assert next(e) == 1 | |
| assert next(e) == -x**2/2 | |
| assert next(e) == x**4/24 | |
| def test_exp(): | |
| e = exp(x).lseries(x) | |
| assert next(e) == 1 | |
| assert next(e) == x | |
| assert next(e) == x**2/2 | |
| assert next(e) == x**3/6 | |
| def test_exp2(): | |
| e = exp(cos(x)).lseries(x) | |
| assert next(e) == E | |
| assert next(e) == -E*x**2/2 | |
| assert next(e) == E*x**4/6 | |
| assert next(e) == -31*E*x**6/720 | |
| def test_simple(): | |
| assert list(x.lseries()) == [x] | |
| assert list(S.One.lseries(x)) == [1] | |
| assert not next((x/(x + y)).lseries(y)).has(Order) | |
| def test_issue_5183(): | |
| s = (x + 1/x).lseries() | |
| assert list(s) == [1/x, x] | |
| assert next((x + x**2).lseries()) == x | |
| assert next(((1 + x)**7).lseries(x)) == 1 | |
| assert next((sin(x + y)).series(x, n=3).lseries(y)) == x | |
| # it would be nice if all terms were grouped, but in the | |
| # following case that would mean that all the terms would have | |
| # to be known since, for example, every term has a constant in it. | |
| s = ((1 + x)**7).series(x, 1, n=None) | |
| assert [next(s) for i in range(2)] == [128, -448 + 448*x] | |
| def test_issue_6999(): | |
| s = tanh(x).lseries(x, 1) | |
| assert next(s) == tanh(1) | |
| assert next(s) == x - (x - 1)*tanh(1)**2 - 1 | |
| assert next(s) == -(x - 1)**2*tanh(1) + (x - 1)**2*tanh(1)**3 | |
| assert next(s) == -(x - 1)**3*tanh(1)**4 - (x - 1)**3/3 + \ | |
| 4*(x - 1)**3*tanh(1)**2/3 | |