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