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29 lines
1.3 KiB
29 lines
1.3 KiB
from sympy.core.function import diff
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from sympy.functions.elementary.complexes import conjugate
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.trigonometric import (cos, sin)
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from sympy.functions.special.mathieu_functions import (mathieuc, mathieucprime, mathieus, mathieusprime)
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from sympy.abc import a, q, z
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def test_mathieus():
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assert isinstance(mathieus(a, q, z), mathieus)
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assert mathieus(a, 0, z) == sin(sqrt(a)*z)
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assert conjugate(mathieus(a, q, z)) == mathieus(conjugate(a), conjugate(q), conjugate(z))
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assert diff(mathieus(a, q, z), z) == mathieusprime(a, q, z)
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def test_mathieuc():
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assert isinstance(mathieuc(a, q, z), mathieuc)
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assert mathieuc(a, 0, z) == cos(sqrt(a)*z)
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assert diff(mathieuc(a, q, z), z) == mathieucprime(a, q, z)
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def test_mathieusprime():
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assert isinstance(mathieusprime(a, q, z), mathieusprime)
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assert mathieusprime(a, 0, z) == sqrt(a)*cos(sqrt(a)*z)
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assert diff(mathieusprime(a, q, z), z) == (-a + 2*q*cos(2*z))*mathieus(a, q, z)
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def test_mathieucprime():
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assert isinstance(mathieucprime(a, q, z), mathieucprime)
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assert mathieucprime(a, 0, z) == -sqrt(a)*sin(sqrt(a)*z)
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assert diff(mathieucprime(a, q, z), z) == (-a + 2*q*cos(2*z))*mathieuc(a, q, z)
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