o oÇ hÎã@s„dZddlmZmZddlmZddlmZmZGdd„deƒZ Gdd„de ƒZ Gd d „d e ƒZ Gd d „d e ƒZ Gd d„de ƒZ dS)z- This module contains the Mathieu functions. é)ÚFunctionÚArgumentIndexError)Úsqrt)ÚsinÚcosc@seZdZdZdZdd„ZdS)Ú MathieuBasezj Abstract base class for Mathieu functions. This class is meant to reduce code duplication. TcCs&|j\}}}| | ¡| ¡| ¡¡S©N)ÚargsÚfuncÚ conjugate)ÚselfÚaÚqÚz©rú}/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/functions/special/mathieu_functions.pyÚ_eval_conjugates zMathieuBase._eval_conjugateN)Ú__name__Ú __module__Ú __qualname__Ú__doc__Ú unbranchedrrrrrr s rc@ó&eZdZdZddd„Zedd„ƒZdS) Úmathieusaè The Mathieu Sine function $S(a,q,z)$. Explanation =========== This function is one solution of the Mathieu differential equation: .. math :: y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 The other solution is the Mathieu Cosine function. Examples ======== >>> from sympy import diff, mathieus >>> from sympy.abc import a, q, z >>> mathieus(a, q, z) mathieus(a, q, z) >>> mathieus(a, 0, z) sin(sqrt(a)*z) >>> diff(mathieus(a, q, z), z) mathieusprime(a, q, z) See Also ======== mathieuc: Mathieu cosine function. mathieusprime: Derivative of Mathieu sine function. mathieucprime: Derivative of Mathieu cosine function. References ========== .. [1] https://en.wikipedia.org/wiki/Mathieu_function .. [2] https://dlmf.nist.gov/28 .. [3] https://mathworld.wolfram.com/MathieuFunction.html .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuS/ écCó*|dkr|j\}}}t|||ƒSt||ƒ‚©Né)r Ú mathieusprimer©r Úargindexr rrrrrÚfdiffFó   zmathieus.fdiffcCs8|jr|jrtt|ƒ|ƒS| ¡r|||| ƒ SdSr)Ú is_NumberÚis_zerorrÚcould_extract_minus_sign©Úclsr rrrrrÚevalMs ÿz mathieus.evalN©r©rrrrr!Ú classmethodr(rrrrró  -rc@r) Úmathieucaã The Mathieu Cosine function $C(a,q,z)$. Explanation =========== This function is one solution of the Mathieu differential equation: .. math :: y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 The other solution is the Mathieu Sine function. Examples ======== >>> from sympy import diff, mathieuc >>> from sympy.abc import a, q, z >>> mathieuc(a, q, z) mathieuc(a, q, z) >>> mathieuc(a, 0, z) cos(sqrt(a)*z) >>> diff(mathieuc(a, q, z), z) mathieucprime(a, q, z) See Also ======== mathieus: Mathieu sine function mathieusprime: Derivative of Mathieu sine function mathieucprime: Derivative of Mathieu cosine function References ========== .. [1] https://en.wikipedia.org/wiki/Mathieu_function .. [2] https://dlmf.nist.gov/28 .. [3] https://mathworld.wolfram.com/MathieuFunction.html .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuC/ rcCrr)r Ú mathieucprimerrrrrr!„r"zmathieuc.fdiffcCs6|jr|jrtt|ƒ|ƒS| ¡r|||| ƒSdSr)r#r$rrr%r&rrrr(‹s ÿz mathieuc.evalNr)r*rrrrr-Vr,r-c@r) ra" The derivative $S^{\prime}(a,q,z)$ of the Mathieu Sine function. Explanation =========== This function is one solution of the Mathieu differential equation: .. math :: y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 The other solution is the Mathieu Cosine function. Examples ======== >>> from sympy import diff, mathieusprime >>> from sympy.abc import a, q, z >>> mathieusprime(a, q, z) mathieusprime(a, q, z) >>> mathieusprime(a, 0, z) sqrt(a)*cos(sqrt(a)*z) >>> diff(mathieusprime(a, q, z), z) (-a + 2*q*cos(2*z))*mathieus(a, q, z) See Also ======== mathieus: Mathieu sine function mathieuc: Mathieu cosine function mathieucprime: Derivative of Mathieu cosine function References ========== .. [1] https://en.wikipedia.org/wiki/Mathieu_function .. [2] https://dlmf.nist.gov/28 .. [3] https://mathworld.wolfram.com/MathieuFunction.html .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuSPrime/ rcCóB|dkr|j\}}}d|td|ƒ|t|||ƒSt||ƒ‚©Nré)r rrrrrrrr!Âó $ zmathieusprime.fdiffcCs>|jr|jrt|ƒtt|ƒ|ƒS| ¡r|||| ƒSdSr)r#r$rrr%r&rrrr(És ÿzmathieusprime.evalNr)r*rrrrr”r,rc@r) r.a! The derivative $C^{\prime}(a,q,z)$ of the Mathieu Cosine function. Explanation =========== This function is one solution of the Mathieu differential equation: .. math :: y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 The other solution is the Mathieu Sine function. Examples ======== >>> from sympy import diff, mathieucprime >>> from sympy.abc import a, q, z >>> mathieucprime(a, q, z) mathieucprime(a, q, z) >>> mathieucprime(a, 0, z) -sqrt(a)*sin(sqrt(a)*z) >>> diff(mathieucprime(a, q, z), z) (-a + 2*q*cos(2*z))*mathieuc(a, q, z) See Also ======== mathieus: Mathieu sine function mathieuc: Mathieu cosine function mathieusprime: Derivative of Mathieu sine function References ========== .. [1] https://en.wikipedia.org/wiki/Mathieu_function .. [2] https://dlmf.nist.gov/28 .. [3] https://mathworld.wolfram.com/MathieuFunction.html .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuCPrime/ rcCr/r0)r rr-rrrrrr!r2zmathieucprime.fdiffcCsB|jr|jrt|ƒ tt|ƒ|ƒS| ¡r|||| ƒ SdSr)r#r$rrr%r&rrrr(s ÿzmathieucprime.evalNr)r*rrrrr.Òr,r.N)rÚsympy.core.functionrrÚ(sympy.functions.elementary.miscellaneousrÚ(sympy.functions.elementary.trigonometricrrrrr-rr.rrrrÚs >>>