
    sg:'                         d Z dgZddlmZ ddlmZ ddlmZmZ ddl	m
Z
mZmZ ddlmZ ddlmZmZ dd	lmZmZ dd
lmZ ddlmZ ddlmZmZmZ ddlmZmZm Z   ejB                  ee z        Z" G d de      Z#y)zb
This module has all the classes and functions related to waves in optics.

**Contains**

* TWave
TWave    )Basic)Expr)
DerivativeFunction)NumberpiI)S)Symbolsymbols)_sympifysympify)exp)sqrt)atan2cossin)speed_of_lightmetersecondc                      e Zd ZdZdej
                  d ed      fdZed        Z	ed        Z
ed        Zed        Zed	        Zed
        Zed        Zed        Zed        Zd ZeZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zy)r   a4  
    This is a simple transverse sine wave travelling in a one-dimensional space.
    Basic properties are required at the time of creation of the object,
    but they can be changed later with respective methods provided.

    Explanation
    ===========

    It is represented as :math:`A \times cos(k*x - \omega \times t + \phi )`,
    where :math:`A` is the amplitude, :math:`\omega` is the angular frequency,
    :math:`k` is the wavenumber (spatial frequency), :math:`x` is a spatial variable
    to represent the position on the dimension on which the wave propagates,
    and :math:`\phi` is the phase angle of the wave.


    Arguments
    =========

    amplitude : Sympifyable
        Amplitude of the wave.
    frequency : Sympifyable
        Frequency of the wave.
    phase : Sympifyable
        Phase angle of the wave.
    time_period : Sympifyable
        Time period of the wave.
    n : Sympifyable
        Refractive index of the medium.

    Raises
    =======

    ValueError : When neither frequency nor time period is provided
        or they are not consistent.
    TypeError : When anything other than TWave objects is added.


    Examples
    ========

    >>> from sympy import symbols
    >>> from sympy.physics.optics import TWave
    >>> A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
    >>> w1 = TWave(A1, f, phi1)
    >>> w2 = TWave(A2, f, phi2)
    >>> w3 = w1 + w2  # Superposition of two waves
    >>> w3
    TWave(sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2), f,
        atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)), 1/f, n)
    >>> w3.amplitude
    sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2)
    >>> w3.phase
    atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2))
    >>> w3.speed
    299792458*meter/(second*n)
    >>> w3.angular_velocity
    2*pi*f

    Nnc                 p   |t        |      }t        j                  |z  }|At        |      }t        j                  |z  }|!|t        j                  |z  k7  rt        d      ||t        d      |}|}t        |      }t        |      }t	        |      }t        j                  | |||||      }|S )Nz/frequency and time_period should be consistent.z*Either frequency or time period is needed.)r   r   One
ValueErrorr   r   __new__)	cls	amplitude	frequencyphasetime_periodr   
_frequency_time_periodobjs	            M/var/www/html/venv/lib/python3.12/site-packages/sympy/physics/optics/waves.pyr   zTWave.__new__Y   s     "";/K{*J  +I55?L&k 11$%VWW!4IJJ"I&KY'	AJmmCIuk1M
    c                      | j                   d   S )a!  
        Returns the amplitude of the wave.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.amplitude
        A
        r   argsselfs    r&   r   zTWave.amplitudev   s     yy|r'   c                      | j                   d   S )a?  
        Returns the frequency of the wave,
        in cycles per second.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.frequency
        f
           r)   r+   s    r&   r    zTWave.frequency         yy|r'   c                      | j                   d   S )a5  
        Returns the phase angle of the wave,
        in radians.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.phase
        phi
           r)   r+   s    r&   r!   zTWave.phase   r/   r'   c                      | j                   d   S )aI  
        Returns the temporal period of the wave,
        in seconds per cycle.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.time_period
        1/f
           r)   r+   s    r&   r"   zTWave.time_period   r/   r'   c                      | j                   d   S )z<
        Returns the refractive index of the medium
           r)   r+   s    r&   r   zTWave.n   s    
 yy|r'   c                 B    t         | j                  | j                  z  z  S )a  
        Returns the wavelength (spatial period) of the wave,
        in meters per cycle.
        It depends on the medium of the wave.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.wavelength
        299792458*meter/(second*f*n)
        )cr    r   r+   s    r&   
wavelengthzTWave.wavelength   s    " $..'((r'   c                 4    | j                   | j                  z  S )a  
        Returns the propagation speed of the wave,
        in meters per second.
        It is dependent on the propagation medium.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.speed
        299792458*meter/(second*n)
        )r8   r    r+   s    r&   speedzTWave.speed   s    " t~~--r'   c                 .    dt         z  | j                  z  S )aS  
        Returns the angular velocity of the wave,
        in radians per second.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.angular_velocity
        2*pi*f
        r1   )r	   r    r+   s    r&   angular_velocityzTWave.angular_velocity   s      tDNN""r'   c                 .    dt         z  | j                  z  S )a_  
        Returns the wavenumber of the wave,
        in radians per meter.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.optics import TWave
        >>> A, phi, f = symbols('A, phi, f')
        >>> w = TWave(A, f, phi)
        >>> w.wavenumber
        pi*second*f*n/(149896229*meter)
        r1   )r	   r8   r+   s    r&   
wavenumberzTWave.wavenumber   s      tDOO##r'   c                 ^    ddl m} t        |       j                   || j                        z   S )z!String representation of a TWave.r   )sstr)sympy.printingr@   type__name__r*   )r,   r@   s     r&   __str__zTWave.__str__  s"    'Dz""T$))_44r'   c                    t        |t              rL| j                  |j                  k(  r'| j                  |j                  k(  rt        t	        | j
                  dz  |j
                  dz  z   d| j
                  z  |j
                  z  t        | j                  |j                  z
        z  z         | j                  t        | j
                  t        | j                        z  |j
                  t        |j                        z  z   | j
                  t        | j                        z  |j
                  t        |j                        z  z               S t        d      t        t        |      j                  dz         )z
        Addition of two waves will result in their superposition.
        The type of interference will depend on their phase angles.
        r1   zJInterference of waves with different frequencies has not been implemented.z# and TWave objects cannot be added.)
isinstancer   r    r8   r   r   r   r!   r   r   NotImplementedError	TypeErrorrB   rC   r,   others     r&   __add__zTWave.__add__  sA   
 eU#~~0T__HXHX5XT$..!"3eooq6H"H1"&..L116LAAD&*jj5;;&>B@L@ #@ A "^^"4>>#djj/#A$s5;;/??$@!^^C

O;$s5;;/??@A	  * +1 2 2 DK003XXYYr'   c                     t        |      }t        |t              r&t        | j                  |z  g| j
                  dd  S t        t        |      j                  dz         )zT
        Multiplying a wave by a scalar rescales the amplitude of the wave.
        r.   Nz( and TWave objects cannot be multiplied.)	r   rF   r   r   r   r*   rH   rB   rC   rI   s     r&   __mul__zTWave.__mul__,  sU     eV$->		!">>DK003]]^^r'   c                 *    | j                  d|z        S NrK   rI   s     r&   __sub__zTWave.__sub__6  s    ||BuH%%r'   c                 $    | j                  d      S rO   rM   r+   s    r&   __neg__zTWave.__neg__9  s    ||Br'   c                 $    | j                  |      S NrQ   rI   s     r&   __radd__zTWave.__radd__<      ||E""r'   c                 $    | j                  |      S rW   rT   rI   s     r&   __rmul__zTWave.__rmul__?  rY   r'   c                 &    |  j                  |      S rW   )rX   rI   s     r&   __rsub__zTWave.__rsub__B  s    &&r'   c                     | j                   t        | j                  t        d      z  | j                  t        d      z  z
  | j
                  z   t        dz  z   d      z  S )Nxtr1   F)evaluate)r   r   r>   r   r<   r!   r	   r,   r*   kwargss      r&   _eval_rewrite_as_sinzTWave._eval_rewrite_as_sinE  s_    ~~c$//&+"=##F3K/#026**#=?A!t#DNSU U 	Ur'   c                     | j                   t        | j                  t        d      z  | j                  t        d      z  z
  | j
                  z         z  S Nr_   r`   )r   r   r>   r   r<   r!   rb   s      r&   _eval_rewrite_as_coszTWave._eval_rewrite_as_cosI  sL    ~~c$//&+"=##F3K/#026**#= > > 	>r'   c                     t        d      \  }}}}t        d      }t         |||      |d      ||z  t         |||      |d      z  z   S )Nzmu, epsilon, x, tEr1   )r   r   r   )r,   r*   rc   muepsilonr_   r`   ri   s           r&   _eval_rewrite_as_pdezTWave._eval_rewrite_as_pdeM  sQ    #$78GQSM!Aq'1a(2g:j1a!Q6O+OOOr'   c           	          | j                   t        t        | j                  t	        d      z  | j
                  t	        d      z  z
  | j                  z   z        z  S rf   )r   r   r
   r>   r   r<   r!   rb   s      r&   _eval_rewrite_as_expzTWave._eval_rewrite_as_expR  sS    ~~c!T__VC[%@##F3K/&026**&= #> ? ? 	?r'   )rC   
__module____qualname____doc__r   Zeror   r   propertyr   r    r!   r"   r   r8   r:   r<   r>   rD   __repr__rK   rM   rR   rU   rX   r[   r]   rd   rg   rl   rn    r'   r&   r   r      s   :~ &&Sk:     "  "  "   ) )& . .$ # #" $ $"5
 HZ,_& ##'U>P
?r'   N)$rq   __all__sympy.core.basicr   sympy.core.exprr   sympy.core.functionr   r   sympy.core.numbersr   r	   r
   sympy.core.singletonr   sympy.core.symbolr   r   sympy.core.sympifyr   r   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r   sympy.physics.unitsr   r   r   
convert_tor7   r   ru   r'   r&   <module>r      sc    ) "   4 . . " / 0 6 9 F F = = NeFl+y?D y?r'   