g:'dZdgZddlmZddlmZddlmZmZddl m Z m Z m Z ddl mZddlmZmZdd lmZmZdd lmZdd lmZdd lmZmZmZdd lmZmZm Z ej!ee z Z"GddeZ#dS)zb This module has all the classes and functions related to waves in optics. **Contains** * TWave TWave)Basic)Expr) DerivativeFunction)NumberpiI)S)Symbolsymbols)_sympifysympify)exp)sqrt)atan2cossin)speed_of_lightmetersecondcPeZdZdZdejdedfdZedZ edZ edZ edZ ed Z ed Zed Zed Zed ZdZeZdZdZdZdZdZdZdZdZdZdZdZdS)ra4 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 Nnc|t|}tj|z }|Bt|}tj|z }|"|tj|z krtd||td||}||}t|}t|}t |}t j||||||}|S)Nz/frequency and time_period should be consistent.z*Either frequency or time period is needed.)rr One ValueErrorrr__new__) cls amplitude frequencyphase time_periodr _frequency _time_periodobjs V/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/physics/optics/waves.pyrz TWave.__new__Ys  "";//K{*J   ++I5?L&k 111$%VWWW  !4IJJ J  "I  &KY''  AJJmCIuk1MM c|jdS)a! Returns the amplitude of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.amplitude A rargsselfs r&rzTWave.amplitudevsy|r'c|jdS)a? Returns the frequency of the wave, in cycles per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.frequency f r)r+s r&r zTWave.frequency y|r'c|jdS)a5 Returns the phase angle of the wave, in radians. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.phase phi r)r+s r&r!z TWave.phaser/r'c|jdS)aI Returns the temporal period of the wave, in seconds per cycle. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.time_period 1/f r)r+s r&r"zTWave.time_periodr/r'c|jdS)z< Returns the refractive index of the medium r)r+s r&rzTWave.ns y|r'c0t|j|jzz S)a Returns the wavelength (spatial period) of the wave, in meters per cycle. It depends on the medium of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavelength 299792458*meter/(second*f*n) )cr rr+s r& wavelengthzTWave.wavelengths"$.'((r'c |j|jzS)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) )r8r r+s r&speedz TWave.speeds"t~--r'c&dtz|jzS)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_velocityzTWave.angular_velocitys tDN""r'c&dtz|jz 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 r8r+s r& wavenumberzTWave.wavenumbers tDO##r'cXddlm}t|j||jzS)z!String representation of a TWave.r)sstr)sympy.printingr@type__name__r*)r,r@s r&__str__z TWave.__str__s2''''''Dzz"TT$)__44r'c t|tr|j|jkr|j|jkrtt |jdz|jdzzd|jz|jzt |j|jz zz|jt|jt|jz|jt|jzz|jt |jz|jt |jzzStdtt|j dz)z Addition of two waves will result in their superposition. The type of interference will depend on their phase angles. r1zJInterference of waves with different frequencies has not been implemented.z# and TWave objects cannot be added.) isinstancerr r8rrrr!rrNotImplementedError TypeErrorrBrCr,others r&__add__z TWave.__add__sR eU # # Z~00T_HX5X5XT$.!"3eoq6H"H1"&.L116LAAD&*j5;&>B@B@L@#@AA"^"4>#dj//#A$s5;/?/??$@!^C OO;$s5;/?/??@AA *+1222DKK03XXYY Yr'ct|}t|tr"t|j|zg|jddRSt t|jdz)zT Multiplying a wave by a scalar rescales the amplitude of the wave. r.Nz( and TWave objects cannot be multiplied.) rrFrrrr*rHrBrCrIs r&__mul__z TWave.__mul__,sf eV $ $ _-> !"" >>> >DKK03]]^^ ^r'c2|d|zSNrKrIs r&__sub__z TWave.__sub__6s||BuH%%%r'c,|dSrOrMr+s r&__neg__z TWave.__neg__9s||Br'c,||SNrQrIs r&__radd__zTWave.__radd__<||E"""r'c,||SrWrTrIs r&__rmul__zTWave.__rmul__?rYr'c.| |SrW)rXrIs r&__rsub__zTWave.__rsub__Bs&&&r'c|jt|jtdz|jtdzz |jzt dz zdzS)Nxtr1F)evaluate)rrr>r r<r!r r,r*kwargss r&_eval_rewrite_as_sinzTWave._eval_rewrite_as_sinEsf~c$/&++"=#F3KK/#026*#=?A!t#DNSUUUU Ur'c|jt|jtdz|jtdzz |jzzSNr_r`)rrr>r r<r!rbs r&_eval_rewrite_as_coszTWave._eval_rewrite_as_cosIsL~c$/&++"=#F3KK/#026*#=>>> >r'ctd\}}}}td}t||||d||zt||||dzzS)Nzmu, epsilon, x, tEr1)r rr)r,r*rcmuepsilonr_r`ris r&_eval_rewrite_as_pdezTWave._eval_rewrite_as_pdeMsd#$788GQ SMM!!Aq''1a((2g:j1a!Q6O6O+OOOr'c |jtt|jt dz|jt dzz |jzzzSrf)rrr r>r r<r!rbs r&_eval_rewrite_as_expzTWave._eval_rewrite_as_expRsS~c!T_VC[[%@#F3KK/&026*&=#>??? ?r')rC __module__ __qualname____doc__r Zeror rpropertyrr r!r"rr8r:r<r>rD__repr__rKrMrRrUrXr[r]rdrgrlrnr'r&rrs::~&fSkk :X X"X"X"X ))X)&..X.$##X#"$$X$"555 HZZZ,___&&&   ######'''UUU>>>PPP ?????r'N)$rq__all__sympy.core.basicrsympy.core.exprrsympy.core.functionrrsympy.core.numbersrr r sympy.core.singletonr sympy.core.symbolr r sympy.core.sympifyrr&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrrrsympy.physics.unitsrrr convert_tor7rrur'r&rsj )"""""" 44444444..........""""""////////00000000666666999999FFFFFFFFFF==========NeFl++y?y?y?y?y?Dy?y?y?y?y?r'