U 9%e1%@sddlZddlmZddlmZmZmZddlmZddl m Z m Z m Z m Z mZddlmZddlmZddlmZd d Zd d ZGd ddeZGdddeZGdddeZdddZdddZd ddZGdddeZddZdS)!N)Expr)sympifySpreorder_traversal) CoordSys3D)Vector VectorMul VectorAddCrossDot) Derivative)Add)MulcCs<t|}t}|D] }t|tr|||qt|SN)rset isinstanceraddskip frozenset)exprgretirU/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/vector/operators.py_get_coord_systems s   rcCs:tdd}|jD]}|t||9<qt|S)NcSstjSr)rZOnerrrrz._split_mul_args_wrt_coordsys..) collections defaultdictargsrlistvalues)rdrrrr_split_mul_args_wrt_coordsyss r$c@s eZdZdZddZddZdS)Gradientz Represents unevaluated Gradient. Examples ======== >>> from sympy.vector import CoordSys3D, Gradient >>> R = CoordSys3D('R') >>> s = R.x*R.y*R.z >>> Gradient(s) Gradient(R.x*R.y*R.z) cCst|}t||}||_|Srrr__new___exprclsrobjrrrr'+s zGradient.__new__cKst|jddSNTdoit)gradientr(selfhintsrrrr.1sz Gradient.doitN__name__ __module__ __qualname____doc__r'r.rrrrr%sr%c@s eZdZdZddZddZdS) Divergencea Represents unevaluated Divergence. Examples ======== >>> from sympy.vector import CoordSys3D, Divergence >>> R = CoordSys3D('R') >>> v = R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> Divergence(v) Divergence(R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k) cCst|}t||}||_|Srr&r)rrrr'Ds zDivergence.__new__cKst|jddSr,) divergencer(r0rrrr.JszDivergence.doitNr3rrrrr85sr8c@s eZdZdZddZddZdS)Curla Represents unevaluated Curl. Examples ======== >>> from sympy.vector import CoordSys3D, Curl >>> R = CoordSys3D('R') >>> v = R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> Curl(v) Curl(R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k) cCst|}t||}||_|Srr&r)rrrr']s z Curl.__new__cKst|jddSr,)curlr(r0rrrr.csz Curl.doitNr3rrrrr:Nsr:Tcs$t|}t|dkrtjSt|dkrtt|}|\}}}|\}}}|\} } } | |} | |} | |}tj}|t || |t | | ||| | 7}|t | | |t || ||| | 7}|t | | |t | | ||| | 7}r| S|St |t tfrddlmz&tt|fdd|jD}Wntk rv|j}YnXtfdd|DSt |ttfrdd|jDd}td d|jD}tt|| |t|d }r| S|St |tttfrt|St|d S) ao Returns the curl of a vector field computed wrt the base scalars of the given coordinate system. Parameters ========== vect : Vector The vector operand doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, curl >>> R = CoordSys3D('R') >>> v1 = R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> curl(v1) 0 >>> v2 = R.x*R.y*R.z*R.i >>> curl(v2) R.x*R.y*R.j + (-R.x*R.z)*R.k rexpresscsg|]}|ddqS)T variablesr.0r)csr>rr szcurl..c3s|]}t|dVqdSr-N)r;rAr-rr szcurl..cSs g|]}t|tttfr|qSrrrr r%rArrrrDscss"|]}t|tttfs|VqdSrrGrArrrrFsr-N)rlenrzeronextiter base_vectors base_scalarslame_coefficientsdotr r.rr r Z sympy.vectorr>r ValueErrorfromiterrrr r/r;r:r%)vectr. coord_sysrjkxyzh1h2h3ZvectxZvectyZvectzZoutvecr vectorscalarresr)rCr.r>rr;gsl           "r;cst|}t|dkrtjSt|dkrt|tttfr>t|St t |}| \}}}| \}}}| \} } } t|||| | | | | } t|||| | | | | } t|||| | | | | }| | |}r|S|St|ttfrtfdd|jDSt|ttfrdd|jDd}tdd|jD}t|t||t|d}r|S|St|tttfrt|St|d S) a Returns the divergence of a vector field computed wrt the base scalars of the given coordinate system. Parameters ========== vector : Vector The vector operand doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, divergence >>> R = CoordSys3D('R') >>> v1 = R.x*R.y*R.z * (R.i+R.j+R.k) >>> divergence(v1) R.x*R.y + R.x*R.z + R.y*R.z >>> v2 = 2*R.y*R.z*R.j >>> divergence(v2) 2*R.z rr<c3s|]}t|dVqdSrE)r9rAr-rrrFszdivergence..cSs g|]}t|tttfr|qSrrGrArrrrDszdivergence..css"|]}t|tttfs|VqdSrrGrArrrrFsr-N)rrHrZerorr r:r%r8rJrKrLrMrN_diff_conditionalrOr.r r rQr rrr r/r9)rRr.rSrrTrUrVrWrXrYrZr[vxvyvzr^r\r]rr-rr9sF       r9cst}t|dkrtjSt|dkrtt|}|\}}}|\}}}|\} } } t | |} t | |} t | |}|r| || ||| S| || |||St t t frt ddjDSt ttfrt}t fdd|DStSdS)a Returns the vector gradient of a scalar field computed wrt the base scalars of the given coordinate system. Parameters ========== scalar_field : SymPy Expr The scalar field to compute the gradient of doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, gradient >>> R = CoordSys3D('R') >>> s1 = R.x*R.y*R.z >>> gradient(s1) R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> s2 = 5*R.x**2*R.z >>> gradient(s2) 10*R.x*R.z*R.i + 5*R.x**2*R.k rr<css|]}t|VqdSrr/rArrrrF$szgradient..c3s|]}|t|VqdSrrdrA scalar_fieldrrrF'sN)rrHrrIrJrKrNrLrMr r.rr r rQr rrr$r%)rfr.rSrYrZr[rrTrUrVrWrXrarbrcsrrerr/s(   r/c@s eZdZdZddZddZdS) Laplacianz Represents unevaluated Laplacian. Examples ======== >>> from sympy.vector import CoordSys3D, Laplacian >>> R = CoordSys3D('R') >>> v = 3*R.x**3*R.y**2*R.z**3 >>> Laplacian(v) Laplacian(3*R.x**3*R.y**2*R.z**3) cCst|}t||}||_|Srr&r)rrrr':s zLaplacian.__new__cKsddlm}||jS)Nr) laplacian)sympy.vector.functionsrir()r1r2rirrrr.@s zLaplacian.doitNr3rrrrrh+srhcCs<ddlm}|||jdd}|||}|r6t||StjS)z First re-expresses expr in the system that base_scalar belongs to. If base_scalar appears in the re-expressed form, differentiates it wrt base_scalar. Else, returns 0 rr=Tr?)rjr>systemr rr_)rZ base_scalarZcoeff_1Zcoeff_2r>Znew_exprargrrrr`Es  r`)T)T)T)rZsympy.core.exprrZ sympy.corerrrZsympy.vector.coordsysrectrZsympy.vector.vectorrrr r r Zsympy.core.functionr Zsympy.core.addr Zsympy.core.mulrrr$r%r8r:r;r9r/rhr`rrrrs"       K C 6