o o h1%@sddlZddlmZddlmZmZmZddlmZddl m Z m Z m Z m Z mZddlmZddlmZddlmZd d Zd d ZGd ddeZGdddeZGdddeZdddZdddZdddZGdddeZddZdS)N)Expr)sympifySpreorder_traversal) CoordSys3D)Vector VectorMul VectorAddCrossDot) Derivative)Add)MulcCs<t|}t}|D]}t|tr|||q t|SN)rset isinstanceraddskip frozenset)exprgretirj/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/vector/operators.py_get_coord_systems s  rcCs:tdd}|jD] }|t||9<q t|S)NcSstjSr)rOnerrrrsz._split_mul_args_wrt_coordsys..) collections defaultdictargsrlistvalues)rdrrrr_split_mul_args_wrt_coordsyss  r$c@ eZdZdZddZddZdS)Gradientz Represents unevaluated Gradient. Examples ======== >>> from sympy.vector import CoordSys3D, Gradient >>> R = CoordSys3D('R') >>> s = R.x*R.y*R.z >>> Gradient(s) Gradient(R.x*R.y*R.z) cCt|}t||}||_|Srrr__new___exprclsrobjrrrr)+ zGradient.__new__cKt|jddSNTdoit)gradientr*selfhintsrrrr21z Gradient.doitN__name__ __module__ __qualname____doc__r)r2rrrrr& r&c@r%) Divergencea Represents unevaluated Divergence. Examples ======== >>> from sympy.vector import CoordSys3D, Divergence >>> R = CoordSys3D('R') >>> v = R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> Divergence(v) Divergence(R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k) cCr'rr(r+rrrr)Dr.zDivergence.__new__cKr/r0) divergencer*r4rrrr2Jr7zDivergence.doitNr8rrrrr>5r=r>c@r%)Curla Represents unevaluated Curl. Examples ======== >>> from sympy.vector import CoordSys3D, Curl >>> R = CoordSys3D('R') >>> v = R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> Curl(v) Curl(R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k) cCr'rr(r+rrrr)]r.z Curl.__new__cKr/r0)curlr*r4rrrr2cr7z Curl.doitNr8rrrrr@Nr=r@Tcst|}t|dkr tjSt|dkrtt|}|\}}}|\}}}|\} } } | |} | |} | |}tj}|t || |t | | ||| | 7}|t | | |t || ||| | 7}|t | | |t | | ||| | 7}r| S|St |t tfrddlmztt|fdd|jD}Wn ty|j}Ynwtfdd|DSt |ttfrdd|jDd}td d|jD}tt|| |t|d }r| S|St |tttfrt|St|) ao Returns the curl of a vector field computed wrt the base scalars of the given coordinate system. Parameters ========== vect : Vector The vector operand doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, curl >>> R = CoordSys3D('R') >>> v1 = R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> curl(v1) 0 >>> v2 = R.x*R.y*R.z*R.i >>> curl(v2) R.x*R.y*R.j + (-R.x*R.z)*R.k rexpresscsg|] }|ddqS)T variablesr.0r)csrDrr szcurl..c3|] }t|dVqdSr1N)rArGr1rr zcurl..cS g|] }t|tttfr|qSrrrr r&rGrrrrJ cs$|] }t|tttfs|VqdSrrPrGrrrrM"r1)rlenrzeronextiter base_vectors base_scalarslame_coefficientsdotr r2rr r sympy.vectorrDr ValueErrorfromiterrrr r3rAr@r&)vectr2 coord_sysrjkxyzh1h2h3vectxvectyvectzoutvecr vectorscalarresr)rIr2rDrrAgsn             "rAcst|}t|dkr tjSt|dkrxt|tttfrt|St t |}| \}}}| \}}}| \} } } t|||| | | | | } t|||| | | | | } t|||| | | | | }| | |}rv|S|St|ttfrtfdd|jDSt|ttfrdd|jDd}tdd|jD}t|t||t|d}r|S|St|tttfrt|St|) 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 rrBc3rKrL)r?rGr1rrrMrNzdivergence..cSrOrrPrGrrrrJrQzdivergence..csrRrrPrGrrrrMrSr1)rrTrZerorr r@r&r>rVrWrXrYrZ_diff_conditionalr[r2r r r^r rrr r3r?)r_r2r`rrarbrcrdrerfrgrhvxvyvzrormrnrr1rr?sF       r?cst}t|dkr tjSt|dkr_tt|}|\}}}|\}}}|\} } } t | |} t | |} t | |}|rS| || ||| S| || |||St t t frqt ddjDSt ttfrt}t fdd|DStS)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 rrBcss|]}t|VqdSrr3rGrrrrM$szgradient..c3s |] }|t|VqdSrrurG scalar_fieldrrrM's)rrTrrUrVrWrZrXrYr r2rr r r^r rrr$r&)rwr2r`rfrgrhrrarbrcrdrerrrsrtsrrvrr3s(   r3c@r%) 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) cCr'rr(r+rrrr):r.zLaplacian.__new__cKsddlm}||jS)Nr) laplacian)sympy.vector.functionsrzr*)r5r6rzrrrr2@s  zLaplacian.doitNr8rrrrry+r=rycCs<ddlm}|||jdd}|||}|rt||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 rrCTrE)r{rDsystemr rrp)r base_scalarcoeff_1coeff_2rDnew_exprargrrrrqEs  rq)T)rsympy.core.exprr sympy.corerrrsympy.vector.coordsysrectrsympy.vector.vectorrrr r r sympy.core.functionr sympy.core.addr sympy.core.mulrrr$r&r>r@rAr?r3ryrqrrrrs$        K C6