o 8Vaq)@sddlZddlmZddlmZmZmZddlmZddl m Z m Z m Z m Z mZddlmZddlmZddlmZdd lmZmZd d Zd!d d ZddZGdddeZGdddeZGdddeZd"ddZd"ddZd"ddZ GdddeZ!dd Z"dS)#N)Expr)sympifySpreorder_traversal) CoordSys3D)Vector VectorMul VectorAddCrossDot) BaseScalar)SymPyDeprecationWarning) Derivative)AddMulcCs<t|}t}|D]}t|tr|||q t|SN)rset isinstanceraddskip frozenset)exprgretir8/usr/lib/python3/dist-packages/sympy/vector/operators.py_get_coord_systems s  rcCs$|durtdddddt|S)z[ expr : expression The coordinate system is extracted from this parameter. Nzcoord_sys parameterz do not use itz1.1iT2)ZfeatureZ useinsteadZdeprecated_since_versionZissue)r warnr)r coord_sysrrr_get_coord_sys_from_exprsr cCs:tdd}|jD] }|t||9<q t|S)NcSstjSr)rZOnerrrr)sz._split_mul_args_wrt_coordsys..) collections defaultdictargsrlistvalues)rdrrrr_split_mul_args_wrt_coordsys(s  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.selfkwargsrrrr6Dz Gradient.doitN__name__ __module__ __qualname____doc__r-r6rrrrr*/ 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-Wr2zDivergence.__new__cKr3r4) divergencer.r8rrrr6]r;zDivergence.doitNr<rrrrrBHrArBc@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-pr2z Curl.__new__cKr3r4)curlr.r8rrrr6vr;z Curl.doitNr<rrrrrDarArDTcst||}t|dkrtjSt|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|) a Returns the curl of a vector field computed wrt the base scalars of the given coordinate system. Parameters ========== vect : Vector The vector operand coord_sys : CoordSys3D The coordinate system to calculate the gradient in. Deprecated since version 1.1 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)TZ variablesr.0r)csrHrr szcurl..c3|] }t|dVqdSr5N)rErJr5rr zcurl..cS g|] }t|tttfr|qSrrrr r*rJrrrrM cs$|] }t|tttfs|VqdSrrSrJrrrrP"r5)r lenrzeronextiter base_vectors base_scalarslame_coefficientsdotrr6rrr Z sympy.vectorrHr$ ValueErrorfromiterrrr r7rErDr*)vectrr6rjkxyzh1h2h3ZvectxZvectyZvectzZoutvecr$vectorscalarresr)rLr6rHrrEzsn "             "rEcst||}t|dkrtjSt|dkryt|tttfr t|St t |}| \}}}| \}}}| \} } } t|||| | | | | } t|||| | | | | } t|||| | | | | }| | |}rw|S|St|ttfrtfdd|jDSt|ttfrdd|jDd}tdd|jD}t|t||t|d}r|S|St|tttfrt|St|) a Returns the divergence of a vector field computed wrt the base scalars of the given coordinate system. Parameters ========== vector : Vector The vector operand coord_sys : CoordSys3D The coordinate system to calculate the gradient in Deprecated since version 1.1 doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, divergence >>> R = CoordSys3D('R') >>> v1 = R.x*R.y*R.z * (R.i+R.j+R.k) >>> divergence(v1) R.x*R.y + R.x*R.z + R.y*R.z >>> v2 = 2*R.y*R.z*R.j >>> divergence(v2) 2*R.z rrFc3rNrO)rCrJr5rrrPrQzdivergence..cSrRrrSrJrrrrMrTzdivergence..csrUrrSrJrrrrPrVr5)r rWrZerorr rDr*rBrYrZr[r\r]_diff_conditionalr^r6rr r`r$rrr r7rC)rarr6rrbrcrdrerfrgrhrivxvyvzrlrjrkrr5rrCsF "       rCcst|}t|dkrtjSt|dkr`tt|}|\}}}|\}}}|\} } } t | |} t | |} t | |}|rT| || ||| S| || |||St t t frrt 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 coord_sys : CoordSys3D The coordinate system to calculate the gradient in Deprecated since version 1.1 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 rrFcss|]}t|VqdSrr7rJrrrrPCszgradient..c3s |] }|t|VqdSrrrrJ scalar_fieldrrrPFs)r rWrrXrYrZr]r[r\rr6rrr r`r$rrr(r*)rtrr6rgrhrirrbrcrdrerfrorprqsrrsrr7s( !   r7c@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-Yr2zLaplacian.__new__cKsddlm}||jS)Nr) laplacian)sympy.vector.functionsrwr.)r9r:rwrrrr6_s  zLaplacian.doitNr<rrrrrvJrArvcCsBddlm}|||jdd}||tvrt||||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 rrGTrI)rxrHsystemZatomsr rrrm)rZ base_scalarZcoeff_1Zcoeff_2rHZnew_exprrrrrnds rnr)NT)#r"Zsympy.core.exprrZ sympy.corerrrZsympy.vector.coordsysrectrZsympy.vector.vectorrrr r r Zsympy.vector.scalarr Zsympy.utilities.exceptionsr Zsympy.core.functionrZsympyrrrr r(r*rBrDrErCr7rvrnrrrrs(        O G: