g1%ddlZddlmZddlmZmZmZddlmZddl m Z m Z m Z m Z mZddlmZddlmZddlmZd Zd ZGd d eZGd deZGddeZddZddZddZGddeZdZdS)N)Expr)sympifySpreorder_traversal) CoordSys3D)Vector VectorMul VectorAddCrossDot) Derivative)Add)Mulct|}t}|D]@}t|tr)|||At |SN)rset isinstanceraddskip frozenset)exprgretis R/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/vector/operators.py_get_coord_systemsr sb4  A %%C  a $ $  GGAJJJ FFHHH S>>ctjd}|jD]}|t|xx|zcc< t |S)NctjSr)rOnerrz._split_mul_args_wrt_coordsys..sr) collections defaultdictargsrlistvalues)rdrs r_split_mul_args_wrt_coordsysr)sc ..A Y&& Q     A%      rceZdZdZdZdZdS)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) c\t|}tj||}||_|Srrr__new___exprclsrobjs rr.zGradient.__new__+*t}}l3%%  rc .t|jdSNTdoit)gradientr/selfhintss rr7z Gradient.doit1s ....rN__name__ __module__ __qualname____doc__r.r7r!rrr+r+s<   /////rr+ceZdZdZdZdZdS) 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) c\t|}tj||}||_|Srr-r0s rr.zDivergence.__new__Dr3rc .t|jdSr5) divergencer/r9s rr7zDivergence.doitJs$*40000rNr<r!rrrBrB5s<   11111rrBceZdZdZdZdZdS)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) c\t|}tj||}||_|Srr-r0s rr.z Curl.__new__]r3rc .t|jdSr5)curlr/r9s rr7z Curl.doitcsDJT****rNr<r!rrrGrGNs<   +++++rrGTcFt|}t|dkr tjSt|dkr`t t |}|\}}}|\}}}|\} } } | |} | |} | |}tj}|t|| z|t| | z|z |z| | zz z }|t| | z|t|| z|z |z| | zz z }|t| | z|t| | z|z |z| | zz z }r| S|St|ttfroddlm t t |fd|jD}n#t$$r |j}YnwxYwtjfd|DSt|t(t*frd|jDd}t)jd|jD}t-t/|| |t1|zz}r| S|St|t,t2t4frt3|St3|) 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 rexpressc,g|]}|dS)T variablesr!).0rcsrNs r zcurl..s*JJJ12666JJJrc3:K|]}t|VdSr6N)rJrRrr7s r zcurl..s0%G%GQd14&8&8&8%G%G%G%G%G%GrcVg|]&}t|tttf$|'Sr!rrr r+rRrs rrTzcurl...WWWAjVUH.:!g!gjVUZ\dLe>f>f!g!!g!g!g!g!g!grr6)rlenrzeronextiter base_vectors base_scalarslame_coefficientsdotr r7rrr sympy.vectorrNr% ValueErrorfromiterrr r r8rJrGr+)vectr7 coord_sysrjkxyzh1h2h3vectxvectyvectzoutvecr%vectorscalarresrSrNs ` @@rrJrJgs9<#4((I 9~~{ Y1  i)) ((**1a((**1a0022 B   :ebj!,,ebj!,,-01257"W> >:ebj!,,ebj!,,-01257"W> >:ebj!,,ebj!,,-01257"W> >  !;;==  dS), - -  , , , , , , !$y//**JJJJJ JJJ ! ! !y !%%G%G%G%G$%G%G%GGG G sI. / / WWWWWXYZF\!g!gTY!g!g!gggF((&1166886$vTXBYBYBY;YYC "xxzz!J udH5 6 6 :: t** s 0G::H HcHt|}t|dkr tjSt|dkr?t |t t tfrt|Stt|}| \}}}| \}}}| \} } } t|||| | | | z| zz } t|||| | | | z| zz } t|||| | | | z| zz }| | z|z}r|S|St |t"t$fr%t#jfd|jDSt |t*t,frd|jDd}t+jd|jD}t/|t1||t3|zz}r|S|St |t t tfrt|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 rrLc3:K|]}t|VdSrV)rErWs rrXzdivergence..s0LLQ 14 8 8 8LLLLLLrcVg|]&}t|tttf$|'Sr!rZr[s rrTzdivergence..r\rc3^K|](}t|tttf$|V)dSrrZr[s rrXzdivergence..r^rr6)rr_rZerorr rGr+rBrarbrcrdre_diff_conditionalrfr7rr rir%rr r r8rE)rjr7rkrrlrmrnrorprqrrrsvxvyvzrzrxrys ` rrErEsx<#4((I 9~~v Y1   dUD(3 4 4 $d## #i)) ((**1a((**1a0022 B txx{{Ar2 6 6R"  txx{{Ar2 6 6R"  txx{{Ar2 6 6R" 2gl  88::  dS), - - #<LLLL$)LLLLL L sI. / / #WWWWWXYZF\!g!gTY!g!g!gggFfhv..//&FQU9V9V9V2VVC "xxzz!J udH5 6 6 #d## #T"" "rc^t}t|dkr tjSt|dkrt t |}|\}}}|\}}}|\} } } t| |z } t| |z } t| |z }|r#| |z| |zz||zz S| |z| |zz||zzStttfr#tjdjDStt t"fr/t%}tjfd|DSt'S)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 rrLc34K|]}t|VdSrr8r[s rrXzgradient..$s(%M%Mahqkk%M%M%M%M%M%Mrc3BK|]}|z t|zVdSrr)rRr scalar_fields rrXzgradient..'s3%P%PlQ&6!&D%P%P%P%P%P%Pr)rr_rr`rarbrercrdr r7rrr rir%rr r)r+)rr7rkrqrrrsrrlrmrnrorprrrss` rr8r8s:#<00I 9~~{ Y1  i)) 0022 B((**1a((**1a  a ( (2 -  a ( (2 -  a ( (2 -  5FR!VOb1f,2244 4AvQa'' lS)$4 5 5 N%%M%M<;L%M%M%MMM M lS)$4 5 5 Q,\::A%%P%P%P%Pa%P%P%PPP P %%%rceZdZdZdZdZdS) 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) c\t|}tj||}||_|Srr-r0s rr.zLaplacian.__new__:r3rc .ddlm}||jS)Nr) laplacian)sympy.vector.functionsrr/)r:r;rs rr7zLaplacian.doit@s&444444y$$$rNr<r!rrrr+s<   %%%%%rrcddlm}|||jd}||z|z}|rt||n tjS)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 rrMTrP)rrNsystemr rr)r base_scalarcoeff_1coeff_2rNnew_exprargs rrrEsZ/.....wt[/4@@@H G h &C+. ::c; ' ' 'AF:r)T)r#sympy.core.exprr sympy.corerrrsympy.vector.coordsysrectrsympy.vector.vectorrr r r r sympy.core.functionr sympy.core.addrsympy.core.mulrrr)r+rBrGrJrEr8rrr!rrrs 5555555555000000HHHHHHHHHHHHHH******/////t///2111111112+++++4+++2HHHHV@#@#@#@#F3&3&3&3&l%%%%%%%%4 ; ; ; ; ;r