\hk%SSKrSSKJr SSKJrJrJr SSKJr SSK J r J r J r J r Jr SSKJr SSKJr SSKJr S rS r"S S \5r"S S\5r"SS\5rSSjrSSjrSSjr"SS\5rSrg)N)Expr)sympifySpreorder_traversal) CoordSys3D)Vector VectorMul VectorAddCrossDot) Derivative)Add)Mulc[U5n[5nUH;n[U[5(dMUR U5 UR 5 M= [ U5$N)rset isinstanceraddskip frozenset)exprgretis N/var/www/auris/envauris/lib/python3.13/site-packages/sympy/vector/operators.py_get_coord_systemsr sJ4 A %C  a $ $ GGAJ FFH S>c[R"S5nURHnU[U5==U-ss'M [ UR 55$)Nc"[R$r)rOnerr._split_mul_args_wrt_coordsys..sr) collections defaultdictargsrlistvalues)rdrs r_split_mul_args_wrt_coordsysr*sG .A YY Q  A%   rc$\rSrSrSrSrSrSrg)Gradientz Represents unevaluated Gradient. Examples ======== >>> from sympy.vector import CoordSys3D, Gradient >>> R = CoordSys3D('R') >>> s = R.x*R.y*R.z >>> Gradient(s) Gradient(R.x*R.y*R.z) cT[U5n[R"X5nXlU$rrr__new___exprclsrobjs rr0Gradient.__new__+#t}ll3%  rc *[URSS9$NTdoit)gradientr1selfhintss rr: Gradient.doit1s ..rr!N__name__ __module__ __qualname____firstlineno____doc__r0r:__static_attributes__r!rrr,r,s  /rr,c$\rSrSrSrSrSrSrg) Divergence5z 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) cT[U5n[R"X5nXlU$rr/r2s rr0Divergence.__new__Dr6rc *[URSS9$r8) divergencer1r<s rr:Divergence.doitJs$**400rr!Nr@r!rrrHrH5s  1rrHc$\rSrSrSrSrSrSrg)CurlNz 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) cT[U5n[R"X5nXlU$rr/r2s rr0 Curl.__new__]r6rc *[URSS9$r8)curlr1r<s rr: Curl.doitcsDJJT**rr!Nr@r!rrrPrPNs  +rrPc ^[U5n[U5S:Xa[R$[U5S:XGa![ [ U55nUR 5up4nUR5upgnUR5upn URU5n URU5n URU5n[RnU[X-U5[X-U5- U-X-- - nU[X-U5[X-U5- U-X-- - nU[X-U5[X-U5- U-X-- - nT(aUR5$U$[U[[45(a]SSKJn [ [ U55nUR"Vs/sH nU"UUSS9PM nn[R&"U4SjU55$[U[([*45(aUR"Vs/sH'n[U[[,[.45(dM%UPM) snSn[(R&"SUR"55n[-[1U5U5R5U[3UTS9--nT(aUR5$U$[U[,[4[.45(a [5U5$[%S 5es snf![$a UR"nGNBf=fs snf) a 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 rexpressT variablesc38># UHn[UTS9v M g7fr9N)rU.0rr:s r curl..s%G$Qd14&8$c3j# UH)n[U[[[45(aM%Uv M+ g7frrrr r,r`rs rrarb$!gYjVUZ\dLe>f!!Y$3 3r9zInvalid argument for curl)rlenrzeronextiter base_vectors base_scalarslame_coefficientsdotr r:rrr sympy.vectorrZr& ValueErrorfromiterrr r r,r;rUrP)vectr: coord_sysrjkxyzh1h2h3vectxvectyvectzoutvecrZcsr&vectorscalarress ` rrUrUgs<#4(I 9~{{ Y1 i) ((*a((*a002    :ej!,ej!,-01257W> >:ej!,ej!,-01257W> >:ej!,ej!,-01257W> > ;;=  dS), - - , !$y/*@D J 126 J%%%G$%GG G sI. / /!%WAjVUH$K;&K;KK87K8c ^[U5n[U5S:Xa[R$[U5S:XGa[ U[ [ [45(a [U5$[[U55nUR5up4nUR5upgnUR5upn [URU5XjU 5X-U -- n [URU5X{U 5X-U -- n [URU5XU 5X-U -- nX-U-nT(aUR!5$U$[ U["[$45(a*["R&"U4SjUR(55$[ U[*[,45(aUR(Vs/sH'n[ U[.[ [45(dM%UPM) snSn[*R&"SUR(55n[1U[3U55U[5UTS9--nT(aUR!5$U$[ U[ [ [45(a [U5$[7S5es snf)a+ Returns the divergence of a vector field computed wrt the base scalars of the given coordinate system. Parameters ========== vector : Vector The vector operand doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, divergence >>> R = CoordSys3D('R') >>> v1 = R.x*R.y*R.z * (R.i+R.j+R.k) >>> divergence(v1) R.x*R.y + R.x*R.z + R.y*R.z >>> v2 = 2*R.y*R.z*R.j >>> divergence(v2) 2*R.z rrXc38># UHn[UTS9v M g7fr^)rMr_s rradivergence..sL)Q 14 8)rcc3j# UH)n[U[[[45(aM%Uv M+ g7frrerfs rrarrgrhr9zInvalid argument for divergence)rrirZerorr rPr,rHrkrlrmrnro_diff_conditionalrpr:rr rsr&rr rr r;rMrr)rtr:rurrvrwrxryrzr{r|r}vxvyvzrrrs ` rrMrMs <#4(I 9~vv Y1  dUD(3 4 4d# #i) ((*a((*a002  txx{A2 6"  txx{A2 6"  txx{A2 6" gl 88:  dS), - -<<L$))LL L sI. / /!%WAjVUH? ?Xs .$I;I;c^[T5n[U5S:Xa[R$[U5S:Xa[ [ U55nUR 5up4nUR5upgnUR5upn [TU 5U- n [TU 5U- n [TU 5U- nU(aX-X--X--R5$X-X--X--$[T[[45(a'[R"STR55$[T[ ["45(a+[%T5n[R"U4SjU55$['T5$)a_ Returns the vector gradient of a scalar field computed wrt the base scalars of the given coordinate system. Parameters ========== scalar_field : SymPy Expr The scalar field to compute the gradient of doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, gradient >>> R = CoordSys3D('R') >>> s1 = R.x*R.y*R.z >>> gradient(s1) R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k >>> s2 = 5*R.x**2*R.z >>> gradient(s2) 10*R.x*R.z*R.i + 5*R.x**2*R.k rrXc38# UHn[U5v M g7frr;rfs rragradient..$s%M;Lahqkk;Lsc3F># UHnTU- [U5-v M g7frr)r`r scalar_fields rrar's%PalQ&6!&Das!)rrirrjrkrlrormrnr r:rrr rsr&rr r*r,)rr:rur{r|r}rrvrwrxryrzrrrss` rr;r;sK:#<0I 9~{{ Y1 i) 002 ((*a((*a  a (2 -  a (2 -  a (2 - FRVObf,224 4v'' lS)$4 5 5%%%M<;L;L%MM M lS)$4 5 5,\:A%%%Pa%PP P %%rc$\rSrSrSrSrSrSrg) Laplaciani+z 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) cT[U5n[R"X5nXlU$rr/r2s rr0Laplacian.__new__:r6rc 2SSKJn U"UR5$)Nr) laplacian)sympy.vector.functionsrr1)r=r>rs rr:Laplacian.doit@s4$$rr!Nr@r!rrrr+s  %rrcSSKJn U"XRSS9nX#-U-nU(a [Xa5$[R $)z First re-expresses expr in the system that base_scalar belongs to. If base_scalar appears in the re-expressed form, differentiates it wrt base_scalar. Else, returns 0 rrYTr[)rrZsystemr rr)r base_scalarcoeff_1coeff_2rZnew_exprargs rrrEs</t//4@H  h &C+.:c ':AFF:r)T)r$sympy.core.exprr sympy.corerrrsympy.vector.coordsysrectrsympy.vector.vectorrr r r r sympy.core.functionr sympy.core.addrsympy.core.mulrrr*r,rHrPrUrMr;rrr!rrrsw 550HH*/t/2112+4+2H:V@@F3&l%%4 ;r