ó 9­\c@slddlZddlmZddlmZmZmZddlmZddl m Z m Z m Z m Z mZmZddlmZddlmZddlmZdd lmZmZd „Zdd „Zd „Zd efd„ƒYZdefd„ƒYZdefd„ƒYZde d„Z!de d„Z"de d„Z#defd„ƒYZ$d„Z%dS(iÿÿÿÿN(tExpr(tsympifytStpreorder_traversal(t CoordSys3D(tVectort VectorMult VectorAddtCrosstDottdot(t BaseScalar(tSymPyDeprecationWarning(t Derivative(tAddtMulcCs\t|ƒ}tgƒ}x7|D]/}t|tƒr|j|ƒ|jƒqqWt|ƒS(N(Rtsett isinstanceRtaddtskipt frozenset(texprtgtretti((s5lib/python2.7/site-packages/sympy/vector/operators.pyt_get_coord_systems s    c Cs>|d k r4tddddddddƒjƒnt|ƒS( s[ expr : expression The coordinate system is extracted from this parameter. tfeaturescoord_sys parametert useinsteads do not use ittdeprecated_since_versions1.1tissueiT2N(tNoneR twarnR(Rt coord_sys((s5lib/python2.7/site-packages/sympy/vector/operators.pyt_get_coord_sys_from_exprs cCsLtjd„ƒ}x'|jD]}|t|ƒc|9)t(t collectionst defaultdicttargsRtlisttvalues(RtdR((s5lib/python2.7/site-packages/sympy/vector/operators.pyt_split_mul_args_wrt_coordsys(stGradientcBs eZdZd„Zd„ZRS(sß 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) cCs+t|ƒ}tj||ƒ}||_|S(N(RRt__new__t_expr(tclsRtobj((s5lib/python2.7/site-packages/sympy/vector/operators.pyR->s  cKst|jdtƒS(Ntdoit(tgradientR.tTrue(tselftkwargs((s5lib/python2.7/site-packages/sympy/vector/operators.pyR1Ds(t__name__t __module__t__doc__R-R1(((s5lib/python2.7/site-packages/sympy/vector/operators.pyR,/s  t DivergencecBs eZdZd„Zd„ZRS(s 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) cCs+t|ƒ}tj||ƒ}||_|S(N(RRR-R.(R/RR0((s5lib/python2.7/site-packages/sympy/vector/operators.pyR-Ws  cKst|jdtƒS(NR1(t divergenceR.R3(R4R5((s5lib/python2.7/site-packages/sympy/vector/operators.pyR1]s(R6R7R8R-R1(((s5lib/python2.7/site-packages/sympy/vector/operators.pyR9Hs  tCurlcBs eZdZd„Zd„ZRS(s 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) cCs+t|ƒ}tj||ƒ}||_|S(N(RRR-R.(R/RR0((s5lib/python2.7/site-packages/sympy/vector/operators.pyR-ps  cKst|jdtƒS(NR1(tcurlR.R3(R4R5((s5lib/python2.7/site-packages/sympy/vector/operators.pyR1vs(R6R7R8R-R1(((s5lib/python2.7/site-packages/sympy/vector/operators.pyR;as  csït||ƒ}t|ƒdkr(tjSt|ƒdkrqtt|ƒƒ}|jƒ\}}}|jƒ\}}}|jƒ\} } } |j |ƒ} |j |ƒ} |j |ƒ}tj}|t || |ƒt | | |ƒ|| | 7}|t | | |ƒt || |ƒ|| | 7}|t | | |ƒt | | |ƒ|| | 7}ˆrm|j ƒS|St |t tfƒrddlm}yAtt|ƒƒ}g|jD]}|||dtƒ^qµ}Wntk ró|j}nXtj‡fd†|DƒƒSt |ttfƒr½g|jD]$}t |tttfƒr0|^q0d}tjd„|jDƒƒ}tt|ƒ|ƒj ƒ|t|dˆƒ}ˆr¹|j ƒS|St |tttfƒrßt|ƒSt|ƒ‚d S( sì 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 iiiÿÿÿÿ(texpresst variablesc3s!|]}t|dˆƒVqdS(R1N(R<(t.0R(R1(s5lib/python2.7/site-packages/sympy/vector/operators.pys »scss-|]#}t|tttfƒs|VqdS(N(RRRR,(R?R((s5lib/python2.7/site-packages/sympy/vector/operators.pys ¾sR1N(R!tlenRtzerotnexttitert base_vectorst base_scalarstlame_coefficientsR R R1RRRt sympy.vectorR=R'R3t ValueErrortfromiterRRRR,R2R<R;(tvectR R1Rtjtktxtytzth1th2th3tvectxtvectytvectztoutvecR=tcsR'tvectortscalartres((R1s5lib/python2.7/site-packages/sympy/vector/operators.pyR<zsN" 111 /  8/  csZt||ƒ}t|ƒdkr(tjSt|ƒdkrMt|tttfƒr\t|ƒSt t |ƒƒ}|j ƒ\}}}|j ƒ\}}}|j ƒ\} } } t|j|ƒ|| | ƒ| | | } t|j|ƒ|| | ƒ| | | } t|j|ƒ|| | ƒ| | | }| | |}ˆrI|jƒS|St|ttfƒr‚tj‡fd†|jDƒƒSt|ttfƒr(g|jD]$}t|tttfƒr¡|^q¡d}tjd„|jDƒƒ}t|t|ƒƒ|t|dˆƒ}ˆr$|jƒS|St|tttfƒrJt|ƒSt|ƒ‚dS(sû 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 iic3s!|]}t|dˆƒVqdS(R1N(R:(R?R(R1(s5lib/python2.7/site-packages/sympy/vector/operators.pys scss-|]#}t|tttfƒs|VqdS(N(RRRR,(R?R((s5lib/python2.7/site-packages/sympy/vector/operators.pys sR1N(R!R@RtZeroRRR;R,R9RBRCRDRERFt_diff_conditionalR R1RRRIR'RRRR R2R:(RJR R1RRKRLRMRNRORPRQRRtvxtvytvzRZRXRY((R1s5lib/python2.7/site-packages/sympy/vector/operators.pyR:És@"   8)  cs{tˆ|ƒ}t|ƒdkr(tjSt|ƒdkrtt|ƒƒ}|jƒ\}}}|jƒ\}}}|jƒ\} } } t ˆ| ƒ|} t ˆ| ƒ|} t ˆ| ƒ|}|rè| || |||j ƒS| || |||St ˆt t fƒr/t jd„ˆjDƒƒSt ˆttfƒrmtˆƒ}t j‡fd†|DƒƒStˆƒSdS(s/ 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 iicss|]}t|ƒVqdS(N(R2(R?R((s5lib/python2.7/site-packages/sympy/vector/operators.pys Csc3s#|]}ˆ|t|ƒVqdS(N(R2(R?R(t scalar_field(s5lib/python2.7/site-packages/sympy/vector/operators.pys FsN(R!R@RRARBRCRFRDRER R1RRRRIR'RRR+R,(R`R R1RPRQRRRRKRLRMRNROR]R^R_ts((R`s5lib/python2.7/site-packages/sympy/vector/operators.pyR2s(! t LaplaciancBs eZdZd„Zd„ZRS(sù 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) cCs+t|ƒ}tj||ƒ}||_|S(N(RRR-R.(R/RR0((s5lib/python2.7/site-packages/sympy/vector/operators.pyR-Ys  cKsddlm}||jƒS(Niÿÿÿÿ(t laplacian(tsympy.vector.functionsRcR.(R4R5Rc((s5lib/python2.7/site-packages/sympy/vector/operators.pyR1_s(R6R7R8R-R1(((s5lib/python2.7/site-packages/sympy/vector/operators.pyRbJs  cCs\ddlm}|||jdtƒ}||jtƒkrRt||||ƒStdƒS(s¿ 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 S(0) iÿÿÿÿ(R=R>i(RdR=tsystemR3tatomsR R R(Rt base_scalartcoeff_1tcoeff_2R=tnew_expr((s5lib/python2.7/site-packages/sympy/vector/operators.pyR\ds (&R%tsympy.core.exprRt sympy.coreRRRtsympy.vector.coordsysrectRtsympy.vector.vectorRRRRR R tsympy.vector.scalarR tsympy.utilities.exceptionsR tsympy.core.functionR tsympyRRRRR!R+R,R9R;R3R<R:R2RbR\(((s5lib/python2.7/site-packages/sympy/vector/operators.pyts& .  OG: