ó ¡¼™\c@s-ddlmZmZmZmZddlmZmZddlm Z ddl m Z ddl Z defd„ƒYZdee fd „ƒYZd eefd „ƒYZd eefd „ƒYZdeefd„ƒYZd„Zee_ee_ee_ee_ee_ee_eƒe_dS(iÿÿÿÿ(tBasisDependenttBasisDependentAddtBasisDependentMultBasisDependentZero(tStPow(t AtomicExpr(tImmutableMatrixNtDyadiccBskeZdZdZed„ƒZd„Zd„Zeje_d„Zd„Z eje _dd„Z RS( så Super class for all Dyadic-classes. References ========== .. [1] https://en.wikipedia.org/wiki/Dyadic_tensor .. [2] Kane, T., Levinson, D. Dynamics Theory and Applications. 1985 McGraw-Hill g*@cCs|jS(s® Returns the components of this dyadic in the form of a Python dictionary mapping BaseDyadic instances to the corresponding measure numbers. (t _components(tself((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt componentss c Cs]tjj}t|tƒr"|jSt||ƒr|j}xL|jjƒD];\}}|jdj |ƒ}||||jd7}qJW|St|t ƒr9t j}x|jjƒD]|\}} xm|jjƒD]\\} } |jdj | jdƒ}|jdj | jdƒ} ||| | | 7}qÑWqµW|St dt t|ƒƒdƒ‚dS(s„ Returns the dot product(also called inner product) of this Dyadic, with another Dyadic or Vector. If 'other' is a Dyadic, this returns a Dyadic. Else, it returns a Vector (unless an error is encountered). Parameters ========== other : Dyadic/Vector The other Dyadic or Vector to take the inner product with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> D1 = N.i.outer(N.j) >>> D2 = N.j.outer(N.j) >>> D1.dot(D2) (N.i|N.j) >>> D1.dot(N.j) N.i iis!Inner product is not defined for s and Dyadics.N(tsympytvectortVectort isinstanceRtzeroR titemstargstdotRtoutert TypeErrortstrttype( R totherRtoutvectktvtvect_dottoutdyadtk1tv1tk2tv2t outer_product((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR$s&   cCs |j|ƒS(N(R(R R((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt__and__TscCs¼tjj}||jkr"tjSt||ƒr˜tj}xW|jjƒD]F\}}|jdj |ƒ}|jdj |ƒ}|||7}qJW|St t t |ƒƒddƒ‚dS(s§ Returns the cross product between this Dyadic, and a Vector, as a Vector instance. Parameters ========== other : Vector The Vector that we are crossing this Dyadic with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> d = N.i.outer(N.i) >>> d.cross(N.j) (N.i|N.k) iis not supported for scross with dyadicsN(R R RRRRR RRtcrossRRRR(R RRRRRt cross_productR((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR$Ys  cCs |j|ƒS(N(R$(R R((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt__xor__}scCs]|dkr|}ntg|D]+}|D]}|j|ƒj|ƒ^q)qƒjddƒS(s% Returns the matrix form of the dyadic with respect to one or two coordinate systems. Parameters ========== system : CoordSys3D The coordinate system that the rows and columns of the matrix correspond to. If a second system is provided, this only corresponds to the rows of the matrix. second_system : CoordSys3D, optional, default=None The coordinate system that the columns of the matrix correspond to. Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> v = N.i + 2*N.j >>> d = v.outer(N.i) >>> d.to_matrix(N) Matrix([ [1, 0, 0], [2, 0, 0], [0, 0, 0]]) >>> from sympy import Symbol >>> q = Symbol('q') >>> P = N.orient_new_axis('P', q, N.k) >>> d.to_matrix(N, P) Matrix([ [ cos(q), -sin(q), 0], [2*cos(q), -2*sin(q), 0], [ 0, 0, 0]]) iN(tNonetMatrixRtreshape(R tsystemt second_systemtitj((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt to_matrix‚s'  N( t__name__t __module__t__doc__t _op_prioritytpropertyR RR#R$R&R'R.(((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR s  0   $  t BaseDyadiccBs/eZdZd„Zdd„ZeZeZRS(s9 Class to denote a base dyadic tensor component. cCstjj}tjj}tjj}t|||fƒ sPt|||fƒ rctddƒ‚n%||jks||jkrˆtjSt t |ƒj |||ƒ}||_ d|_ itdƒ|6|_|j|_d|jd|jd|_d|jd|jd|_|S( Ns*BaseDyadic cannot be composed of non-base tvectorsiu(t|t)t(s{|}(R R Rt BaseVectort VectorZeroRRRRtsuperR4t__new__t_base_instancet_measure_numberRR t_syst _pretty_formt _latex_form(tclstvector1tvector2RR9R:tobj((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR<µs"       cCs.dt|jdƒdt|jdƒdS(NR8iR6iR7(RR(R tprinter((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt__str__ÎsN(R/R0R1R<R'RGt _sympystrt _sympyrepr(((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR4°s   t DyadicMulcBs5eZdZd„Zed„ƒZed„ƒZRS(s% Products of scalars and BaseDyadics cOstj|||Ž}|S(N(RR<(RBRtoptionsRE((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR<ØscCs|jS(s) The BaseDyadic involved in the product. (R=(R ((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt base_dyadicÜscCs|jS(sU The scalar expression involved in the definition of this DyadicMul. (R>(R ((s2lib/python2.7/site-packages/sympy/vector/dyadic.pytmeasure_numberás(R/R0R1R<R3RLRM(((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyRJÕs t DyadicAddcBs/eZdZd„Zdd„ZeZeZRS(s Class to hold dyadic sums cOstj|||Ž}|S(N(RR<(RBRRKRE((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR<ìscCsnd}t|jjƒƒ}|jdd„ƒx5|D]-\}}||}||j|ƒd7}q5W|d S(NttkeycSs|djƒS(Ni(RG(tx((s2lib/python2.7/site-packages/sympy/vector/dyadic.pytóROs + iýÿÿÿ(tlistR RtsortRG(R RFtret_strRRRt temp_dyad((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyRGðs N(R/R0R1R<R'RGt__repr__RH(((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyRNés   t DyadicZerocBs)eZdZdZdZdZd„ZRS(s' Class to denote a zero dyadic g333333*@u(0|0)s#(\mathbf{\hat{0}}|\mathbf{\hat{0}})cCstj|ƒ}|S(N(RR<(RBRE((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyR<s(R/R0R1R2R@RAR<(((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyRXýs cCset|tƒr-t|tƒr-tdƒ‚n4t|tƒrUt|t|tjƒƒStdƒ‚dS(s' Helper for division involving dyadics sCannot divide two dyadicssCannot divide by a dyadicN(RRRRJRRt NegativeOne(toneR((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyt _dyad_div s (tsympy.vector.basisdependentRRRRt sympy.coreRRtsympy.core.exprRR RR(t sympy.vectorRR4RJRNRXR[t _expr_typet _mul_funct _add_funct _zero_funct _base_funct _div_helperR(((s2lib/python2.7/site-packages/sympy/vector/dyadic.pyts"" §%