o 8Va!@sddlmZddlmZmZmZmZddlmZm Z ddl m Z ddl m ZddlZ GdddeZGd d d ee ZGd d d eeZGd ddeeZGdddeeZee_ee_ee_ee_ee_ee_dS))Type)BasisDependentBasisDependentAddBasisDependentMulBasisDependentZero)SPow) AtomicExpr)ImmutableMatrixNc@szeZdZdZdZdZdZdZdZdZ dZ e ddZ ddZ dd Ze je_d d Zd d Zeje_dddZddZdS)Dyadicz 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*@NcC|jS)z Returns the components of this dyadic in the form of a Python dictionary mapping BaseDyadic instances to the corresponding measure numbers. ) _componentsselfr5/usr/lib/python3/dist-packages/sympy/vector/dyadic.py components!s zDyadic.componentsc Cstjj}t|tr |jSt||r3|j}|jD]\}}|jd |}||||jd7}q|St|t rqt j}|jD].\}} |jD]$\} } |jd | jd}|jd | jd} ||| | | 7}qIq@|St dt t|d)a Returns the dot product(also called inner product) of this Dyadic, with another Dyadic or Vector. If 'other' is a Dyadic, this returns a Dyadic. Else, it returns a Vector (unless an error is encountered). Parameters ========== other : Dyadic/Vector The other Dyadic or Vector to take the inner product with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> D1 = N.i.outer(N.j) >>> D2 = N.j.outer(N.j) >>> D1.dot(D2) (N.i|N.j) >>> D1.dot(N.j) N.i rz!Inner product is not defined for z and Dyadics.)sympyvectorVector isinstancerzeroritemsargsdotr outer TypeErrorstrtype) rotherrZoutveckvZvect_dotoutdyadZk1Zv1Zk2Zv2Z outer_productrrrr-s.    z Dyadic.dotcC ||SNrrr rrr__and__] zDyadic.__and__cCstjj}||jkr tjSt||r6tj}|jD]\}}|jd |}|jd |}|||7}q|St t t |dd)a Returns the cross product between this Dyadic, and a Vector, as a Vector instance. Parameters ========== other : Vector The Vector that we are crossing this Dyadic with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> d = N.i.outer(N.i) >>> d.cross(N.j) (N.i|N.k) rrz not supported for zcross with dyadics)rrrrr rrrrcrossrrrr)rr rr#r!r"Z cross_productrrrrr*bs  z Dyadic.crosscCr$r%)r*r'rrr__xor__r)zDyadic.__xor__cs,dur|tfdd|DddS)a% 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]]) Ncs&g|]}D] }||qqSrr&).0ij second_systemrrr sz$Dyadic.to_matrix..)MatrixZreshape)rsystemr0rr/r to_matrixs 'zDyadic.to_matrixcCs@t|trt|trtdt|trt|t|tjStd)z' Helper for division involving dyadics zCannot divide two dyadicszCannot divide by a dyadic)rr r DyadicMulrrZ NegativeOne)Zoner rrr _div_helpers  zDyadic._div_helperr%)__name__ __module__ __qualname____doc__ _op_priority _expr_type _mul_func _add_func _zero_func _base_funcrpropertyrrr(r*r+r5r7rrrrr s&   0$  -r cs(eZdZdZfddZddZZS) BaseDyadicz9 Class to denote a base dyadic tensor component. cstjj}tjj}tjj}t|||frt|||fstd||jks(||jkr+tjSt |||}||_ d|_ |t ji|_|j|_d|jd|jd|_d|jd|jd|_|S)Nz1BaseDyadic cannot be composed of non-base vectorsr(|)z{|})rrr BaseVector VectorZerorrrr super__new___base_instance_measure_numberrZOner _sys _pretty_form _latex_form)clsZvector1Zvector2rrGrHobj __class__rrrJs2    zBaseDyadic.__new__cCs$d||jd||jdS)Nz({}|{})rr)format_printr)rprinterrrr _sympystrszBaseDyadic._sympystr)r8r9r:r;rJrW __classcell__rrrRrrCs rCc@s0eZdZdZddZeddZeddZdS) r6z% Products of scalars and BaseDyadics cOtj|g|Ri|}|Sr%)rrJrProptionsrQrrrrJzDyadicMul.__new__cCr )z) The BaseDyadic involved in the product. )rKrrrr base_dyadicszDyadicMul.base_dyadiccCr )zU The scalar expression involved in the definition of this DyadicMul. )rLrrrrmeasure_numberszDyadicMul.measure_numberN)r8r9r:r;rJrBr]r^rrrrr6s r6c@s eZdZdZddZddZdS) DyadicAddz Class to hold dyadic sums cOrYr%)rrJrZrrrrJr\zDyadicAdd.__new__cs6t|j}|jddddfdd|DS)NcSs |dS)Nr)__str__)xrrrs z%DyadicAdd._sympystr..)keyz + c3s"|] \}}||VqdSr%)rU)r,r!r"rVrr s z&DyadicAdd._sympystr..)listrrsortjoin)rrVrrrdrrWszDyadicAdd._sympystrN)r8r9r:r;rJrWrrrrr_s r_c@s$eZdZdZdZdZdZddZdS) DyadicZeroz' Class to denote a zero dyadic g333333*@z(0|0)z#(\mathbf{\hat{0}}|\mathbf{\hat{0}})cCst|}|Sr%)rrJ)rPrQrrrrJs zDyadicZero.__new__N)r8r9r:r;r<rNrOrJrrrrris  ri)typingrZsympy.vector.basisdependentrrrrZ sympy.corerrZsympy.core.exprr rr r3Z sympy.vectorr rCr6r_rir=r>r?r@rArrrrrs$   8#