U 9%e{!@sddlmZddlmZmZmZmZddlmZm Z ddl m Z ddl m ZddlZGdddeZGd d d ee ZGd d d eeZGd ddeeZGdddeeZee_ee_ee_ee_ee_ee_dS)) annotations)BasisDependentBasisDependentAddBasisDependentMulBasisDependentZero)SPow) AtomicExpr)ImmutableDenseMatrixNc@seZdZUdZdZded<ded<ded<ded<ded<d ed <ed d Zd dZddZ eje _ddZ ddZ e je _dddZ ddZ dS)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*@z type[Dyadic] _expr_type _mul_func _add_func _zero_func _base_func DyadicZerozerocCs|jS)z Returns the components of this dyadic in the form of a Python dictionary mapping BaseDyadic instances to the corresponding measure numbers. ) _componentsselfrR/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/vector/dyadic.py components!s zDyadic.componentsc Cstjj}t|tr|jSt||rf|j}|jD].\}}|jd |}||||jd7}q2|St|t rt j}|jD]\\}} |jD]H\} } |jd | jd}|jd | jd} ||| | | 7}qq|St dt t|ddS)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.N)sympyvectorVector isinstancerrritemsargsdotr outer TypeErrorstrtype) rotherrZoutveckvZvect_dotoutdyadZk1Zv1Zk2Zv2Z outer_productrrrr -s,    z Dyadic.dotcCs ||SNr rr%rrr__and__]szDyadic.__and__cCstjj}||jkrtjSt||rltj}|jD]4\}}|jd |}|jd |}|||7}q2|St t t |dddS)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 dyadicsN)rrrrr rrrrcrossr!r"r#r$)rr%rr(r&r'Z cross_productr!rrrr-bs  z Dyadic.crosscCs ||Sr))r-r+rrr__xor__szDyadic.__xor__Ncs,dkr |tfdd|DddS)a% Returns the matrix form of the dyadic with respect to one or two coordinate systems. Parameters ========== system : CoordSys3D The coordinate system that the rows and columns of the matrix correspond to. If a second system is provided, this only corresponds to the rows of the matrix. second_system : CoordSys3D, optional, default=None The coordinate system that the columns of the matrix correspond to. Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> v = N.i + 2*N.j >>> d = v.outer(N.i) >>> d.to_matrix(N) Matrix([ [1, 0, 0], [2, 0, 0], [0, 0, 0]]) >>> from sympy import Symbol >>> q = Symbol('q') >>> P = N.orient_new_axis('P', q, N.k) >>> d.to_matrix(N, P) Matrix([ [ cos(q), -sin(q), 0], [2*cos(q), -2*sin(q), 0], [ 0, 0, 0]]) Ncs&g|]}D]}||q qSrr*).0ij second_systemrrr sz$Dyadic.to_matrix..)MatrixZreshape)rsystemr3rr2r to_matrixs 'zDyadic.to_matrixcCsFt|trt|trtdn$t|tr:t|t|tjStddS)z' Helper for division involving dyadics zCannot divide two dyadicszCannot divide by a dyadicN)rr r" DyadicMulrrZ NegativeOne)oner%rrr _div_helpers   zDyadic._div_helper)N)__name__ __module__ __qualname____doc__ _op_priority__annotations__propertyrr r,r-r.r8r;rrrrr s$   0$ -r cs0eZdZdZfddZddZddZZS) BaseDyadicz9 Class to denote a base dyadic tensor component. cstjj}tjj}tjj}t|||fr4t|||fs>tdn||jksR||jkrXtjSt |||}||_ d|_ |t ji|_|j|_d|jd|jd|_d|jd|jd|_|S) Nz1BaseDyadic cannot be composed of non-base vectorsr(|)z\left(z {\middle|}z\right))rrr BaseVector VectorZerorr"rr super__new___base_instance_measure_numberrZOner_sys _pretty_form _latex_form)clsZvector1Zvector2rrGrHobj __class__rrrJs2     zBaseDyadic.__new__cCs$d||jd||jdS)Nz({}|{})rrformat_printrrprinterrrr _sympystrszBaseDyadic._sympystrcCs$d||jd||jdS)NzBaseDyadic({}, {})rrrTrWrrr _sympyreprszBaseDyadic._sympyrepr)r<r=r>r?rJrYrZ __classcell__rrrRrrCs rCc@s0eZdZdZddZeddZeddZdS) r9z% Products of scalars and BaseDyadics cOstj|f||}|Sr))rrJrProptionsrQrrrrJszDyadicMul.__new__cCs|jS)z) The BaseDyadic involved in the product. )rKrrrr base_dyadicszDyadicMul.base_dyadiccCs|jS)zU The scalar expression involved in the definition of this DyadicMul. )rLrrrrmeasure_numberszDyadicMul.measure_numberN)r<r=r>r?rJrBr^r_rrrrr9s  r9c@s eZdZdZddZddZdS) DyadicAddz Class to hold dyadic sums cOstj|f||}|Sr))rrJr\rrrrJszDyadicAdd.__new__cs6t|j}|jddddfdd|DS)NcSs |dS)Nr)__str__)xrrrz%DyadicAdd._sympystr..)keyz + c3s |]\}}||VqdSr))rV)r/r&r'rXrr sz&DyadicAdd._sympystr..)listrrsortjoin)rrXrrrfrrYszDyadicAdd._sympystrN)r<r=r>r?rJrYrrrrr`sr`c@s$eZdZdZdZdZdZddZdS)rz' Class to denote a zero dyadic g333333*@z(0|0)z#(\mathbf{\hat{0}}|\mathbf{\hat{0}})cCst|}|Sr))rrJ)rPrQrrrrJs zDyadicZero.__new__N)r<r=r>r?r@rNrOrJrrrrr s r) __future__rZsympy.vector.basisdependentrrrrZ sympy.corerrZsympy.core.exprr Zsympy.matrices.immutabler r6Z sympy.vectorrr rCr9r`rr r rrrrrrrrs"   8'