o o h{!@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 DyadicZerozerocC|jS)z Returns the components of this dyadic in the form of a Python dictionary mapping BaseDyadic instances to the corresponding measure numbers. ) _componentsselfrg/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-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]$\} } |jd | jd}|jd | jd} ||| | | 7}qIq@|St dt t|d)a Returns the dot product(also called inner product) of this Dyadic, with another Dyadic or Vector. If 'other' is a Dyadic, this returns a Dyadic. Else, it returns a Vector (unless an error is encountered). Parameters ========== other : Dyadic/Vector The other Dyadic or Vector to take the inner product with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> D1 = N.i.outer(N.j) >>> D2 = N.j.outer(N.j) >>> D1.dot(D2) (N.i|N.j) >>> D1.dot(N.j) N.i rz!Inner product is not defined for z and Dyadics.)sympyvectorVector isinstancerrritemsargsdotr outer TypeErrorstrtype) rotherroutveckvvect_dotoutdyadk1v1k2v2 outer_productrrrr!-s.    z Dyadic.dotcC ||SNr!rr&rrr__and__] zDyadic.__and__cCstjj}||jkr tjSt||r6tj}|jD]\}}|jd |}|jd |}|||7}q|St t t |dd)a Returns the cross product between this Dyadic, and a Vector, as a Vector instance. Parameters ========== other : Vector The Vector that we are crossing this Dyadic with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> d = N.i.outer(N.i) >>> d.cross(N.j) (N.i|N.k) rrz not supported for zcross with dyadics)rrrrr rrrr crossr"r#r$r%)rr&rr+r(r) cross_productr"rrrr7bs  z Dyadic.crosscCr1r2)r7r4rrr__xor__r6zDyadic.__xor__Ncs,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] }||qqSrr3).0ij second_systemrrr sz$Dyadic.to_matrix..)Matrixreshape)rsystemr>rr=r to_matrixs 'zDyadic.to_matrixcCs@t|trt|trtdt|trt|t|tjStd)z' Helper for division involving dyadics zCannot divide two dyadicszCannot divide by a dyadic)rr r# DyadicMulrr NegativeOne)oner&rrr _div_helpers  zDyadic._div_helperr2)__name__ __module__ __qualname____doc__ _op_priority__annotations__propertyrr!r5r7r9rDrHrrrrr s&    0$  -r cs0eZdZdZfddZddZddZZS) 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\left(z {\middle|}z\right))rrr BaseVector VectorZerorr#rr super__new___base_instance_measure_numberrOner_sys _pretty_form _latex_form)clsvector1vector2rrTrUobj __class__rrrWs2    zBaseDyadic.__new__cC$d||jd||jdS)Nz({}|{})rrformat_printr rprinterrrr _sympystrzBaseDyadic._sympystrcCrd)NzBaseDyadic({}, {})rrrerhrrr _sympyreprrkzBaseDyadic._sympyrepr)rIrJrKrLrWrjrl __classcell__rrrbrrPs  rPc@s0eZdZdZddZeddZeddZdS) rEz% Products of scalars and BaseDyadics cOtj|g|Ri|}|Sr2)rrWr^r optionsrarrrrWzDyadicMul.__new__cCr)z) The BaseDyadic involved in the product. )rXrrrr base_dyadicszDyadicMul.base_dyadiccCr)zU The scalar expression involved in the definition of this DyadicMul. )rYrrrrmeasure_numberszDyadicMul.measure_numberN)rIrJrKrLrWrOrrrsrrrrrEs rEc@s eZdZdZddZddZdS) DyadicAddz Class to hold dyadic sums cOrnr2)rrWrorrrrWrqzDyadicAdd.__new__cs6t|j}|jddddfdd|DS)NcSs |dS)Nr)__str__)xrrrs z%DyadicAdd._sympystr..)keyz + c3s"|] \}}||VqdSr2)rg)r:r(r)rirr s z&DyadicAdd._sympystr..)listrrsortjoin)rrirrryrrjszDyadicAdd._sympystrN)rIrJrKrLrWrjrrrrrts rtc@s$eZdZdZdZdZdZddZdS)rz' Class to denote a zero dyadic g333333*@z(0|0)z#(\mathbf{\hat{0}}|\mathbf{\hat{0}})cCst|}|Sr2)rrW)r^rarrrrWs zDyadicZero.__new__N)rIrJrKrLrMr\r]rWrrrrr s  r) __future__rsympy.vector.basisdependentrrrr sympy.corerrsympy.core.exprr sympy.matrices.immutabler rA sympy.vectorrr rPrErtrr r rrrrrrrrs$   8'