o
    *ήcZF                     @  s~  d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	 d dl
mZmZ d dlmZ d dlmZ d d	lmZ d d
lmZ d dlmZ d dlmZ d dlmZmZmZmZ d dlm Z  d dl!m"Z"m#Z#m$Z$ G dd deZ%G dd de%eZ&G dd dee%Z'G dd dee%Z(G dd dee%Z)G dd de%Z*G dd deZ+dd Z,d d! Z-e%e%_.e(e%_/e'e%_0e)e%_1e&e%_2e) e%_3d"S )#    )annotations)product)Type)Add)	StdFactKB)
AtomicExprExpr)Pow)S)default_sort_key)sympifysqrt)ImmutableDenseMatrix)BasisDependentZeroBasisDependentBasisDependentMulBasisDependentAdd)
CoordSys3D)Dyadic
BaseDyadic	DyadicAddc                   @  s   e Zd ZU dZdZdZdZdZdZdZ	dZ
dZded< edd	 Zd
d Zdd Zdd Zdd Zeje_dd Zdd Zeje_dd Zd$ddZedd Zdd Zeje_dd Zd d! Zd"d# ZdS )%Vectorz
    Super class for all Vector classes.
    Ideally, neither this class nor any of its subclasses should be
    instantiated by the user.
    FTg      (@N
VectorZerozeroc                 C     | j S )a  
        Returns the components of this vector in the form of a
        Python dictionary mapping BaseVector instances to the
        corresponding measure numbers.

        Examples
        ========

        >>> from sympy.vector import CoordSys3D
        >>> C = CoordSys3D('C')
        >>> v = 3*C.i + 4*C.j + 5*C.k
        >>> v.components
        {C.i: 3, C.j: 4, C.k: 5}

        )_componentsself r   :/tmp/pip-target-vg8gfxp4/lib/python/sympy/vector/vector.py
components&   s   zVector.componentsc                 C  s   t | | @ S )z7
        Returns the magnitude of this vector.
        r   r   r   r   r    	magnitude;      zVector.magnitudec                 C  s   | |    S )z@
        Returns the normalized version of this vector.
        )r"   r   r   r   r    	normalizeA   r#   zVector.normalizec                   s   t |tr/t  trtjS tj}|j D ]\}}|jd  }||| |jd  7 }q|S ddl	m
} t ||tfsFtt|d d t ||rS fdd}|S t |S )aN  
        Returns the dot product of this Vector, either with another
        Vector, or a Dyadic, or a Del operator.
        If 'other' is a Vector, returns the dot product scalar (SymPy
        expression).
        If 'other' is a Dyadic, the dot product is returned as a Vector.
        If 'other' is an instance of Del, returns the directional
        derivative operator as a Python function. If this function is
        applied to a scalar expression, it returns the directional
        derivative of the scalar field wrt this Vector.

        Parameters
        ==========

        other: Vector/Dyadic/Del
            The Vector or Dyadic we are dotting with, or a Del operator .

        Examples
        ========

        >>> from sympy.vector import CoordSys3D, Del
        >>> C = CoordSys3D('C')
        >>> delop = Del()
        >>> C.i.dot(C.j)
        0
        >>> C.i & C.i
        1
        >>> v = 3*C.i + 4*C.j + 5*C.k
        >>> v.dot(C.k)
        5
        >>> (C.i & delop)(C.x*C.y*C.z)
        C.y*C.z
        >>> d = C.i.outer(C.i)
        >>> C.i.dot(d)
        C.i

        r      )Delz is not a vector, dyadic or zdel operatorc                   s   ddl m} ||  S )Nr   )directional_derivative)sympy.vector.functionsr'   )fieldr'   r   r   r    r'   ~   s   
z*Vector.dot.<locals>.directional_derivative)
isinstancer   r   r   r   r!   itemsargsdotsympy.vector.deloperatorr&   	TypeErrorstr)r   otheroutveckvvect_dotr&   r'   r   r   r    r-   G   s"   
(


z
Vector.dotc                 C  
   |  |S Nr-   r   r1   r   r   r    __and__      
zVector.__and__c                 C  sn   t |tr2t | trtjS tj}|j D ]\}}| |jd }||jd }||| 7 }q|S t| |S )a  
        Returns the cross product of this Vector with another Vector or
        Dyadic instance.
        The cross product is a Vector, if 'other' is a Vector. If 'other'
        is a Dyadic, this returns a Dyadic instance.

        Parameters
        ==========

        other: Vector/Dyadic
            The Vector or Dyadic we are crossing with.

        Examples
        ========

        >>> from sympy.vector import CoordSys3D
        >>> C = CoordSys3D('C')
        >>> C.i.cross(C.j)
        C.k
        >>> C.i ^ C.i
        0
        >>> v = 3*C.i + 4*C.j + 5*C.k
        >>> v ^ C.i
        5*C.j + (-4)*C.k
        >>> d = C.i.outer(C.i)
        >>> C.j.cross(d)
        (-1)*(C.k|C.i)

        r   r%   )	r*   r   r   r   r!   r+   crossr,   outer)r   r1   outdyadr3   r4   cross_productr=   r   r   r    r<      s   
 

zVector.crossc                 C  r6   r7   r<   r9   r   r   r    __xor__   r;   zVector.__xor__c                 C  sT   t |ts	tdt | tst |trtjS dd t| j |j D }t	| S )a  
        Returns the outer product of this vector with another, in the
        form of a Dyadic instance.

        Parameters
        ==========

        other : Vector
            The Vector with respect to which the outer product is to
            be computed.

        Examples
        ========

        >>> from sympy.vector import CoordSys3D
        >>> N = CoordSys3D('N')
        >>> N.i.outer(N.j)
        (N.i|N.j)

        z!Invalid operand for outer productc                 S  s*   g | ]\\}}\}}|| t || qS r   )r   ).0k1v1k2v2r   r   r    
<listcomp>   s   * z Vector.outer.<locals>.<listcomp>)
r*   r   r/   r   r   r   r   r!   r+   r   )r   r1   r,   r   r   r    r=      s   

zVector.outerc                 C  sL   |  tjr|rtjS tjS |r| || |  S | || |  |  S )a  
        Returns the vector or scalar projection of the 'other' on 'self'.

        Examples
        ========

        >>> from sympy.vector.coordsysrect import CoordSys3D
        >>> C = CoordSys3D('C')
        >>> i, j, k = C.base_vectors()
        >>> v1 = i + j + k
        >>> v2 = 3*i + 4*j
        >>> v1.projection(v2)
        7/3*C.i + 7/3*C.j + 7/3*C.k
        >>> v1.projection(v2, scalar=True)
        7/3

        )equalsr   r   r
   Zeror-   )r   r1   scalarr   r   r    
projection   s
   zVector.projectionc                   sP   ddl m} t trtjtjtjfS tt|  }t	 fdd|D S )a  
        Returns the components of this vector but the output includes
        also zero values components.

        Examples
        ========

        >>> from sympy.vector import CoordSys3D, Vector
        >>> C = CoordSys3D('C')
        >>> v1 = 3*C.i + 4*C.j + 5*C.k
        >>> v1._projections
        (3, 4, 5)
        >>> v2 = C.x*C.y*C.z*C.i
        >>> v2._projections
        (C.x*C.y*C.z, 0, 0)
        >>> v3 = Vector.zero
        >>> v3._projections
        (0, 0, 0)
        r   )_get_coord_systemsc                      g | ]}  |qS r   r8   rB   ir   r   r    rG         z'Vector._projections.<locals>.<listcomp>)
sympy.vector.operatorsrL   r*   r   r
   rI   nextiterbase_vectorstuple)r   rL   base_vecr   r   r    _projections   s
   
zVector._projectionsc                 C  r6   r7   )r=   r9   r   r   r    __or__  r;   zVector.__or__c                   s   t  fdd| D S )a  
        Returns the matrix form of this vector with respect to the
        specified coordinate system.

        Parameters
        ==========

        system : CoordSys3D
            The system wrt which the matrix form is to be computed

        Examples
        ========

        >>> from sympy.vector import CoordSys3D
        >>> C = CoordSys3D('C')
        >>> from sympy.abc import a, b, c
        >>> v = a*C.i + b*C.j + c*C.k
        >>> v.to_matrix(C)
        Matrix([
        [a],
        [b],
        [c]])

        c                   rM   r   r8   )rB   unit_vecr   r   r    rG   4  rP   z$Vector.to_matrix.<locals>.<listcomp>)MatrixrT   )r   systemr   r   r    	to_matrix  s   zVector.to_matrixc                 C  s:   i }| j  D ]\}}||jtj||  ||j< q|S )a  
        The constituents of this vector in different coordinate systems,
        as per its definition.

        Returns a dict mapping each CoordSys3D to the corresponding
        constituent Vector.

        Examples
        ========

        >>> from sympy.vector import CoordSys3D
        >>> R1 = CoordSys3D('R1')
        >>> R2 = CoordSys3D('R2')
        >>> v = R1.i + R2.i
        >>> v.separate() == {R1: R1.i, R2: R2.i}
        True

        )r!   r+   getr[   r   r   )r   partsvectmeasurer   r   r    separate7  s   zVector.separatec                 C  sR   t | trt |trtdt | tr%|tjkrtdt| t|tjS td)z( Helper for division involving vectors. zCannot divide two vectorszCannot divide a vector by zeroz#Invalid division involving a vector)	r*   r   r/   r
   rI   
ValueError	VectorMulr	   NegativeOne)oner1   r   r   r    _div_helperQ  s   

zVector._div_helper)F)__name__
__module____qualname____doc__	is_scalar	is_Vector_op_priority
_expr_type	_mul_func	_add_func
_zero_func
_base_func__annotations__propertyr!   r"   r$   r-   r:   r<   rA   r=   rK   rW   rX   r\   ra   rf   r   r   r   r    r      s<   
 
>,
$
r   c                      sJ   e Zd ZdZd fdd	Zedd Zdd Zd	d
 Zedd Z	  Z
S )
BaseVectorz)
    Class to denote a base vector.

    Nc                   s   |d u r	d |}|d u rd |}t|}t|}|tddvr%tdt|ts.td|j| }t 	| t
||}||_|t
ji|_t
j|_|jd | |_d| |_||_||_||f|_d	d
i}t||_||_|S )Nzx{}zx_{}r      zindex must be 0, 1 or 2zsystem should be a CoordSys3D. commutativeT)formatr0   rangerb   r*   r   r/   _vector_namessuper__new__r
   _base_instanceOner   _measure_number_name_pretty_form_latex_form_system_idr   _assumptions_sys)clsindexr[   
pretty_str	latex_strnameobjassumptions	__class__r   r    r~   c  s0   






zBaseVector.__new__c                 C  r   r7   )r   r   r   r   r    r[        zBaseVector.systemc                 C  r   r7   )r   )r   printerr   r   r    	_sympystr  s   zBaseVector._sympystrc                 C  s"   | j \}}||d |j|  S )Nrw   )r   _printr|   )r   r   r   r[   r   r   r    
_sympyrepr  s   
zBaseVector._sympyreprc                 C  s   | hS r7   r   r   r   r   r    free_symbols  r   zBaseVector.free_symbols)NN)rg   rh   ri   rj   r~   rt   r[   r   r   r   __classcell__r   r   r   r    ru   ]  s    #
ru   c                   @      e Zd ZdZdd Zdd ZdS )	VectorAddz2
    Class to denote sum of Vector instances.
    c                 O     t j| g|R i |}|S r7   )r   r~   r   r,   optionsr   r   r   r    r~        zVectorAdd.__new__c           	      C  sz   d}t |   }|jdd d |D ]"\}}| }|D ]}||jv r5| j| | }|||d 7 }qq|d d S )Nrx   c                 S  s   | d   S )Nr   )__str__)xr   r   r    <lambda>  s    z%VectorAdd._sympystr.<locals>.<lambda>keyz + )listra   r+   sortrT   r!   r   )	r   r   ret_strr+   r[   r_   
base_vectsr   	temp_vectr   r   r    r     s   
zVectorAdd._sympystrN)rg   rh   ri   rj   r~   r   r   r   r   r    r     s    r   c                   @  s0   e Zd ZdZdd Zedd Zedd ZdS )	rc   z>
    Class to denote products of scalars and BaseVectors.
    c                 O  r   r7   )r   r~   r   r   r   r    r~     r   zVectorMul.__new__c                 C  r   )z) The BaseVector involved in the product. )r   r   r   r   r    base_vector  s   zVectorMul.base_vectorc                 C  r   )zU The scalar expression involved in the definition of
        this VectorMul.
        )r   r   r   r   r    measure_number  s   zVectorMul.measure_numberN)rg   rh   ri   rj   r~   rt   r   r   r   r   r   r    rc     s    
rc   c                   @  s$   e Zd ZdZdZdZdZdd ZdS )r   z'
    Class to denote a zero vector
    g333333(@0z\mathbf{\hat{0}}c                 C  s   t | }|S r7   )r   r~   )r   r   r   r   r    r~     s   
zVectorZero.__new__N)rg   rh   ri   rj   rm   r   r   r~   r   r   r   r    r     s    r   c                   @  r   )Crossa  
    Represents unevaluated Cross product.

    Examples
    ========

    >>> from sympy.vector import CoordSys3D, Cross
    >>> R = CoordSys3D('R')
    >>> v1 = R.i + R.j + R.k
    >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k
    >>> Cross(v1, v2)
    Cross(R.i + R.j + R.k, R.x*R.i + R.y*R.j + R.z*R.k)
    >>> Cross(v1, v2).doit()
    (-R.y + R.z)*R.i + (R.x - R.z)*R.j + (-R.x + R.y)*R.k

    c                 C  sJ   t |}t |}t|t|krt|| S t| ||}||_||_|S r7   )r   r   r   r   r~   _expr1_expr2r   expr1expr2r   r   r   r    r~     s   zCross.__new__c                 K     t | j| jS r7   )r<   r   r   r   hintsr   r   r    doit     z
Cross.doitNrg   rh   ri   rj   r~   r   r   r   r   r    r     s    
r   c                   @  r   )Dota  
    Represents unevaluated Dot product.

    Examples
    ========

    >>> from sympy.vector import CoordSys3D, Dot
    >>> from sympy import symbols
    >>> R = CoordSys3D('R')
    >>> a, b, c = symbols('a b c')
    >>> v1 = R.i + R.j + R.k
    >>> v2 = a * R.i + b * R.j + c * R.k
    >>> Dot(v1, v2)
    Dot(R.i + R.j + R.k, a*R.i + b*R.j + c*R.k)
    >>> Dot(v1, v2).doit()
    a + b + c

    c                 C  sB   t |}t |}t||gtd\}}t| ||}||_||_|S )Nr   )r   sortedr   r   r~   r   r   r   r   r   r    r~     s   zDot.__new__c                 K  r   r7   )r-   r   r   r   r   r   r    r     r   zDot.doitNr   r   r   r   r    r     s    	r   c                   s  t  trtfdd jD S t tr$t fddjD S t  trt tr jjkre jd }jd }||krEtjS h d	||h
 }|d d |krZdnd}| j |  S dd	lm} z| j}W n ty   t  Y S w t|S t  tst trtjS t  trtt j \}}	|	t| S t trttj \}
}|t |
 S t S )
a^  
    Returns cross product of two vectors.

    Examples
    ========

    >>> from sympy.vector import CoordSys3D
    >>> from sympy.vector.vector import cross
    >>> R = CoordSys3D('R')
    >>> v1 = R.i + R.j + R.k
    >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k
    >>> cross(v1, v2)
    (-R.y + R.z)*R.i + (R.x - R.z)*R.j + (-R.x + R.y)*R.k

    c                 3      | ]}t | V  qd S r7   r@   rN   vect2r   r    	<genexpr>"      zcross.<locals>.<genexpr>c                 3      | ]}t  |V  qd S r7   r@   rN   vect1r   r    r   $  r   r   >   r   r%      r%   rv   express)r*   r   r   fromiterr,   ru   r   r   r   
differencepoprT   	functionsr   rb   r   r<   r   rc   rR   rS   r!   r+   )r   r   n1n2n3signr   r4   rD   m1rF   m2r   r   r   r    r<     s:   







r<   c                   s@  t  trtfdd jD S t tr$t fddjD S t  tr`t tr` jjkr> kr;tjS tjS ddl	m
} z| j}W n tyZ   t  Y S w t |S t  tsjt trmtjS t  trtt j \}}|t| S t trttj \}}|t | S t S )a2  
    Returns dot product of two vectors.

    Examples
    ========

    >>> from sympy.vector import CoordSys3D
    >>> from sympy.vector.vector import dot
    >>> R = CoordSys3D('R')
    >>> v1 = R.i + R.j + R.k
    >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k
    >>> dot(v1, v2)
    R.x + R.y + R.z

    c                 3  r   r7   r8   rN   r   r   r    r   R  r   zdot.<locals>.<genexpr>c                 3  r   r7   r8   rN   r   r   r    r   T  r   r%   r   )r*   r   r   r,   ru   r   r
   r   rI   r   r   rb   r   r-   r   rc   rR   rS   r!   r+   )r   r   r   r4   rD   r   rF   r   r   r   r    r-   A  s.   





r-   N)4
__future__r   	itertoolsr   typingr   sympy.core.addr   sympy.core.assumptionsr   sympy.core.exprr   r   sympy.core.powerr	   sympy.core.singletonr
   sympy.core.sortingr   sympy.core.sympifyr   (sympy.functions.elementary.miscellaneousr   sympy.matrices.immutabler   rZ   sympy.vector.basisdependentr   r   r   r   sympy.vector.coordsysrectr   sympy.vector.dyadicr   r   r   r   ru   r   rc   r   r   r   r<   r-   rn   ro   rp   rq   rr   r   r   r   r   r    <module>   s@      K9 !0*