o
    GZh&                     @   s  d 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 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 Z$dddZ%d de&fddZ'dddZ(dS )!zA
Several methods to simplify expressions involving unit objects.
    )reduce)Iterable)Optional)default_sort_key)Add)Tuple)Mul)Pow)ordered)sympify)Function)NonInvertibleMatrixError)	DimensionDimensionSystem)Prefix)Quantity
UnitSystem)siftc           
         s   ddl m}  t| }j|dd fdd|D fddD }t }|t|s7d S t fdd|D }|fd	d|D }| fd
d|D }z||}	W |	S  t	yl   Y d S w )Nr   )MatrixTZmark_dimensionlessc                    s   g | ]	}t  |qS  )r   get_dimensional_expr).0x)unit_systemr   G/var/www/auris/lib/python3.10/site-packages/sympy/physics/units/util.py
<listcomp>   s    z3_get_conversion_matrix_for_expr.<locals>.<listcomp>c                    s$   g | ]} j |d dD ]}|qqS )Tr   )get_dimensional_dependencies)r   r   i)dimension_systemr   r   r       s   $ c                    s"   g | ]}| v s  |s|qS r   )addr   r   )seenr   r   r   '      " c                    s    g | ]  fd dD qS )c                    s"   g | ]} j |d ddqS )Tr   r   )r   getr"   )r    jr   r   r   )   r$   z>_get_conversion_matrix_for_expr.<locals>.<listcomp>.<listcomp>r   )r   )r    target_dims)r&   r   r   )   s     c                    s   g | ]}  |d qS r   )r%   )r   k)dim_dependenciesr   r   r   *       )
Zsympy.matrices.denser   get_dimension_systemr   r   r   setissubsetZsolver   )
exprtarget_unitsr   r   Zexpr_dimZcanon_dim_unitsZcanon_expr_unitsZcamatZexprmatZres_exponentsr   )r*   r    r#   r'   r   r   _get_conversion_matrix_for_expr   s&   r1   SIc                    s  ddl m} |tttfsgfdd}t| tr%|| S t| tr8t| jtr8|| j| j	 S t
| } t
t| trI|  } t| ts`| tr`| dd fdd}  fdd	 t| }|d
u rs| S  | }|t fddt|D  S )a  
    Convert ``expr`` to the same expression with all of its units and quantities
    represented as factors of ``target_units``, whenever the dimension is compatible.

    ``target_units`` may be a single unit/quantity, or a collection of
    units/quantities.

    Examples
    ========

    >>> from sympy.physics.units import speed_of_light, meter, gram, second, day
    >>> from sympy.physics.units import mile, newton, kilogram, atomic_mass_constant
    >>> from sympy.physics.units import kilometer, centimeter
    >>> from sympy.physics.units import gravitational_constant, hbar
    >>> from sympy.physics.units import convert_to
    >>> convert_to(mile, kilometer)
    25146*kilometer/15625
    >>> convert_to(mile, kilometer).n()
    1.609344*kilometer
    >>> convert_to(speed_of_light, meter/second)
    299792458*meter/second
    >>> convert_to(day, second)
    86400*second
    >>> 3*newton
    3*newton
    >>> convert_to(3*newton, kilogram*meter/second**2)
    3*kilogram*meter/second**2
    >>> convert_to(atomic_mass_constant, gram)
    1.660539060e-24*gram

    Conversion to multiple units:

    >>> convert_to(speed_of_light, [meter, second])
    299792458*meter/second
    >>> convert_to(3*newton, [centimeter, gram, second])
    300000*centimeter*gram/second**2

    Conversion to Planck units:

    >>> convert_to(atomic_mass_constant, [gravitational_constant, speed_of_light, hbar]).n()
    7.62963087839509e-20*hbar**0.5*speed_of_light**0.5/gravitational_constant**0.5

    r   r   c                    s   t  fdd| jD S )Nc                 3   s    | ]	}t | V  qd S N
convert_tor"   r0   r   r   r   	<genexpr>g   s    z2convert_to.<locals>.handle_Adds.<locals>.<genexpr>)r   fromiterargsr/   r6   r   r   handle_Addsf   s   zconvert_to.<locals>.handle_Addsc                 S   s
   t | tS r3   )
isinstancer   r   r   r   r   <lambda>v   s   
 zconvert_to.<locals>.<lambda>c                    s   |   S r3   r4   r=   r6   r   r   r>   w   s    c                    sZ   t | trtdd  fdd| jD S t | tr! | j| j S t | tr+| S | S )Nc                 S   s   | | S r3   r   )r   yr   r   r   r>   {   s    z<convert_to.<locals>.get_total_scale_factor.<locals>.<lambda>c                    s   g | ]} |qS r   r   r"   get_total_scale_factorr   r   r   |       z>convert_to.<locals>.get_total_scale_factor.<locals>.<listcomp>)	r<   r   r   r9   r	   baseexpr   Zget_quantity_scale_factorr:   )rA   r   r   r   rA   y   s   



z*convert_to.<locals>.get_total_scale_factorNc                 3   s(    | ]\}}d  | | | V  qdS )   Nr   )r   upr@   r   r   r7      s    
zconvert_to.<locals>.<genexpr>)sympy.physics.unitsr   get_unit_systemr<   r   r   r   r	   rC   rD   r   r   Ztogetherr   hasreplacer1   r   r8   zip)r/   r0   r   r   r;   ZdepmatZexpr_scale_factorr   )rA   r0   r   r   r5   4   s2   ,





r5   FNacross_dimensionsc                    s8  | j s	| tts| S | t}| dd |D } t| tdd }|D ],}t|| dkr1q&tt	|| }|d |d j
  |  fdd|dd D } q&|r|du r]td	t|}| }|| }|j|d
d}	d}
|j D ]\}}||	kr|}
 nqy|
du r| S |j|
}|rt| ||} | S )a  Return an equivalent expression in which prefixes are replaced
    with numerical values and all units of a given dimension are the
    unified in a canonical manner by default. `across_dimensions` allows
    for units of different dimensions to be simplified together.

    `unit_system` must be specified if `across_dimensions` is True.

    Examples
    ========

    >>> from sympy.physics.units.util import quantity_simplify
    >>> from sympy.physics.units.prefixes import kilo
    >>> from sympy.physics.units import foot, inch, joule, coulomb
    >>> quantity_simplify(kilo*foot*inch)
    250*foot**2/3
    >>> quantity_simplify(foot - 6*inch)
    foot/2
    >>> quantity_simplify(5*joule/coulomb, across_dimensions=True, unit_system="SI")
    5*volt
    c                 S   s   i | ]}||j qS r   scale_factor)r   rG   r   r   r   
<dictcomp>   rB   z%quantity_simplify.<locals>.<dictcomp>c                 S   s   | j S r3   )	dimension)r   r   r   r   r>      s    z#quantity_simplify.<locals>.<lambda>rE   r   c                    s   i | ]}| |j  qS r   rN   )r   virefr   r   rP      r+   Nz:unit_system must be specified if across_dimensions is TrueTr   )Zis_AtomrJ   r   r   atomsxreplacer   lenlistr
   rO   
ValueErrorr   rI   r,   r   r   Zdimensional_dependenciesitemsZderived_unitsr%   r5   )r/   rM   r   rG   dr)   vr    Zdim_exprZdim_depsZtarget_dimensionZds_dimZds_dim_depsZtarget_unitr   rS   r   quantity_simplify   s<   
"

r]   c              	   C   sJ  ddl m} ||}dd }| t}| j}|D ]c}t }|jD ]Z}|j	r.|
d q#g }	d}
i }t|D ]"}|trGt||}|trT||||}q9|jr[d}
 nq9|	|  |
s}|
tt|	td t|d	kr}td
|q#qi }| tD ]}tdd |jD r|jdd |jD  ||< q| |S )z[Return expr if units in addends have the same
    base dimensions, else raise a ValueError.r   r   c                 S   sP   i | |}|  D ]\}}|| v r||v r|| |  ||< q
dd |  D S )z]Merge dictionaries by adding values of common keys and
        removing keys with value of 0.c                 S   s   i | ]\}}|d kr||qS r(   r   )r   keyvalr   r   r   rP      s    z5check_dimensions.<locals>.addDict.<locals>.<dictcomp>)rZ   )Zdict1Zdict2Zdict3r^   valuer   r   r   addDict   s   z!check_dimensions.<locals>.addDictr   FT)r^   rE   z(addends have incompatible dimensions: {}c                 s   s    | ]}t |tV  qd S r3   )r<   r   r"   r   r   r   r7     s    z#check_dimensions.<locals>.<genexpr>c                 S   s   g | ]}|j s|qS r   )	is_numberr"   r   r   r   r     s
    z$check_dimensions.<locals>.<listcomp>)rH   r   rI   rU   r   r,   r   r-   r9   rb   r!   r   Z	make_argsrJ   r   r   r   Zfree_symbolsextendrZ   tuplesortedr   rW   rY   formatanyfuncrV   )r/   r   r   ra   ZaddsZDIM_OFaZdesetZaidimsskipZdimdictr   Zrepsmr   r   r   check_dimensions   sP   


	






rm   )r2   )FN))__doc__	functoolsr   collections.abcr   typingr   Zsympyr   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.mulr   Zsympy.core.powerr	   Zsympy.core.sortingr
   Zsympy.core.sympifyr   Zsympy.core.functionr   Zsympy.matrices.exceptionsr   Zsympy.physics.units.dimensionsr   r   Zsympy.physics.units.prefixesr   Zsympy.physics.units.quantitiesr   Zsympy.physics.units.unitsystemr   Zsympy.utilities.iterablesr   r1   r5   boolr]   rm   r   r   r   r   <module>   s,    
YD