a
    kº”h7  ã                   @   sh   d dl mZ d dlmZ d dlmZ d dlmZmZ dd„ Z	dd„ Z
d	d
„ Zdd„ Zdd„ Zdd„ ZdS )é    ©ÚPermutation)Úsymbols©ÚMatrix)Ú
variationsÚrotate_leftc                 c   s"   dd„ t t| ƒ| ƒD ƒE dH  dS )zß
    Generates the symmetric group of order n, Sn.

    Examples
    ========

    >>> from sympy.combinatorics.generators import symmetric
    >>> list(symmetric(3))
    [(2), (1 2), (2)(0 1), (0 1 2), (0 2 1), (0 2)]
    c                 s   s   | ]}t |ƒV  qd S ©Nr   )Ú.0Úperm© r   úL/var/www/auris/lib/python3.9/site-packages/sympy/combinatorics/generators.pyÚ	<genexpr>   ó    zsymmetric.<locals>.<genexpr>N)r   Úrange)Únr   r   r   Ú	symmetric   s    r   c                 c   s2   t t| ƒƒ}t| ƒD ]}t|ƒV  t|dƒ}qdS )a  
    Generates the cyclic group of order n, Cn.

    Examples
    ========

    >>> from sympy.combinatorics.generators import cyclic
    >>> list(cyclic(5))
    [(4), (0 1 2 3 4), (0 2 4 1 3),
     (0 3 1 4 2), (0 4 3 2 1)]

    See Also
    ========

    dihedral
    é   N)Úlistr   r   r   ©r   ÚgenÚir   r   r   Úcyclic   s    
r   c                 c   s,   t t| ƒ| ƒD ]}t|ƒ}|jr|V  qdS )zÍ
    Generates the alternating group of order n, An.

    Examples
    ========

    >>> from sympy.combinatorics.generators import alternating
    >>> list(alternating(3))
    [(2), (0 1 2), (0 2 1)]
    N)r   r   r   Zis_even)r   r   Úpr   r   r   Úalternating,   s    r   c                 c   s®   | dkr&t ddgƒV  t ddgƒV  n„| dkrht g d¢ƒV  t g d¢ƒV  t g d¢ƒV  t g d¢ƒV  nBtt| ƒƒ}t| ƒD ],}t |ƒV  t |ddd	… ƒV  t|dƒ}q|dS )
aÔ  
    Generates the dihedral group of order 2n, Dn.

    The result is given as a subgroup of Sn, except for the special cases n=1
    (the group S2) and n=2 (the Klein 4-group) where that's not possible
    and embeddings in S2 and S4 respectively are given.

    Examples
    ========

    >>> from sympy.combinatorics.generators import dihedral
    >>> list(dihedral(3))
    [(2), (0 2), (0 1 2), (1 2), (0 2 1), (2)(0 1)]

    See Also
    ========

    cyclic
    r   r   é   )r   r   r   é   )r   r   r   r   )r   r   r   r   )r   r   r   r   Néÿÿÿÿ)r   r   r   r   r   r   r   r   Údihedral=   s    
r   c                  C   s6   g d¢g d¢g d¢g d¢g d¢g d¢g} dd„ | D ƒS )	zpReturn the permutations of the 3x3 Rubik's cube, see
    https://www.gap-system.org/Doc/Examples/rubik.html
    ))r   r   é   é   )r   é   é   é   )é	   é!   é   é   )é
   é"   é   é   )é   é#   é   é   ))r$   r,   é   é   )r(   é   é   é   )r   r'   é)   é(   )r#   é   é,   é%   )r    é   é.   r-   ))r'   r/   é   r:   )r+   é   é   r7   )r    r&   é+   r0   )r"   é   é*   r2   )r   é   r5   r,   ))r&   r.   é    rB   )r*   é   é   r@   )r   é&   r?   r/   )r!   é$   é-   r=   )r   r%   é0   r<   ))r%   r-   r6   rF   )r)   r9   é'   rG   )r   r$   r;   rC   )r   r4   é/   rD   )r   r1   rI   r.   ))r5   r?   rI   r;   )rA   rH   rK   r8   )r1   r:   rB   rF   )r3   r>   rE   rJ   )r0   r<   rC   r6   c                 S   s"   g | ]}t d d„ |D ƒdd‘qS )c                 S   s   g | ]}d d„ |D ƒ‘qS )c                 S   s   g | ]}|d  ‘qS )r   r   )r
   r   r   r   r   Ú
<listcomp>s   r   z?rubik_cube_generators.<locals>.<listcomp>.<listcomp>.<listcomp>r   )r
   Úxir   r   r   rL   s   r   z4rubik_cube_generators.<locals>.<listcomp>.<listcomp>rI   )Úsizer   )r
   Úxr   r   r   rL   s   r   z)rubik_cube_generators.<locals>.<listcomp>r   )Úar   r   r   Úrubik_cube_generatorsa   s    õrQ   c                    sÐ  ˆdk rt dƒ‚‡
‡fdd„‰‡
fdd„‰‡
fdd„‰‡
‡fd	d
„‰‡
‡fdd„‰‡
‡fdd„‰‡
‡fdd„‰‡
‡fdd„‰d)‡
‡fdd„	‰	‡	fdd„‰d*‡‡‡‡‡‡	‡‡‡‡‡‡‡‡fdd„	‰‡fdd„}d+‡ ‡‡‡‡‡‡‡	‡
f	dd„	‰‡fdd„}d,‡ ‡‡‡‡‡‡‡	‡
f	d d!„	‰‡fd"d#„}td$ƒ \‰‰‰‰ ‰‰‰i ‰
d%}td&ƒD ]D}g }tˆd ƒD ]}| |¡ |d7 }q\tˆˆ|ƒˆ
ˆ| < qHd-‡
‡‡fd'd(„	}g ‰ttd&ˆd  ƒƒ}	tˆd ƒD ]}
ˆ|
ƒ |ƒ  ||
ƒ qÄ|dƒ|	ksôJ ‚ˆƒ  tˆd ƒD ](}
ˆ|
ƒ |ƒ  |ƒ  ˆƒ  ||
ƒ q|ƒ  |dƒ|	ksHJ ‚ˆƒ  |ƒ  |ƒ  tˆd ƒD ]@}
ˆ|
ƒ ˆƒ  ˆƒ  |ƒ  |ƒ  ˆƒ  |ƒ  |ƒ  ||
ƒ qfˆƒ  ˆƒ  |ƒ  |dƒ|	ksÌJ ‚ˆS ).a)  Return permutations for an nxn Rubik's cube.

    Permutations returned are for rotation of each of the slice
    from the face up to the last face for each of the 3 sides (in this order):
    front, right and bottom. Hence, the first n - 1 permutations are for the
    slices from the front.
    r   zdimension of cube must be > 1c                    s   ˆ |    ˆ| ¡S r	   ©Úcol©Úfr   ©Úfacesr   r   r   Úgetrƒ   s    zrubik.<locals>.getrc                    s   ˆ |    |d ¡S ©Nr   rR   rT   ©rW   r   r   Úgetl†   s    zrubik.<locals>.getlc                    s   ˆ |    |d ¡S rY   ©ÚrowrT   rZ   r   r   Úgetu‰   s    zrubik.<locals>.getuc                    s   ˆ |    ˆ| ¡S r	   r\   rT   rV   r   r   ÚgetdŒ   s    zrubik.<locals>.getdc                    s$   t ˆd|ƒˆ |  d d …ˆ| f< d S rY   r   ©rU   r   ÚsrV   r   r   Úsetr   s    zrubik.<locals>.setrc                    s$   t ˆd|ƒˆ |  d d …|d f< d S rY   r   r`   rV   r   r   Úsetl’   s    zrubik.<locals>.setlc                    s$   t dˆ|ƒˆ |  |d d d …f< d S rY   r   r`   rV   r   r   Úsetu•   s    zrubik.<locals>.setuc                    s$   t dˆ|ƒˆ |  ˆ| d d …f< d S rY   r   r`   rV   r   r   Úsetd˜   s    zrubik.<locals>.setdr   c                    sd   t |ƒD ]V}ˆ |  }g }t ˆƒD ],}t ˆd ddƒD ]}| |||f ¡ q4q tˆˆ|ƒˆ | < qd S )Nr   r   )r   Úappendr   )ÚFÚrÚ_ÚfaceÚrvÚcrV   r   r   Úcwœ   s    zrubik.<locals>.cwc                    s   ˆ | dƒ d S ©Nr   r   )rg   )rm   r   r   Úccw¥   s    zrubik.<locals>.ccwc              	      s–   t |ƒD ]ˆ}| dkrˆˆƒ | d7 } ˆˆ| ƒ}ˆˆ| tˆ	ˆ | ƒƒƒ ˆˆ | ttˆˆ| ƒƒƒƒ ˆˆ| tˆˆ| ƒƒƒ ˆ
ˆ| tt|ƒƒƒ | d8 } qd S )Nr   r   )r   r   Úreversed)r   rh   ri   Útemp)ÚDrg   ÚLÚRÚUrm   r_   r[   rX   r^   re   rc   rb   rd   r   r   Úfcw«   s    
zrubik.<locals>.fcwc                    s   ˆ | dƒ d S rn   r   )r   )rv   r   r   Úfccw·   s    zrubik.<locals>.fccwc                    sv   t | ƒD ]h}ˆˆƒ ˆˆ ƒ ˆˆƒ ˆˆ }ˆˆƒ ˆˆ ˆˆ< ˆˆƒ ˆˆ ˆˆ< ˆˆƒ ˆˆ ˆˆ< |ˆˆ< qd S r	   ©r   ©rh   ri   Út©	ÚBrr   rg   rs   rt   ru   ro   rm   rW   r   r   ÚFCW»   s    zrubik.<locals>.FCWc                      s   ˆ dƒ d S rn   r   r   )r}   r   r   ÚFCCWÉ   s    zrubik.<locals>.FCCWc                    sV   t | ƒD ]H}ˆˆƒ ˆˆƒ ˆˆ }ˆˆ ˆˆ< ˆˆ  ˆˆ< ˆˆ ˆˆ < |ˆˆ< qd S r	   rx   ry   r{   r   r   ÚUCWÍ   s    zrubik.<locals>.UCWc                      s   ˆ dƒ d S rn   r   r   )r   r   r   ÚUCCW×   s    zrubik.<locals>.UCCWzU, F, R, B, L, Dr   r    c                    s6   g }ˆD ]}|  ˆ | ¡ q| r$|S ˆ t|ƒ¡ d S r	   )Úextendrf   r   )Úshowr   rU   )rW   ÚgÚnamesr   r   r   ê   s    zrubik.<locals>.perm)r   )r   )r   )r   )r   )Ú
ValueErrorr   r   rf   r   r   )r   rw   r~   r€   ÚcountÚfirU   rP   r   ÚIr   r   )r|   rr   rg   r}   rs   rt   ru   r   ro   rm   rW   rv   rƒ   r_   r[   rX   r^   r   r„   re   rc   rb   rd   r   Úrubikv   s|    		(

	r‰   N)Z sympy.combinatorics.permutationsr   Zsympy.core.symbolr   Zsympy.matricesr   Zsympy.utilities.iterablesr   r   r   r   r   r   rQ   r‰   r   r   r   r   Ú<module>   s   $