o
    FZŽh7  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   úM/var/www/auris/lib/python3.10/site-packages/sympy/combinatorics/generators.pyÚ	<genexpr>   s   € zsymmetric.<locals>.<genexpr>N)r   Úrange)Únr   r   r   Ú	symmetric   s   €"r   c                 c   s4    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   €
þr   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   €€ýr   c                 c   s´    | dkrt ddgƒV  t ddgƒV  dS | dkr7t g d¢ƒV  t g d¢ƒV  t g d¢ƒV  t g d¢ƒV  dS tt| ƒƒ}t| ƒD ]}t |ƒV  t |ddd	… ƒV  t|dƒ}qAd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   €
ýr   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   r9   )r*   é   é   r6   )r   r%   é+   r/   )r!   é   é*   r1   )r   é   r4   r+   ))r%   r-   é    rA   )r)   é   é   r?   )r   é&   r>   r.   )r    é$   é-   r<   )r   r$   é0   r;   ))r$   r,   r5   rE   )r(   r8   é'   rF   )r   r#   r:   rB   )r   r3   é/   rC   )r   r0   rH   r-   ))r4   r>   rH   r:   )r@   rG   rJ   r7   )r0   r9   rA   rE   )r2   r=   rD   rI   )r/   r;   rB   r5   c                 S   s"   g | ]}t d d„ |D ƒdd‘qS )c                 S   s   g | ]	}d d„ |D ƒ‘qS )c                 S   s   g | ]}|d  ‘qS ©r   r   )r
   r   r   r   r   Ú
<listcomp>s   s    z?rubik_cube_generators.<locals>.<listcomp>.<listcomp>.<listcomp>r   )r
   Úxir   r   r   rL   s   s    z4rubik_cube_generators.<locals>.<listcomp>.<listcomp>rH   )Úsizer   )r
   Úxr   r   r   rL   s   s   " z)rubik_cube_generators.<locals>.<listcomp>r   )Úar   r   r   Úrubik_cube_generatorsa   s   õrQ   c                    sÆ  ˆdk rt dƒ‚‡
‡fdd„‰‡
fdd„‰‡
fdd„‰‡
‡fd	d
„‰‡
‡fdd„‰‡
‡fdd„‰‡
‡fdd„‰‡
‡fdd„‰d*‡
‡fdd„	‰	‡	fdd„‰d*‡‡‡‡‡‡	‡‡‡‡‡‡‡‡fdd„	‰‡fdd„}d*‡ ‡‡‡‡‡‡‡	‡
f	dd„	‰‡fdd„}d*‡ ‡‡‡‡‡‡‡	‡
f	d d!„	‰‡fd"d#„}td$ƒ \‰‰‰‰ ‰‰‰i ‰
d%}td&ƒD ] }g }tˆd ƒD ]}| |¡ |d7 }q®tˆˆ|ƒˆ
ˆ| < q¤d+‡
‡‡fd'd(„	}g ‰ttd&ˆd  ƒƒ}	tˆd ƒD ]}
ˆ|
ƒ |ƒ  ||
ƒ qà|dƒ|	ksöJ ‚ˆƒ  tˆd ƒD ]}
ˆ|
ƒ |ƒ  |ƒ  ˆƒ  ||
ƒ qÿ|ƒ  |dƒ|	ksJ ‚ˆƒ  |ƒ  |ƒ  tˆd ƒD ] }
ˆ|
ƒ ˆƒ  ˆƒ  |ƒ  |ƒ  ˆƒ  |ƒ  |ƒ  ||
ƒ q.ˆƒ  ˆƒ  |ƒ  |dƒ|	ksaJ ‚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                    ó   ˆ |    ˆ| ¡S r	   ©Úcol©Úfr   ©Úfacesr   r   r   Úgetrƒ   ó   zrubik.<locals>.getrc                    ó   ˆ |    |d ¡S ©Nr   rS   rU   ©rX   r   r   Úgetl†   rZ   zrubik.<locals>.getlc                    r[   r\   ©ÚrowrU   r]   r   r   Úgetu‰   rZ   zrubik.<locals>.getuc                    rR   r	   r_   rU   rW   r   r   ÚgetdŒ   rZ   zrubik.<locals>.getdc                    s$   t ˆd|ƒˆ |  d d …ˆ| f< d S r\   r   ©rV   r   ÚsrW   r   r   Úsetr   ó   $zrubik.<locals>.setrc                    s$   t ˆd|ƒˆ |  d d …|d f< d S r\   r   rc   rW   r   r   Úsetl’   rf   zrubik.<locals>.setlc                    s$   t dˆ|ƒˆ |  |d d d …f< d S r\   r   rc   rW   r   r   Úsetu•   rf   zrubik.<locals>.setuc                    s$   t dˆ|ƒˆ |  ˆ| d d …f< d S r\   r   rc   rW   r   r   Úsetd˜   rf   zrubik.<locals>.setdr   c                    sd   t |ƒD ]+}ˆ |  }g }t ˆƒD ]}t ˆd ddƒD ]}| |||f ¡ qqtˆˆ|ƒˆ | < qd S )Nr   r   )r   Úappendr   )ÚFÚrÚ_ZfaceÚrvÚcrW   r   r   Úcwœ   s   ÿúzrubik.<locals>.cwc                    ó   ˆ | dƒ d S ©Nr   r   )rk   )rp   r   r   Úccw¥   ó   zrubik.<locals>.ccwc              	      s–   t |ƒD ]D}| dkrˆˆƒ | d7 } ˆˆ| ƒ}ˆˆ| tˆ	ˆ | ƒƒƒ ˆˆ | ttˆˆ| ƒƒƒƒ ˆˆ| tˆˆ| ƒƒƒ ˆ
ˆ| tt|ƒƒƒ | d8 } qd S )Nr   r   )r   r   Úreversed)r   rl   rm   Útemp)ÚDrk   ÚLÚRÚUrp   rb   r^   rY   ra   ri   rg   re   rh   r   r   Úfcw«   s   

÷zrubik.<locals>.fcwc                    rq   rr   r   )r   )r{   r   r   Úfccw·   rt   zrubik.<locals>.fccwc                    sv   t | ƒD ]4}ˆˆƒ ˆˆ ƒ ˆˆƒ ˆˆ }ˆˆƒ ˆˆ ˆˆ< ˆˆƒ ˆˆ ˆˆ< ˆˆƒ ˆˆ ˆˆ< |ˆˆ< qd S r	   ©r   ©rl   rm   Út©	ÚBrw   rk   rx   ry   rz   rs   rp   rX   r   r   ÚFCW»   s   
õzrubik.<locals>.FCWc                      ó   ˆ dƒ d S rr   r   r   )r‚   r   r   ÚFCCWÉ   ó   zrubik.<locals>.FCCWc                    sV   t | ƒD ]$}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	   r}   r~   r€   r   r   ÚUCWÍ   s   
ùzrubik.<locals>.UCWc                      rƒ   rr   r   r   )r†   r   r   ÚUCCW×   r…   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extendrj   r   )Úshowr   rV   )rX   ÚgÚnamesr   r   r   ê   s   zrubik.<locals>.permNrK   )r   )Ú
ValueErrorr   r   rj   r   r   )r   r|   r„   r‡   ÚcountÚfirV   rP   r   ÚIr   r   )r   rw   rk   r‚   rx   ry   rz   r†   rs   rp   rX   r{   rŠ   rb   r^   rY   ra   r   r‹   ri   rg   re   rh   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    $