o
    à8VaD  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(    t tt| ƒƒ| ƒD ]}t|ƒV  q
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)]
    N)r   ÚlistÚranger   )ÚnÚperm© r   ú@/usr/lib/python3/dist-packages/sympy/combinatorics/generators.pyÚ	symmetric   s   €ÿr   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)r	   r
   r   r   ©r   ÚgenÚir   r   r   Úcyclic   s   €
þr   c                 c   s2    t tt| ƒ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
   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 )	zoReturn the permutations of the 3x3 Rubik's cube, see
    http://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$   é   é   é   )r   r#   é)   é(   )r   é   é,   é%   )r   é   é.   r)   ))r#   r+   é   r6   )r'   é   é   r3   )r   r"   é+   r,   )r   é   é*   r.   )r   é   r1   r(   ))r"   r*   é    r>   )r&   é   é   r<   )r   é&   r;   r+   )r   é$   é-   r9   )r   r!   é0   r8   ))r!   r)   r2   rB   )r%   r5   é'   rC   )r   r    r7   r?   )r   r0   é/   r@   )r   r-   rE   r*   ))r1   r;   rE   r7   )r=   rD   rG   r4   )r-   r6   r>   rB   )r/   r:   rA   rF   )r,   r8   r?   r2   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   )Ú.0r   r   r   r   Ú
<listcomp>t   s    z?rubik_cube_generators.<locals>.<listcomp>.<listcomp>.<listcomp>r   )rI   Zxir   r   r   rJ   t   s    z4rubik_cube_generators.<locals>.<listcomp>.<listcomp>rE   )Úsizer   )rI   Úxr   r   r   rJ   t   s   " z)rubik_cube_generators.<locals>.<listcomp>r   )Úar   r   r   Úrubik_cube_generatorsb   s   õrN   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 ©N©Úcol©Úfr   ©Úfacesr   r   r   Úgetr„   ó   zrubik.<locals>.getrc                    ó   ˆ |    |d ¡S ©Nr   rQ   rS   ©rV   r   r   Úgetl‡   rX   zrubik.<locals>.getlc                    rY   rZ   ©ÚrowrS   r[   r   r   ÚgetuŠ   rX   zrubik.<locals>.getuc                    rO   rP   r]   rS   rU   r   r   Úgetd   rX   zrubik.<locals>.getdc                    s$   t ˆd|ƒˆ |  d d …ˆ| f< d S rZ   r   ©rT   r   ÚsrU   r   r   Úsetr   ó   $zrubik.<locals>.setrc                    s$   t ˆd|ƒˆ |  d d …|d f< d S rZ   r   ra   rU   r   r   Úsetl“   rd   zrubik.<locals>.setlc                    s$   t dˆ|ƒˆ |  |d d d …f< d S rZ   r   ra   rU   r   r   Úsetu–   rd   zrubik.<locals>.setuc                    s$   t dˆ|ƒˆ |  ˆ| d d …f< d S rZ   r   ra   rU   r   r   Úsetd™   rd   zrubik.<locals>.setdr   c                    sd   t |ƒD ]+}ˆ |  }g }t ˆƒD ]}t ˆd ddƒD ]}| |||f ¡ qqtˆˆ|ƒˆ | < qd S )Nr   r   )r
   Úappendr   )ÚFÚrÚ_ZfaceZrvÚcrU   r   r   Úcw   s   ÿúzrubik.<locals>.cwc                    ó   ˆ | dƒ d S ©Nr   r   )ri   )rm   r   r   Úccw¦   ó   zrubik.<locals>.ccwc              	      s–   t |ƒD ]D}| dkrˆˆƒ | d7 } ˆˆ| ƒ}ˆˆ| tˆ	ˆ | ƒƒƒ ˆˆ | ttˆˆ| ƒƒƒƒ ˆˆ| tˆˆ| ƒƒƒ ˆ
ˆ| tt|ƒƒƒ | d8 } qd S )Nr   r   )r
   r	   Úreversed)r   rj   rk   Ztemp)ÚDri   ÚLÚRÚUrm   r`   r\   rW   r_   rg   re   rc   rf   r   r   Úfcw¬   s   

÷zrubik.<locals>.fcwc                    rn   ro   r   )r   )rw   r   r   Úfccw¸   rq   zrubik.<locals>.fccwc                    sv   t | ƒD ]4}ˆˆƒ ˆˆ ƒ ˆˆƒ ˆˆ }ˆˆƒ ˆˆ ˆˆ< ˆˆƒ ˆˆ ˆˆ< ˆˆƒ ˆˆ ˆˆ< |ˆˆ< qd S rP   ©r
   ©rj   rk   Út©	ÚBrs   ri   rt   ru   rv   rp   rm   rV   r   r   ÚFCW¼   s   
õzrubik.<locals>.FCWc                      ó   ˆ dƒ d S ro   r   r   )r~   r   r   ÚFCCWÊ   ó   zrubik.<locals>.FCCWc                    sV   t | ƒD ]$}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 rP   ry   rz   r|   r   r   ÚUCWÎ   s   
ùzrubik.<locals>.UCWc                      r   ro   r   r   )r‚   r   r   ÚUCCWØ   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 rP   )Úextendrh   r   )Zshowr   rT   )rV   ÚgÚnamesr   r   r   ë   s   zrubik.<locals>.permNrH   )r   )Ú
ValueErrorr   r
   rh   r   r	   )r   rx   r€   rƒ   ÚcountÚfirT   rM   r   ÚIr   r   )r}   rs   ri   r~   rt   ru   rv   r‚   rp   rm   rV   rw   r…   r`   r\   rW   r_   r   r†   rg   re   rc   rf   r   Úrubikw   s|   		(


	

r‹   N)Z sympy.combinatorics.permutationsr   Zsympy.core.symbolr   Zsympy.matricesr   Zsympy.utilities.iterablesr   r   r   r   r   r   rN   r‹   r   r   r   r   Ú<module>   s    $