a
    kº”h7  ã                   @   sÐ   d dl mZ d dlmZ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mZmZ d
d„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ ZdS )é    )Úsymbols)ÚcosÚsin)ÚQQÚZZ)ÚPoly)ÚNotInvertible)ÚFiniteExtension)ÚDomainMatrix)Úraises)ÚxÚyÚtc                     s¼  t ttd d tƒƒ‰ ˆ jdks$J ‚tˆ ƒdks4J ‚ˆ j‰ˆ ¡ ˆ u sJJ ‚ˆˆ ˆ dƒks^J ‚tt‡fdd„ƒ ˆ j	ˆ j
ˆfks„J ‚ˆ dƒˆ j
ks–J ‚ˆd ˆ dƒksªJ ‚ˆd dksºJ ‚dˆ dˆ  dˆ ksÖJ ‚dˆ d ˆ d	ƒksîJ ‚ˆ dƒ ¡ ˆ dƒksJ ‚tt‡ fd
d„ƒ t ttd t d tddƒ‰ˆjdksHJ ‚ˆj} ˆj	ˆdƒ| | d fkslJ ‚| d | ks~J ‚| d ˆdƒks”J ‚| d ˆdƒksªJ ‚| d | d ksÀJ ‚| d | d ksÖJ ‚| d | d |  d ksôJ ‚ˆtd t ƒ ¡ d|  ksJ ‚ˆtd ƒd ˆtd ƒ ¡ ks<J ‚| d | d  ˆdƒksZJ ‚| d d| d  d  | d d ks„J ‚| d d| d  d  | d d ks®J ‚d| d d  | d |  d ksÔJ ‚| d d d | d  d ksøJ ‚tt‡fdd„ƒ t ttd td  t d tddƒ}|jdks@J ‚t|ƒdksRJ ‚|j}dtd td  t d  }|t |t   ¡ ||ƒks–J ‚|t |t  | |dƒks¸J ‚d S )Né   é   zZZ[x]/(x**2 + 1)éÿÿÿÿc                      s   ˆ d S )N© r   r   )Úir   úT/var/www/auris/lib/python3.9/site-packages/sympy/polys/agca/tests/test_extensions.pyÚ<lambda>   ó    z&test_FiniteExtension.<locals>.<lambda>é   é   é   c                      s   ˆ dƒ  ¡ S )Nr   ©Úinverser   )ÚAr   r   r       r   )Úmodulusé   é   é   é	   é   é   iíÿÿÿc                      s   ˆ dƒ  ¡ S )Nr   r   r   )ÚFr   r   r   4   r   T)ÚfieldzZZ(x)[t]/(t**2 - x**3 - x + 1))r	   r   r   ZrankÚstrÚ	generatorÚparentr   Ú	TypeErrorZbasisÚoner   ÚNotImplementedErrorr   r   )ÚaÚKr   Úcr   )r   r$   r   r   Útest_FiniteExtension   sP    "&**&$&"r/   c                  C   s’   t td d ttd} t td d ttd}t| ƒ}t|ƒ}|tt td d ƒƒksXJ ‚|tt td d ƒƒkstJ ‚t||t| ƒhƒdksŽJ ‚d S )Nr   ©Údomain)r   r   r   r   r	   Úlen)Úp1Úp2ÚK1ÚK2r   r   r   Útest_FiniteExtension_eq_hash@   s    r7   c                     s>  t ttd d ttdƒ} | tƒ‰ ˆ d d d | jks<J ‚dˆ d d  | jksVJ ‚ˆ d d ˆ d  ˆ d ksvJ ‚ˆ d d ˆ d  ˆ d ks–J ‚ˆ d d ˆ d  | jks´J ‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ t ttd d ttdƒ} | tƒ‰ ˆ d d d | jks(J ‚tt	‡ fd	d„ƒ d S )
Nr   r   r0   r   c                      s   ˆ d d d S )Nr   r   r   r   r   ©Úxfr   r   r   T   r   z*test_FiniteExtension_mod.<locals>.<lambda>c                      s   ˆ g  S ©Nr   r   r8   r   r   r   U   r   c                      s   g ˆ  S r:   r   r   r8   r   r   r   V   r   c                      s   ˆ d d ˆ d  S )Nr   r   r   r   r8   r   r   r   \   r   )
r	   r   r   r   Úzeror   ÚZeroDivisionErrorr)   r   r+   ©r-   r   r8   r   Útest_FiniteExtension_modK   s      r>   c                  C   sJ   t ttd d ttdƒ} | tƒ}|  t¡|ks4J ‚|  |¡tksFJ ‚d S )Nr   r   r0   )r	   r   r   r   Z
from_sympyÚto_sympy©r-   r9   r   r   r   Útest_FiniteExtension_from_sympy_   s    rA   c                  C   sJ   t ttd d tddƒ} t ttd d tddƒ}|  t¡|ksFJ ‚d S )Nr   r   r   r0   r   )r	   r   r   Z
set_domainr   )ÚKZÚKQr   r   r   Útest_FiniteExtension_set_domaing   s    rD   c                  C   sD   t ttd d ƒƒ} | tƒ}|  |d d |d ¡|d ks@J ‚d S )Né   r   r   )r	   r   r   Zexquor@   r   r   r   Útest_FiniteExtension_exquom   s    rF   c                  C   sŽ   t ttd d ƒƒ} tt }| tƒ|tƒ }}|  |¡|ks@J ‚| |¡|ksRJ ‚t ttd d tdƒ}| tddƒt¡|jd ksŠJ ‚d S ©Nr   r   r0   )r	   r   r   r   ÚconvertZconvert_fromr*   )r5   r6   Úx1Zx2r-   r   r   r   Útest_FiniteExtension_convertt   s    rJ   c                     sº  t ttd d ttdƒ} t ttd d ttdƒ}t ttd d ttt dƒ}t ttd d tt t¡dƒ}| jdu s€J ‚|jdu sŽJ ‚|jdu sœJ ‚|jdu sªJ ‚| |||fD ]þ‰ ˆ  t¡‰ˆˆ j	 ˆksÖJ ‚ˆˆ j	 ˆksèJ ‚ˆˆ j	 ˆ j
ksüJ ‚tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ tt‡ ‡fd	d„ƒ ˆ jr~ˆˆ ˆ j	ksTJ ‚ˆˆ ˆ j	kshJ ‚ˆˆ ˆ j
ks´J ‚q¶tt‡fd
d„ƒ tt‡fdd„ƒ tt‡fdd„ƒ q¶d S )Nr   r   r0   TFc                      s
   ˆˆ j  S r:   ©r;   r   ©r-   ÚxKr   r   r      r   z4test_FiniteExtension_division_ring.<locals>.<lambda>c                      s
   ˆˆ j  S r:   rK   r   rL   r   r   r      r   c                      s
   ˆˆ j  S r:   rK   r   rL   r   r   r   ‘   r   c                      s   ˆ ˆ  S r:   r   r   ©rM   r   r   r   —   r   c                      s   ˆ ˆ  S r:   r   r   rN   r   r   r   ˜   r   c                      s   ˆ ˆ  S r:   r   r   rN   r   r   r   ™   r   )r	   r   r   r   r   r   Z
frac_fieldZis_FieldrH   r*   r;   r   r<   r+   )rC   rB   ZKQtZKQtfr   rL   r   Ú"test_FiniteExtension_division_ring€   s.     
rO   c                  C   s  t ttd d ƒƒ} ttt| d}|j| ks0J ‚| ¡ tks@J ‚|d  ¡ dksTJ ‚t ttd d ttdƒ} t ttd d t| dƒ}t|ƒdks˜J ‚| 	tt ¡}| 
|¡tt ks¼J ‚| 
|d ¡ddt t  ksÞJ ‚ttt t|d}|d tddt t  t|dksJ ‚d S )Nr   r0   zQQ[x]/(x**2 - 2)[t]/(t**2 - 2)rE   )r	   r   r   r   r1   Zas_exprr   r   r&   rH   r?   )r-   Úpr6   ZeKr   r   r   Útest_FiniteExtension_Polyœ   s    "rQ   c                     s  t dƒ\} ‰‰tˆƒtˆƒ | tˆƒ tˆƒ |  tˆƒ tˆƒ gtˆƒtˆƒ | tˆƒ tˆƒ | tˆƒ tˆƒ gtˆƒ|  tˆƒ dgg}‡‡fdd„}|t|  ƒ}|tƒ|  }||fD ]X‰ ‡ fdd„|D ƒ}t|dˆ ƒ}| ¡ d ˆ j d	  }|ˆ  | d
 tˆƒ ¡ksÀJ ‚qÀd S )Nzrho, phi, thetar   c                    sp   t ttˆ ƒd tˆ ƒd  d tˆ ƒ| tˆ ƒ dƒ} t ttˆƒd tˆƒd  d tˆƒ| tˆƒ dƒ} | S rG   )r	   r   r   r   r=   )rP   r   r   r   Úmake_extension¸   s    66z<test_FiniteExtension_sincos_jacobian.<locals>.make_extensionc                    s   g | ]}‡ fd d„|D ƒ‘qS )c                    s   g | ]}ˆ   |¡‘qS r   )rH   )Ú.0Úer=   r   r   Ú
<listcomp>Á   r   zCtest_FiniteExtension_sincos_jacobian.<locals>.<listcomp>.<listcomp>r   )rS   Úrowr=   r   r   rU   Á   r   z8test_FiniteExtension_sincos_jacobian.<locals>.<listcomp>)r   r   r   r   r   )r   r   r   r   r
   Zcharpolyr*   rH   )ÚrÚelementsrR   ZKsc1ZKsc2Z
elements_KÚJZdetr   )r-   rP   r   r   Ú$test_FiniteExtension_sincos_jacobian®   s    64ýrZ   N) Zsympy.core.symbolr   Z(sympy.functions.elementary.trigonometricr   r   Zsympy.polysr   r   Zsympy.polys.polytoolsr   Zsympy.polys.polyerrorsr   Zsympy.polys.agca.extensionsr	   Zsympy.polys.domainmatrixr
   Zsympy.testing.pytestr   Z	sympy.abcr   r   r   r/   r7   r>   rA   rD   rF   rJ   rO   rQ   rZ   r   r   r   r   Ú<module>   s$   2