o
    e¦iv4  ã                   @   sp  d dl mZ d dlmZ d dlmZmZmZ d dlm	Z	m
Z
mZ d dlmZmZ d dlmZmZ d dlmZmZmZ d dlmZmZmZmZ d d	lmZ d d
lmZ d dlm Z m!Z!m"Z"m#Z#m$Z$m%Z% d dl&m'Z'm(Z(m)Z)m*Z* d dl+m,Z, d dl-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4 d dl5m6Z6 d dl7m8Z8m9Z9m:Z: d dl;m<Z<m=Z= d dl-m>Z> edƒ\Z?Z@ZAZBedƒZCdd„ ZDdd„ ZEdd„ ZFdd„ ZGd d!„ ZHd"d#„ ZId$d%„ ZJd&d'„ ZKd(d)„ ZLd*d+„ ZMd,d-„ ZNd.d/„ ZOd0d1„ ZPd2d3„ ZQd4d5„ ZRd6d7„ ZSe<d8d9„ ƒZTd:d;„ ZUd<d=„ ZVd>d?„ ZWd@dA„ ZXdBdC„ ZYdDdE„ ZZdFdG„ Z[dHdI„ Z\e=dJdK„ ƒZ]dLdM„ Z^dNdO„ Z_dPdQ„ Z`dRdS„ ZadTdU„ ZbdVS )Wé    )ÚSum)ÚAdd)Ú
DerivativeÚFunctionÚdiff)ÚIÚRationalÚpi)ÚEqÚNe)ÚSymbolÚsymbols)ÚLambertWÚexpÚlog)ÚasinhÚcoshÚsinhÚtanh©Úsqrt)Ú	Piecewise)ÚacosÚasinÚatanÚcosÚsinÚtan)ÚbesseljÚbesselkÚbesselyÚjn)Úerf)ÚIntegral)ÚAnd)ÚMatrix)Úratsimp)Úsimplify)Ú
componentsÚheurischÚheurisch_wrapper)ÚXFAILÚslow)Ú	integratezx,y,z,nuÚfc                   C   s   t tt tƒthksJ ‚t dtt  tƒthksJ ‚t ttƒtƒttƒthks)J ‚t ttƒtttƒƒ tƒttƒttƒtttƒƒthksFJ ‚t ttttƒt ƒ tƒttttƒ ƒtttƒhksbJ ‚t ttddƒ tttƒƒ tƒttƒttddƒ tttƒƒthks…J ‚t ttƒtƒtttƒhks”J ‚t t	ttƒtƒtƒtttƒt	ttƒtƒhks¬J ‚t ttƒt
ttƒtƒ tƒtttƒt	ttƒtƒt	ttƒtƒhksÎJ ‚d S )Né   é   é6   )r(   ÚxÚyr   r   r   r   r   r.   r   r   © r4   r4   úa/home/ubuntu/transcripts/venv/lib/python3.10/site-packages/sympy/integrals/tests/test_heurisch.pyÚtest_components   s*   ÿÿ ÿ
ÿÿ"ÿr6   c                	   C   s0   t ttttttttƒ ƒ ƒ tƒtƒsJ ‚d S ©N)Ú
isinstancer-   r2   r   r#   r4   r4   r4   r5   Útest_issue_10680-   s   0r9   c                   C   s,   t tttttƒƒ ƒtddfƒdksJ ‚d S )Néÿÿÿÿr/   r   )r-   r   r2   r   Úabsr4   r4   r4   r5   Útest_issue_211661   s   ,r<   c                   C   sd   t dtƒtks	J ‚t ttƒtd d ksJ ‚t td tƒtd d ks%J ‚tttƒtt ks0J ‚d S )Nr/   é   r0   é   )r)   r2   r*   r3   r4   r4   r4   r5   Útest_heurisch_polynomials5   s   r?   c                   C   sN  t dt tƒttƒksJ ‚t ddt  tƒttd ƒksJ ‚t dtttƒ  tƒttttƒ ƒks3J ‚t dtd  dtd  d  tƒdtdtd  d ƒ d dtdtd  d ƒ d fv sbJ ‚t dtd  dtd  d  tƒdtdtd  d ƒ d ksƒJ ‚t dtd  tƒdt ks’J ‚t dtd  tƒddtd   ks¥J ‚d S )	Nr/   r=   é   é   é   éþÿÿÿr:   é   )r)   r2   r   r   r3   r4   r4   r4   r5   Útest_heurisch_fractions=   s   "*ÿÿ6ÿB*rE   c                   C   s    t ttƒtƒtttƒ t ksJ ‚t tdt ƒtƒt ttdƒ  tttƒ  ks+J ‚t ttd ƒtƒtttd ƒ dt  dt ttƒ dt  fv sNJ ‚d S )Né   r=   )r)   r   r2   r4   r4   r4   r5   Útest_heurisch_logN   s   "4JrG   c                  C   s  t ttƒtƒttƒksJ ‚t tt ƒtƒtt ƒ ksJ ‚t tdt ƒtƒtdt ƒd ks0J ‚t tttƒ tƒtttƒ ttƒ ksEJ ‚t tttd ƒ tƒttd ƒd ksZJ ‚t ttd  ƒtƒd u shJ ‚t dt tƒdt tdƒ ksyJ ‚t tdt  tƒtdt  tdƒ dt tdƒd   ks˜J ‚t ttt t tddftddfƒjtƒttt  t td  ksºJ ‚t ttt tddfƒjtƒtt ttƒ ksÒJ ‚ttƒ t	tt ƒttt	tt ƒ ƒ ttt	tt ƒ ƒ  } t ttƒtt t	tt ƒ ƒ tƒ| ksJ ‚d S )Nr0   r=   rC   r/   rF   )
r)   r   r2   r   r#   Úzr3   Úfunctionr   r   )Úantir4   r4   r5   Útest_heurisch_expT   s    &**">D0>2rK   c                   C   sš  t ttƒtƒttƒ ksJ ‚t tttƒ d tƒttttƒ  ks#J ‚t ttƒtƒttƒks0J ‚t ttƒtƒtdttƒd  ƒd tttƒt ƒtt  tttƒt ƒtt  fv s\J ‚t ttƒttƒ tƒttƒ ttƒ ksrJ ‚t ttƒttƒ tƒttƒ ttƒ ksˆJ ‚t ttƒttƒ tƒttƒd d ttƒd  d fv s¦J ‚t ttƒttƒ tƒtttƒƒks¹J ‚t ttdt ƒ tƒtdt ƒd ttdt ƒ d  ksØJ ‚t dt d td  ttƒ tƒdt d td ttƒ dttƒ  dt ttƒ   ksJ ‚t t	td ƒt
td ƒ tƒdt tdtd  ƒt
td ƒ  tdtd  ƒt	td ƒ  tt
td ƒ t	td ƒ  ksHJ ‚t ttƒttƒd d  tƒtttƒƒ ksaJ ‚t dttƒd  tƒdtdƒ ttdƒttd ƒ d ƒ d ks…J ‚t dttƒ ttƒ ttƒd d  tƒttdƒttƒ d ƒttdƒttƒ d ƒ ksµJ ‚t dttƒ tƒdtttd ƒƒ ksËJ ‚d S )Nr/   r=   é   é1   rD   é   rF   )r)   r   r2   r   r	   r   r   r   r3   r   r   r   r   r   r   r4   r4   r4   r5   Útest_heurisch_trigonometrich   s>   *
ý,,<&>8
ÿÿ>ÿÿ2H8ÿÿ0rO   c                   C   sâ   t ttƒtƒttƒksJ ‚t ttƒtƒttƒksJ ‚t tttƒ tƒtttƒ ttƒ ks/J ‚t tttƒ tƒtttƒ ttƒ ksDJ ‚t tttd ƒ tƒtd ttd ƒ d ttd ƒ ttdtd  ƒ d  ksoJ ‚d S ©Nr=   rD   )r)   r   r2   r   r   r   r4   r4   r4   r5   Útest_heurisch_hyperbolic‰   s   **ÿ:ÿrQ   c                   C   sœ   t ttƒttƒ tƒttƒttƒ d ttƒttƒ d  ks!J ‚t tttt ƒ ƒtƒdt tttt ƒ ƒ tt ƒ dtttt ƒ ƒ  ksLJ ‚d S ©Nr=   )r)   r   r2   r   r   r   r4   r4   r4   r5   Útest_heurisch_mixed”   s   BZrS   c                  C   sÒ  t dttƒ tƒdttƒ ksJ ‚t dttƒd  tƒdttƒ ks$J ‚t ttƒd tƒdttƒd  d ks9J ‚t ttƒtttƒƒ tƒdtttƒƒd  d ksTJ ‚tdƒ} t t| ttƒ ƒtƒd| d  t| ttƒ ƒ dttƒ t| ttƒ ƒ |   ksƒJ ‚tt| ttƒ ƒtƒtdttƒ tttƒ|  ƒ |  dtttƒ|  ƒ | d   t| dƒfdƒks¶J ‚tdd	d
} tt| ttƒ ƒtƒd| d  t| ttƒ ƒ dttƒ t| ttƒ ƒ |   ksçJ ‚d S )Nr/   r=   rF   rC   r@   r3   r   )r   TT©Úpositive)	r)   r   r2   r   r   r   r*   r   r   ©r3   r4   r4   r5   Útest_heurisch_radicals™   s    "&*6.
ÿD
þ.ÿrW   c                   C   sp   t ttƒtƒtttƒ ttd  ƒttƒ  ksJ ‚t ttd  ƒttƒ tƒttƒttƒd  d ks6J ‚d S rP   )r)   r"   r2   r   r   r	   r4   r4   r4   r5   Útest_heurisch_specialª   s   4<rX   c                   C   s„   t dtt  tƒttt ƒksJ ‚t dttdƒ  tƒtttdƒ ƒks&J ‚ttt ttt t ƒtƒtƒƒttt t ƒks@J ‚d S ©Nr/   r=   )r)   r2   r3   r   r   r'   r   rH   r4   r4   r4   r5   Útest_heurisch_symbolic_coeffs¯   s   "*8rZ   c                  C   s¼   t dƒ} tdtd |   tƒtttt|  ƒ ƒdt|  ƒ  ttt|  ƒ ƒdt|  ƒ   t| dƒfdt dfƒks=J ‚t ddd} tdtd |   tƒttt| ƒ ƒt| ƒ ks\J ‚d S )Nr3   r/   r=   r   r:   TrT   )r   r*   r2   r   r   r   r   r   rV   r4   r4   r5   Ú"test_heurisch_symbolic_coeffs_1130µ   s   >ÿ

þ6r[   c                	   C   sN  t tddtd   ƒtg dttddtd   ƒ d tdƒttdƒt ƒ d  ks-J ‚t tddtd   ƒtg dttddtd   ƒ d tdƒttdƒt ƒ d  ksZJ ‚t dtddtd   ƒ tg dtdƒttdƒt ƒ d ks{J ‚t dtddtd   ƒ tg dtdƒttdƒt ƒ d ksœJ ‚t tdtd  ƒtg dtdt ƒttdƒt ƒ d ks»J ‚t dtddtd   ƒ tg dtttdd	ƒ ƒd ksÙJ ‚t dtddtd   ƒ tg dtttdd	ƒ ƒd ks÷J ‚t dtd	td  d ƒ tg dtd	ƒt	d	t td	ƒtd	td  d ƒ  ƒ d	 ks%J ‚d S )
Nr/   rL   r=   ©Úhintsé   iùÿÿÿé	   rD   rF   )
r)   r   r2   r   r   r   r	   r"   r   r   r4   r4   r4   r5   Útest_heurisch_hacking¾   s0   6ÿ6ÿ ÿ ÿÿ ÿ ÿ 2ÿr`   c                   C   s   t ttƒtƒd u sJ ‚d S r7   )r)   r.   r2   r4   r4   r4   r5   Útest_heurisch_functionÖ   s   ra   c                  C   s„   t ttƒtƒ} tttƒ|  tƒttƒd d ksJ ‚tttƒd |  tƒttƒd d ks/J ‚t| ttƒ tƒtttƒƒks@J ‚d S )Nr=   rF   )r   r.   r2   r)   r   )Údfr4   r4   r5   Ú!test_heurisch_function_derivativeÙ   s   &*&rc   c                  C   s,  dt t  } t| tƒttt  ƒksJ ‚dt t  } t| tƒttt  ƒ ks'J ‚dt t t t   } t| tƒtttt  ƒ dt   ttt  ƒdt    tt dƒfdt dfƒksYJ ‚ttd t t t t   ƒ} t| tƒtttd  td t d   ƒ t d ttd  td t d   ƒ t  ks”J ‚d S )Nr/   r=   r   T)r3   r2   r*   r   r   r   r   )r.   r4   r4   r5   Útest_heurisch_wrapperæ   s   
<
ÿ((ÿrd   c                   C   s2   t dtdttƒd    tƒtttƒƒksJ ‚d S rY   )r)   r2   r   r   r4   r4   r4   r5   Útest_issue_3609ô   s   2re   c                  C   sÈ   dd„ } t d dt d   dt d   dt   d t d dt d   d	t d   dt d    }ddt d   dt   d
t d
   t d dt d
   dt    tt ƒ }| tt|t ƒƒt ƒ|ksbJ ‚d S )Nc                    s"   | j rt‡ fdd„| jD ƒŽ S | S )Nc                    s   g | ]	}|  ˆ ¡r|‘qS r4   )Úhas)Ú.0Úarg©r2   r4   r5   Ú
<listcomp>  s    z6test_pmint_rat.<locals>.drop_const.<locals>.<listcomp>)Úis_Addr   Úargs)Úexprr2   r4   ri   r5   Ú
drop_constÿ   s   z"test_pmint_rat.<locals>.drop_constrL   é   rD   r=   é   rA   rB   rF   r@   )r2   r   r&   r)   )rn   r.   Úgr4   r4   r5   Útest_pmint_ratû   s   XH rr   c                  C   sh   t tt ƒ tt ƒd  tt ƒ } t d  d t tt ƒ  ttt ƒd d ƒd  }t| t ƒ|ks2J ‚d S )Nr=   r/   )r2   r   r   r)   ©r.   rq   r4   r4   r5   Útest_pmint_trig  s    2rt   c                  C   s’   dt  t tt ƒ  t tt ƒ tt ƒ d  t tt ƒ tt ƒ d  t  } tt tt ƒ tt ƒ ƒdt tt ƒ tt ƒ   }tt| t ƒƒ|ksGJ ‚d S rY   )r2   r   r   r&   r)   rs   r4   r4   r5   Útest_pmint_logexp  s   H0ru   c                  C   s¤   t td  ƒttƒ ttƒd ttƒd  ttƒ d  } ttƒtttƒd ƒ d ttƒtttƒd ƒ d  ttƒdttƒ d   }tt| tƒƒ|ksPJ ‚d S )Nr=   rF   r/   rp   rD   )r   r2   r"   r   r	   r   r&   r)   rs   r4   r4   r5   Útest_pmint_erf  s   :Prv   c                  C   s:   t tƒ} tt tƒ t tt tƒ  }t| tƒ|ksJ ‚d S r7   )r   r2   r)   rs   r4   r4   r5   Útest_pmint_LambertW   s   rw   c                  C   sÌ   t td tƒt ttƒ } tttƒ tt ttƒƒ }t| tƒ|ks"J ‚tt ttƒ tt td tƒ  t } t ttƒ}t| tƒ|ksBJ ‚ttd tƒtttƒ } tttƒ ttttƒƒ }t| tƒ|ksdJ ‚d S )Nr/   )r   Únur2   r   r)   r!   rs   r4   r4   r5   Útest_pmint_besselj'  s   $
ry   c                  C   sø   t ttt ƒ ttdt  ƒ } dt  ttt ƒ ttd dt  ƒ d t ttd t ƒ ttdt  ƒ d  }t| t ƒ|ks=J ‚t ttt ƒ ttdt  ƒ } dt  ttt ƒ ttd dt  ƒ d t ttd t ƒ ttdt  ƒ d  }t| t ƒ|kszJ ‚d S )Nr=   rC   r/   rF   r@   )r2   r   rx   r    r)   r   rs   r4   r4   r5   Útest_pmint_bessel_products8  s   LLrz   c                  C   s‚   dd„ } d| t ƒdt| t ƒƒt | t ƒ     d| t ƒ  t | t ƒ  }tt ttt ƒƒ ƒtttt ƒƒƒ }t|t ƒ|ks?J ‚d S )Nc                 S   s   t t| ƒƒS r7   )r   r   ri   r4   r4   r5   ÚomegaF  s   z%test_pmint_WrightOmega.<locals>.omegar/   r=   )r2   r   r   r   r   r   r)   )r{   r.   rq   r4   r4   r5   Útest_pmint_WrightOmegaE  s   @$r|   c                   C   sR   t tddtd   ƒtg ddt tdtd  d ƒ dtdt ƒ  ks'J ‚d S )Nr/   g      Ð?r=   r\   ç      à?g      ð?)r)   r   r2   r   r4   r4   r4   r5   Útest_RRO  s   *ÿr~   c                     sX   t dƒ\} ‰ tdƒ| ƒ}‡ fdd„}t||ƒ|ƒ}t|| ƒ| ƒ}|| || ¡ks*J ‚d S )Nzt RrH   c                    s   | t ˆ d | d  ƒ S rR   r   ri   ©ÚRr4   r5   r.   c  s   ztest_issue_22527.<locals>.f)r   r   r-   Úsubs)ÚtrH   r.   ÚUzÚUtr4   r   r5   Útest_issue_22527`  s   r…   c                  C   s  t ddd} t| d  ddt d   ƒ}t|| g dd u s J ‚ttƒtdt d ƒ d }ttt | d  d ƒ| ddfƒ|t|  ksGJ ‚ttd  ddt d   ƒ}t|tg dd u saJ ‚ttƒtdt d ƒ d }ttt td  d ƒtddfƒ|t|  ksˆJ ‚d S )NÚrT)Úrealr=   r\   r/   r   )	r   r   r   r)   r   r	   r"   r-   r2   )r†   Úar4   r4   r5   Ú%test_heurisch_complex_erf_issue_26338j  s   26r‰   c                  C   sž  t dƒ} tdddd\}}}}tt| | ƒggƒ}tddƒ}dd|dd	d
dg\}}}	}
}}}||
| dt||  | ƒ  || dt||  | ƒ    }||
| t||  | ƒ t|	| | ƒd  || t||  | ƒ t|	| | ƒd    }td||k f|t||k||	k ƒf||	|kfƒ}t| |ƒ|ƒ}t|| |ƒ ggƒ}|| ||¡d  | |j	|j
¡ ||¡ }t|d |d|fƒ}|d usÍJ ‚d S )NÚZ0zk01 k10 t sT)r‡   rU   éS   éd   r}   é2   g333333ã?r=   éx   r/   r   r:   )r   r   r%   r   r   r   r$   r
   r   ÚlhsÚrhsr-   )rŠ   Úk01Úk10r‚   ÚsÚmÚ_83rˆ   ÚbÚcÚdÚer.   rq   ÚAIF_btfÚAIF_atfÚAIF_symÚaif_eqÚf_vecÚ	integrandÚsolutionr4   r4   r5   Útest_issue_15498w  s   
 @.,ÿ.,r¡   N)cÚsympy.concrete.summationsr   Úsympy.core.addr   Úsympy.core.functionr   r   r   Úsympy.core.numbersr   r   r	   Úsympy.core.relationalr
   r   Úsympy.core.symbolr   r   Ú&sympy.functions.elementary.exponentialr   r   r   Ú%sympy.functions.elementary.hyperbolicr   r   r   r   Ú(sympy.functions.elementary.miscellaneousr   Ú$sympy.functions.elementary.piecewiser   Ú(sympy.functions.elementary.trigonometricr   r   r   r   r   r   Úsympy.functions.special.besselr   r   r    r!   Ú'sympy.functions.special.error_functionsr"   Úsympy.integrals.integralsr#   Úsympy.logic.boolalgr$   Úsympy.matricesr%   Úsympy.simplify.ratsimpr&   Úsympy.simplify.simplifyr'   Úsympy.integrals.heurischr(   r)   r*   Úsympy.testing.pytestr+   r,   r-   r2   r3   rH   rx   r.   r6   r9   r<   r?   rE   rG   rK   rO   rQ   rS   rW   rX   rZ   r[   r`   ra   rc   rd   re   rr   rt   ru   rv   rw   ry   rz   r|   r~   r…   r‰   r¡   r4   r4   r4   r5   Ú<module>   sp     !	



