U
    ZÊ¹jÊ“  ã                   @   sð  d dl mZmZmZmZmZmZmZ d dl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mZmZ d dlmZ d dlmZ d dlmZmZ d d	l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/m0Z0m1Z1m2Z2 d dl3m4Z4 d dl5m6Z6m7Z7m8Z8 d dl9m:Z:m;Z; d dl<m=Z= d dl>m?Z? d dl@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZH d dlImJZJmKZKmLZLmMZM d dlNmOZOmPZP d dlQmRZRmSZS d dlTmUZU eOdd„ ƒZVeOdd„ ƒZWeOdd„ ƒZXeOd d!„ ƒZYd"S )#é    )Úlaplace_transformÚinverse_laplace_transformÚLaplaceTransformÚInverseLaplaceTransformÚ_laplace_deep_collectÚlaplace_correspondenceÚlaplace_initial_conds)ÚFunctionÚ
expand_mul)Ú
EulerGammaÚSubsÚ
DerivativeÚdiff)Úfactor_terms)ÚIÚooÚpi)ÚEq)ÚS)ÚSymbolÚsymbols©Úsimplify)ÚAbsÚre)ÚexpÚlogÚ	exp_polar)ÚcoshÚsinhÚcothÚasinh)Úsqrt)Ú	Piecewise)ÚatanÚcosÚsin)ÚAnd)Ú
lowergammaÚgammaÚ
uppergamma)Ú
DiracDeltaÚ	Heaviside)ÚSingularityFunction)Úlerchphi)ÚfresnelcÚfresnelsÚerfÚerfcÚEiÚCiÚexpintÚE1)ÚbesseliÚbesseljÚbesselkÚbessely)ÚslowÚwarns_deprecated_sympy)ÚMatrixÚeye)Úsc               
   C   s =  t } t}tddd�\}}}tdddd�}tdƒ\}}}tdƒ}	tdƒ}
td	ƒ}td
ƒ}tdƒ}tt|| ||  ƒtdt|| ||  |d  ƒƒ |ƒt|| |d  |||   ƒtdt|| |||   ƒƒ ksÜt‚t t||ƒ|dƒ|t	dd�}t
|||iƒ}t|||dddddgiƒ}|t	d |t	ƒ dt	d   dt	  d k�sRt‚dtt|ƒ|t	ƒ d  ¡ ddt	d   k�s„t‚| || |d  |tdƒd   |t	ƒ|t	d  dt	d   dttƒ dt	tdƒd     ddfk�sðt‚| |||  |t	ƒ| t| t	 ƒ t| t	 ƒ ddfk�s2t‚| dt|| ƒ |t	ƒttƒtdt	 ƒ t|t	 ƒ tt|ƒtt	ƒ ƒ ddfk�sŠt‚| t|ƒ||  |t	ƒt t|ƒ t|t	 ƒ tt|ƒtt	ƒ ƒ ttƒtdt	 ƒ  ddfk�sðt‚| || tdƒ d  |t	ƒdttƒ tt	ƒ t|t	 ƒ tt|ƒtt	ƒ ƒ dt|ƒ  ddfk�sZt‚| |tdƒd  || d  |t	ƒt t|ƒ t|t	 ƒ tt|ƒtt	ƒ ƒ ttƒtdt	 ƒ  ddfk�sÌt‚| d|t|ƒ |d   |t	ƒtt|ƒ t|t	 ƒ tt|ƒtt	ƒ ƒ ddfk�s$t‚| || | |t	ƒt	| d  t| t	 ƒ t|d |t	 ƒ ddfk�srt‚| |d ||  |t	ƒd|d  td|t	 ƒ ddfk�s°t‚| t|ƒ|t	ƒdt	d  ddfk�sØt‚| td| ƒ|t	ƒdt	d  ddfk�st‚| t|| ƒ|t	ƒdt	|  |dfk�s0t‚| t|||  ƒ|t	ƒt| | ƒ| t	  |dfk�slt‚| |t| | ƒ |t	ƒ|t	 d | dfk�s t‚| |t| ||  ƒ |t	ƒt|| ƒ|t	 d  | dfk�sät‚| || t| | ƒ |t	ƒ||t	 d  | dfk�s t‚| t| t| ƒ ƒ|t	ƒtt	|ƒ|t	  ddfk�sZt‚| t| t|ƒ ƒ|t	ƒ|t	 tt	 |ƒ ddfk�s”t‚| |tdƒd  td| ƒ ttdƒd ƒ |t	ƒt	d tdƒ d  ddfk�sêt‚| |tdƒd  td| ƒ |t	ƒdttƒ dt	d tdƒd    ddfk�s>t‚| || t| | ƒ |t	ƒ|t	 | d  t|d ƒ | dfk�sˆt‚| |t| |d  ƒ |t	ƒttƒ| tt	d d|  ƒ tt	dt|ƒ  ƒ dt|ƒ  ddfk�sòt‚| td|d  ƒ|t	ƒtdƒttƒ tt	d d ƒ ttdƒt	 d ƒ d ddfk�sNt‚| |td|d  ƒ |t	ƒ|ttd|d  ƒ|t	ƒ t dfk�s”t‚| |t| |d  ƒ |t	ƒdd|  t	tt	dt|ƒ  ƒ dttƒ |tdƒd     ddfk�sþt‚| t| | ƒ|t	ƒdt|ƒ tdt	 ƒ tddt|ƒ tt	ƒ ƒ ddfk�	sRt‚| t|ƒt| | ƒ |t	dd�ttƒt|ƒtt	ƒ dtdƒ   tt	d  ƒ tdt|ƒ tt	ƒ ƒ ddfk�	sÈt‚| t| | ƒt|ƒ |t	ƒttƒtdt	 ƒ tdt|ƒ tt	ƒ ƒ ddfk�
st‚| t| | ƒ|t|ƒ  |t	ƒttƒtd| ƒ tdt|ƒ tt	ƒ ƒ ddfk�
sxt‚| tdt|| ƒ ƒ|t	ƒdt	 ttƒt|ƒ t|t	 ƒ tt|ƒtdt	 ƒ ƒ t	tdƒd    ddfk�
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k�s¶t‚| t|ƒd |t	dd�tt	ƒt d td d*  t	 ddfk�sút‚| t| | ƒt|ƒ |t	dd�t|t	 ƒ t |t	  | dfk�sDt‚| t|| ƒ|t	ƒ||d t	d   ddfk�sxt‚| t!t|| ƒƒ|t	ƒ|t"tt	 d|  ƒ |d t	d   ddfk�sÄt‚| t|| ƒ| |t	ƒt#|t	 ƒddfk�sôt‚| t|| ƒd | |t	ƒtd|d  t	d  d ƒd ddfk�s<t‚| t|| ƒd |d  |t	ƒ|t#d| t	 ƒ t	td|d  t	d  d ƒ d  ddfk�s t‚| tdt|| ƒ ƒ|t	ƒttƒt|ƒ t| t	 ƒ t	tdƒd   ddfk�söt‚| tdt|| ƒ ƒ| |t	ƒttt|ƒtdt	 ƒ ƒ ddfk�s>t‚| t|| ƒ|t	ƒt	|d t	d   ddfk�srt‚| t|| ƒd |t	ƒd|d  t	d  t	d|d  t	d    ddfk�sÂt‚| t|ƒtdt|| ƒ ƒ |t	dd�ttƒ| t	d   t| t	 ƒ t	tdƒd   ddfk�s*t‚| tdt|| ƒ ƒt|ƒ |t	ƒttƒtdt	 ƒ t| t	 ƒ ddfk�s|t‚| t|| ƒt|| ƒ |t	ƒd| | t	 t	d || d  t	d || d    ddfk�sàt‚| t|| ƒt|| ƒ |t	ƒ||d  |d  t	d   t	d || d  t	d || d    ddfk�sRt‚| t|| ƒt|| ƒ |t	ƒt	|d |d  t	d   t	d || d  t	d || d    ddfk�sÂt‚| | | t|| ƒ t|| ƒ |t	dd�d|d  |d d|d  t	d   t	d   ddfk�s,t‚| |t| | ƒ t|| ƒ |t	ƒ|| |d |t	 d   | dfk�s|t‚| |t| | ƒ t|| ƒ |t	ƒ||t	  |d |t	 d   | dfk�sÐt‚| t|d ƒ|t	dd�\}}}|dk�süt‚|t	tdƒ tdƒ t	d d   dk�s*t‚| t|| ƒ|t	ƒtt	d d|d   ƒtt	d|  ƒ t	 ddfk�svt‚| tt|| ƒƒ|t	ƒt|ƒt	t|t	 ƒ  ddfk�s²t‚| t|| ƒtt|| ƒƒ |t	dd�t|ƒ tt	ƒ|t	   |dfk�s t‚| tt|| ƒd ƒ|t	dd�dt	 tt|ƒ tt	ƒ ƒt	  ddfk�sNt‚| tt|| ƒƒ|t	dd�t|ƒ t	t|t	 ƒ  dt	  | dfk�sšt‚| t|| ƒtt|| ƒƒ |t	ƒdt|ƒtt	ƒ t	  ddfk�sât‚| tt|| ƒd ƒ|t	ƒtt|ƒ tt	ƒ ƒt	 ddfk�s$t‚| td|| ƒ|t	ƒdt|d t	d  ƒ ddfk�s^t‚| td|| ƒ|t	dd�||d t	d  t	t|d t	d  ƒ   ddfk�s°t‚| td|| ƒ|t	dd�|d t|d t	d  ƒt	t|d t	d  ƒ d   ddfk�st‚| |td|| ƒ |t	ƒt	|d t	d  tdƒd   ddfk�sTt‚| |td|| ƒ |t	ƒ||d t	d  tdƒd   ddfk�sšt‚| |d td|| ƒ |t	ƒd|d  |d t	d  tdƒd   ddfk�sìt‚| tddt|| ƒ ƒ|t	ƒt| t	 ƒt	 ddfk�s(t‚| |tdƒd  tddt|| ƒ ƒ |t	ƒ|tdƒd  t| t	 ƒ t	d  ddfk�sˆt‚| td|t|d ||  ƒ ƒ|t	dd�t|t	t|d t	d  ƒ  ƒt|d t	d  ƒ ddfk�sòt‚| t$d|| ƒ|t	ƒdt|d  t	d  ƒ |dfk� 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||	|
iƒ|
t	ƒd |
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   	      s¼  t dƒ‰t ddd�\} }‰t ddd�\}}}}tdƒ‰tdƒ‰ ‡‡fd	d
„}‡‡fdd„}‡ ‡‡‡fdd„}|t| ˆ ƒˆ ˆƒ ƒˆ| ˆ ƒks˜t‚|| ˆ ˆ| ƒ ƒ| ˆˆƒ t| ˆ ƒ ksÊt‚|tˆ ˆƒˆdƒƒˆd  ˆˆƒ ksôt‚|tˆ ˆƒˆdƒƒˆd ˆˆƒ k�st‚|dƒdtˆƒ k�s8t‚|dˆ ƒtˆƒk�sRt‚|dˆd  ƒˆtˆƒ k�stt‚|dˆd  ƒˆd tˆƒ d k�sžt‚|dˆ|  ƒˆ|d  tˆƒ t|ƒ k�sÐt‚|||ˆ  ƒ|t| ˆ ƒ tˆƒ k�s t‚|ˆ|ˆ  ƒ| t| ˆ ƒ tˆƒ tˆƒ k�s:t‚||ˆ ˆ| d  ƒ|| ˆ t| ˆ ƒ tˆƒ t| ˆ ƒtˆƒ   k�s’t‚||ˆ| ˆ|   ƒ|t|ˆ ƒt|ˆ ƒ  tˆ ||  ƒ tˆƒ ||  k�sît‚||ˆ ˆ| ˆ|   ƒ||t|ˆ ƒ |t|ˆ ƒ   tˆ ||  ƒ tˆƒ ||  k�sVt‚|ˆ|ˆ d  ƒˆ| ˆ d  t| ˆ ƒ tˆƒ d k�sœt‚|dˆ|ˆ d   ƒ|d  ˆd  d| ˆ  dt|ˆ ƒ  d t| ˆ ƒ tˆƒ d|d   k�st‚|dˆ|ˆ |   ƒtˆƒt||ˆ ƒ || t|ƒ  k�sRt‚|ˆ| |  ƒˆ|d  t|ˆ ƒ tˆƒ t|ƒ k�s’t‚||ˆ d ƒˆt| ˆ ƒ tˆƒ k�sÂt‚||ˆ d ƒˆd t| ˆ ƒ tˆƒ d k�sút‚|ˆd ˆd d  ƒt	ˆƒ tˆƒ tˆƒ k�s2t‚|ddˆd d   ƒt	ˆƒ tˆƒ tˆƒ k�sjt‚|||d ˆd   ƒt	|ˆ ƒtˆƒ k�sœt‚|ˆˆd |d   ƒt
|ˆ ƒtˆƒ k�sÎt‚|||d |ˆ d   ƒt| ˆ ƒt	|ˆ ƒ tˆƒ k�st‚||ˆ |d |ˆ d   ƒ|| t| ˆ ƒ t	|ˆ ƒ | t| ˆ ƒt
|ˆ ƒ   tˆƒ k�s‚t‚|dˆd ˆd d   ƒˆtˆƒ t	ˆƒtˆƒ  k�sÀt‚||ˆ |d ˆ| d  |d   ƒ|| | t	|ˆ | ƒ |t
|ˆ | ƒ   t| ˆ ƒ tˆƒ ||d   k�sBt‚||ˆd  | |d ˆd  d  ƒd|d  | t	|ˆ ƒ |d | | |ˆ t
|ˆ ƒ t	|ˆ ƒ   tˆƒ d|d   k�sÐt‚||ˆd |d   ƒ|t|ˆ ƒ tˆƒ | k�s
t‚||ˆd |d   ƒ|t|ˆ ƒtˆƒ d|  t| ˆ ƒtˆƒ d|    k�sft‚||ˆ ˆd |d   ƒ|t|ˆ ƒ tˆƒ k�s t‚||ˆˆ|   ƒ|tˆƒ| t| ˆ ƒtˆƒ |   k�sät‚|ˆd ˆd ˆd dˆ  d   ƒdt	dˆ ƒ dt
dˆ ƒ  tˆƒ d tdˆ ƒ tˆƒ d k�	sVt‚|d|ˆd  |ˆ  |  ƒdt| ˆ d|  ƒ t	ˆtd| | |d  ƒ d|  ƒ tˆƒ td| | |d  ƒ k�	sÞt‚|dtˆƒ |ˆ |  ƒt|ˆ | ƒtˆƒ tt|ƒtˆƒ t|ƒ ƒ t|ƒt|ƒ  k�
sDt‚|dt| ˆ ƒ |ˆ |  ˆ ƒd| tˆƒ ttƒ|  |tdƒd  t|ˆ | ƒ tt|ƒtˆƒ t|ƒ ƒ |tdƒd    tˆƒ |t| ƒ  k�
sêt‚|dt|ˆ ƒ|  ƒ| t|d ˆ | ƒ t|tˆƒ t|ƒ ƒ | dttƒt|ƒ tˆƒ   tˆƒ k�sbt‚||ˆ |tˆƒ |  ƒt|d ˆ |d  ƒ t|tˆƒ | ƒ d tˆƒ k�s¾t‚||| tˆƒ tˆƒt|ƒ  ˆ|  ƒt|ƒt|ƒ t|ˆ ƒ tt|ƒtˆƒ ƒ |t|ˆ ƒ tt|ƒtˆƒ ƒ  |t|ˆ ƒ  tˆƒ k�s\t‚|dtˆƒ t|ˆ ƒ|  ƒt|d ˆ | ƒtˆƒ t|tˆƒ t|ƒ ƒ t|ƒ k�s¾t‚||d tˆƒ|  ˆtdƒd   ƒd| tˆƒ ttƒ t|d ˆ ƒt|tˆƒ ƒ  d tˆƒ k�s0t‚||| t|ƒ ˆ|  tˆƒ tˆƒt|ƒ  ƒt|ƒt|ˆ ƒ tt|ƒtˆƒ ƒ t|ƒt|ˆ ƒ tt|ƒtˆƒ ƒ  t|ƒt|ˆ ƒ  tˆƒ k�sÖt‚|dtˆƒt|ƒ d  ƒdt|ƒ tˆƒ ttƒ d| ˆ d tt|ƒtˆƒ ƒd  t|ˆ ƒ  d tˆƒ k�sTt‚|dtˆƒt|ƒ d  ˆ ƒdˆ d|  t|ˆ ƒ tt|ƒtˆƒ ƒ d|  dtˆƒ ttƒt|ƒ   tˆƒ k�sÖt‚|dtˆƒ| d  tˆƒ ƒd| ˆ t|d ˆ ƒ t|tˆƒ ƒ dtˆƒ ttƒ  tˆƒ k�sDt‚|dtˆƒ| d  ƒ| ˆ d|d  ˆ d  t|d ˆ ƒ t|tˆƒ ƒ dtˆƒ |d ˆ d  ttƒ  tˆƒ k�sÌt‚|tˆƒtˆƒ| d  ƒ dttƒ|d  ˆ dttƒ t|tˆƒ ƒ dt|d  ˆ ƒ |tˆƒ    |d  ˆd  d|d  ˆ d  tj  t|d ˆ ƒ d ttƒ| tˆƒ |d ˆ d  d   tˆƒ t|d  ˆ    ¡ }	|	dk�sÒt‚|dtˆƒ tˆƒ| d  ƒ tˆƒtˆƒd|d  ˆ d ttƒ| tˆƒ t|d ˆ ƒ t|tˆƒ ƒ d  d  ttƒ|     ¡ }	|	dk�srt‚t|dtˆƒ| d  ƒƒdd|d  ˆtdƒd   d|d  ˆ d  dttƒ  ˆd|d  ˆd  d|d  ˆ  d  t|d ˆ ƒ t|tˆƒ ƒ d   tˆƒ k�s,t‚|tˆƒ| ˆtˆƒ|   ƒdt|d ˆ ƒ t|tˆƒ ƒ d tˆƒ k�s‚t‚|tˆƒ| d ˆtˆƒ| d   ƒdd|d  ˆ t|d ˆ ƒ t|tˆƒ ƒ  dttƒ | tˆƒ  tˆƒ k�st‚|tˆƒ| d ˆtˆƒ| d   ƒtˆƒdd|d  ˆd  d|d  ˆ  d  t|d ˆ ƒ t|tˆƒ ƒ dttƒ | tˆƒ d|d  ˆ d   d  k�s¶t‚|tˆ| ƒˆ|  ƒtˆƒt| ˆ ƒtˆƒ ttƒ t|| ƒt| ˆ ƒ tt|| ƒtˆƒ ƒ   k�s,t‚|dtˆ| ƒ ˆ|  ƒtˆƒdt|| ƒ t| ˆ ƒ tt|| ƒtˆƒ ƒ  k�sŒt‚|dtˆd |d  ƒ ƒtˆƒtd|ˆ ƒ k�sÄt‚|dtˆd |d  ƒ ƒtˆƒtd|ˆ ƒ k�süt‚|ˆd tdˆ ƒ dtˆƒ  d tdˆ ƒ ˆˆd d   ƒ t
ˆƒtˆƒ  dt
ˆd ƒ tˆd ƒ  dt
ˆd ƒ tˆd ƒ  dtˆd ƒ  dtˆd ƒ   ¡ dk�s¸t‚d S )Nr?   zk, n, tT©Úrealz
a, b, c, dr@   rD   rE   c                    s   t | ˆ ˆƒS ©N©r   ©rF   ©r?   ro   rv   rw   rk   ñ  s    z+test_inverse_laplace_transform.<locals>.ILTc                    s   t | ˆ ˆdd�S )NTr   r|   r}   r~   rv   rw   ÚILTSô  s    z,test_inverse_laplace_transform.<locals>.ILTSc                    s   t t| ˆˆƒˆˆ iƒS r{   )r   r   r}   ©rE   rD   r?   ro   rv   rw   ÚILTF÷  s    
 ÿz,test_inverse_laplace_transform.<locals>.ILTFrJ   rM   rI   rQ   rS   rb   rV   rX   rN   r_   r^   rT   r   é   )r   r	   r   rg   r   r+   r,   r)   r(   r&   r%   r   r   r"   r1   r   r   r2   ZHalfr   r   r8   r7   )
ÚkÚnrl   rm   rn   Údrk   r   r�   rq   rv   r€   rw   Útest_inverse_laplace_transformé  s"   ,2**"*20:8ÿ
<ÿ
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F0 ÿÿ
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@088822DHÿ
>&Rÿ
&:
ÿþ
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:(ÿ
&Bÿ
@ÿÿÿ
Bÿÿ"Jÿþ
þÿÿJÿÿÿ8ÿÿ*."ÿÿÿÿÿ:ÿÿ&:ÿÿÿ2&&ÿþþÿÿ ÿ
ÿÿþþÿÿ6ÿÿÿÿ*ÿÿÿÿ<"ÿÿÿÿ. ÿ*þþþ&ýüüÿÿÿ "ÿÿÿþ
ýÿÿÿ<:ÿÿÿþÿÿ.ÿÿ&2ÿþÿ,:ÿ*ÿÿÿÿ0ÿÿÿ 4ÿÿ ÿÿ ÿÿDÿÿþþýür†   c                  C   s¸  ddl m}  t}tddd�\}}}}tddd�\}}tdƒ\}}	td	ƒ}
td
ƒ}dd„ }||tƒt|ƒ}t||
|iƒ|
|ƒks‚t‚|t| t ƒt t|ƒt	| | ƒks®t‚|t| t ƒ|t  t|ƒt| | |  ƒt	| | ƒ ksòt‚||t |d |t d   t|ƒt| | ƒt
|| ƒ t	|ƒ k�s>t‚|t| t ƒt|  t|ƒ| | |d  t	| | ƒ t|ƒ k�sŠt‚|t| t ƒttd d ƒ t|ƒt	| | ƒtd|| ƒ k�sÒt‚|dtttd ƒ  t|ƒt	|ƒtt|ƒƒ k�st‚|t| t ƒt|  t|ƒ|| |d  t	|| ƒ t|ƒ k�sPt‚|t| t ƒtdtd  ƒ t|ƒt	|| ƒtd|| ƒ k�s–t‚t||| tttd |d  ƒ |   ttd |d  ƒ t|ƒ t¡ƒt	|ƒt||| ƒ k�sþt‚||| tttd |d  ƒ |   ttd |d  ƒ t|dd� t¡t	|ƒt||| ƒ k�sft‚|dtttd ƒ  t|ƒt	|ƒtt|ƒƒ k�sœt‚|ttdƒ tddgddggƒ  ¡ t|ƒtt|ƒt	|ƒ dgdtd| ƒt	|ƒ ggƒk�sþt‚|td |
tƒ t|ƒtt|
tƒt|d ƒ|dfƒk�s8t‚|t
tƒt|ƒtt
tƒt|d ƒk�s`t‚|dtdt ƒ dtdt ƒ  t|ƒdttdt ƒt|d ƒ d| |d ƒ  k�s¸t‚t
tdƒd ƒ}||tdt ƒ t|ƒ|| |d ƒ k�söt‚|tdt ƒt|ƒttdt ƒt|d ƒk�s&t‚tddd�}|t|t ƒt|ƒtt|t ƒt|d ƒk�sbt‚|td |d td   t|ƒ| t|| ƒ t	|ƒ | |ƒ k�sªt‚|td |
tƒd|d td     t|ƒ| t|| ƒ t	|ƒ | |ƒ tt|
tƒt|d ƒ|dfƒ k�st‚|t|t ƒt|dd�tt|t ƒt|d ƒdfk�sRt‚tddd�tdddd�fD ]F}	|t|	t ƒt|dd�}
t|
tƒ�rœ|
d n|
}
|
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   Úrewriter&   )Úexprrv   rv   rw   Úsimp_hypª  s    z4test_inverse_laplace_transform_old.<locals>.simp_hyprI   rQ   r   r\   rJ   rS   iùÿÿÿrU   rZ   ÚrFrK   Úz)Zextended_real)Z	imaginaryÚzero)Ú'sympy.functions.special.delta_functionsr+   r   r   r	   r?   r   rg   r   r,   r%   r)   r"   r8   r1   r   r‡   r7   r>   r=   Úinvr   r   r&   r   Ú
isinstanceÚtupleÚfunc)r+   rk   rl   rm   rn   r…   r„   rŠ   ro   r‹   rD   rE   r‰   rr   rv   rv   rw   Ú"test_inverse_laplace_transform_old   s¤    ,D" ÿ
&ÿ
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ÿr’   c                  C   sÈ  t dƒ} t dƒ}t ddd�}tt| ƒ| tƒtdtd  ƒ d t ddfksPt‚tt|| ƒ| tdd	�tttt	t
 ƒ d|ƒdt|ƒtjkfks’t‚ttd| ƒ| tdd	�ttd ƒt ddfksÂt‚ttd| ƒ| tdd	�tttd ƒ td  ddfksút‚ttdtd  ƒ d t t|ƒ ¡ t|ƒt|ƒ k�s6t‚tttd ƒt t| dd	� t¡t| ƒt| ƒ k�snt‚ttttd ƒ td  t| dd	� t¡ ¡ td| ƒt| ƒ  t¡ t¡ ¡ k�sÄt‚d S )
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ÿÿþÿ  þþ ýÿr”   N)ZZsympy.integrals.laplacer   r   r   r   r   r   r   Zsympy.core.functionr	   r
   Z
sympy.corer   r   r   r   Zsympy.core.exprtoolsr   Zsympy.core.numbersr   r   r   Zsympy.core.relationalr   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Zsympy.simplify.simplifyr   Z$sympy.functions.elementary.complexesr   r   Z&sympy.functions.elementary.exponentialr   r   r   Z%sympy.functions.elementary.hyperbolicr   r   r    r!   Z(sympy.functions.elementary.miscellaneousr"   Z$sympy.functions.elementary.piecewiser#   Z(sympy.functions.elementary.trigonometricr$   r%   r&   Zsympy.logic.boolalgr'   Z'sympy.functions.special.gamma_functionsr(   r)   r*   r�   r+   r,   Z-sympy.functions.special.singularity_functionsr-   Z&sympy.functions.special.zeta_functionsr.   Z'sympy.functions.special.error_functionsr/   r0   r1   r2   r3   r4   r5   r6   Zsympy.functions.special.besselr7   r8   r9   r:   Zsympy.testing.pytestr;   r<   Zsympy.matricesr=   r>   Z	sympy.abcr?   rx   r†   r’   r”   rv   rv   rv   rw   Ú<module>   sH   $(
   I
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