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    jg}  ã                   @   s’   d dl mZ d dl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mZ d dlmZmZ edƒZed	ƒ\ZZZZZd
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DiracDeltaÚ	Heaviside)Ú
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ttt
 ƒ tt
t ƒ }t |t
ƒtttt ƒ tt
t ƒ ksJ ‚ttd  t ttt ƒ ttt ƒ ttt ƒ }t |tƒtd t ttt ƒd  ttt ƒ ksTJ ‚t td tdt ƒ tƒtjttƒ kskJ ‚t td tttddƒ tddƒ ƒ tƒtjtttddƒ ƒ ksJ ‚td	d
d\}}}t ttt ƒtt| ƒ tt| ƒ tƒtt| ƒtt| ƒ ttt ƒ ksÂJ ‚tt| ƒttt ƒ tt| ƒ tt| ƒ }t |tƒtt| ƒtt| ƒ tt| ƒ ttt ƒ ksúJ ‚ttt ƒtt| ƒ tt| ƒ ttt ƒ }t |tƒttt ƒtt| ƒ tt| ƒ ttt ƒ ks2J ‚d S )Nr   é
   é   r   é   éÿÿÿÿé   é	   za b cF)Úcommutative)r   r   r	   r
   Úranger   r   r   r   r   Úx_2Úx_1Úzr   ÚHalfr   r   )ÚnÚpÚaÚbÚcr   r   r   Útest_deltaintegrate   sl   $"""&ÿ&,6,.44
ÿ0*ÿþý
ý,48.(
ÿ("
ÿ0@0*
ÿr%   N)Úsympy.core.functionr   Úsympy.core.numbersr   r   Úsympy.core.singletonr   Úsympy.core.symbolr   Ú(sympy.functions.elementary.trigonometricr   r   Ú'sympy.functions.special.delta_functionsr	   r
   Úsympy.integrals.deltafunctionsr   r   r   r   r   r   r   r   r   r%   r   r   r   r   Ú<module>   s    