�
��g�R � � � d Z ddlZddlZddlmZmZmZ ddlmZ ddl m
Z
ddlmZ ddl
mZmZmZmZmZmZmZmZmZmZ ddlmZmZ dd lmZmZmZmZm Z m!Z!m"Z"m#Z# dd
l$m%Z% ddl&m'Z'm(Z(m)Z) ddl*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0 dd
l1m2Z2m3Z3 ddl4m5Z5m6Z6m7Z7m8Z8 ddl9m:Z:m;Z;m<Z< ddl=m>Z>m?Z? ddl@mAZAmBZBmCZCmDZD ddlEmFZFmGZGmHZHmIZI ddlJmKZKmLZL ddlMmNZNmOZOmPZP ddlQmRZRmSZSmTZTmUZU ddlVmWZW ddlXmYZYmZZZ ddl[m\Z\m]Z]m^Z^ ddl_m`Z`maZambZbmcZcmdZd ddlemfZf ddlgmhZh ddlimjZj ddlkmlZl ddlmmnZn ddlompZp dd lqmrZr dd!lsmtZtmuZumvZv dd"lwmxZx dayd#� Zzd$� Z{d%� Z|ezd&� � � Z}ezd'� � � Z~ezd(� � � Ze
d)� � � Z�ezd*� � � Z�ezd+� � � Z�ezd,� � � Z�ezd-� � � Z�ezd.� � � Z�ezd/� � � Z�ezd0� � � Z�ezd1� � � Z�ezd2� � � Z�ezd3� � � Z�ezd4� � � Z�ezd5� � � Z�ezd6� � � Z�ezd7� � � Z�d8� Z�d9� Z�ezd:� � � Z� G d;� d<e]� � Z�dQd>�Z�ezd?� � � Z�ezd@� � � Z�e
dA� � � Z�ezdB� � � Z�ezdC� � � Z�ezdD� � � Z�ezdE� � � Z�ezdF� � � Z�ezdG� � � Z�ezdH� � � Z�ezdI� � � Z�ezdJ� � � Z�ezdK� � � Z�ezdL� � � Z� G dM� dNe]� � Z�dRdO�Z�dP� Z�dS )SzLaplace Transforms� N)�S�pi�I)�Add)�cacheit)�Expr)
�AppliedUndef�
Derivative�expand�expand_complex�
expand_mul�expand_trig�Lambda�WildFunction�diff�Subs)�Mul�prod)�
_canonical�Ge�Gt�Lt�
Unequality�Eq�Ne�
Relational)�ordered)�Dummy�symbols�Wild)�re�im�arg�Abs�
polar_lift�periodic_argument)�exp�log)�cosh�coth�sinh�asinh)�Max�Min�sqrt)� Piecewise�piecewise_exclusive)�cos�sin�atan�sinc)�besseli�besselj�besselk�bessely)�
DiracDelta� Heaviside)�erf�erfc�Ei)�digamma�gamma�
lowergamma�
uppergamma)�SingularityFunction)� integrate�Integral)� _simplify�IntegralTransform�IntegralTransformError)�to_cnf� conjuncts� disjuncts�Or�And)�
MatrixBase)�_lin_eq2dict)�PolynomialError)�roots)�Poly)�together)�RootSum)�sympy_deprecation_warning�SymPyDeprecationWarning�ignore_warnings)�debugfc � � � � fd�}|S )Nc �b �� ddl m} |s �| i |��S t dk rt dt j �� � t ddt z ��j �| ��t j �� � t dz
a�j dk s�j d k rGd
t _ t ddt z z t j �� � �| i |��}dt _ n �| i |��}t dz at ddt z �d
|��t j �� � t dk rt dt j �� � |S )Nr ��SYMPY_DEBUGzO
------------------------------------------------------------------------------��file�-LT- � � �_laplace_transform_integration�&_inverse_laplace_transform_integrationFz**** %sIntegrating ...Tz---> zO------------------------------------------------------------------------------
)�sympyr\ � _LT_level�print�sys�stderr�__name__)�args�kwargsr\ �result�funcs ��g/home/asafur/pinokio/api/open-webui.git/app/env/lib/python3.11/site-packages/sympy/integrals/laplace.py�wrapzDEBUG_WRAP.<locals>.wrap1 sV �� �%�%�%�%�%�%� � )��4��(��(�(�(���>�>��-�c�j�1�1�1�1�
��t�I�~�~�t�}�}�d�d�C��:� � � � ��Q�� ��
�!A�A�A��
�!I�I�I� %�E���*�d�9�n�=�C�J�O�O�O�O��T�4�*�6�*�*�F� $�E����T�4�*�6�*�*�F��Q�� �
��$�y�.�.�.�&�&�9��
�K�K�K�K���>�>��-�c�j�1�1�1�1��
� � )rm ro s ` rn �
DEBUG_WRAPrr 0 s# �� �� � � � �4 �Krp c �j � ddl m} |r*t ddt z �| ��t j �� � d S d S )Nr r[ r_ r` r] )rd r\ rf re rg rh )�textr\ s rn �_debugru N sU � �!�!�!�!�!�!� � E�
��T�)�^�^�T�T�2���D�D�D�D�D�D�E� Erp c �� ������ �fd������fd���fd���fd�}d� }ddl m} || � � } || t �� � } || t �fd�� � } || t |� � } t | � � S ) a
Naively simplify some conditions occurring in ``expr``,
given that `\operatorname{Re}(s) > a`.
Examples
========
>>> from sympy.integrals.laplace import _simplifyconds
>>> from sympy.abc import x
>>> from sympy import sympify as S
>>> _simplifyconds(abs(x**2) < 1, x, 1)
False
>>> _simplifyconds(abs(x**2) < 1, x, 2)
False
>>> _simplifyconds(abs(x**2) < 1, x, 0)
Abs(x**2) < 1
>>> _simplifyconds(abs(1/x**2) < 1, x, 1)
True
>>> _simplifyconds(S(1) < abs(x), x, 1)
True
>>> _simplifyconds(S(1) < abs(1/x), x, 1)
False
>>> from sympy import Ne
>>> _simplifyconds(Ne(1, x**3), x, 1)
True
>>> _simplifyconds(Ne(1, x**3), x, 2)
True
>>> _simplifyconds(Ne(1, x**3), x, 0)
Ne(1, x**3)
c �J �� | �k rdS | j r| j �k r| j S d S )Nra )�is_Pow�baser'