
    Rie                        d dl Z  e j        dd          Ze                                dv Zerwd dlmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7 d dl8m9Z: d dlm;Z; nd dl<m1Z1 d d	l=m7Z7 d d
l>m(Z(m.Z.m;Z;m-Z-m3Z3 d dl?m2Z2 d dl@m:Z:mZmZmZm6Z6mZ d dlAmZ d dlBmZm0Z0m/Z/ d dlCm	Z	mZ d dlDmZm
Z
 d dlEm!Z!mZm#Z#m%Z%m Z m"Z"m$Z$mZ d dlFmZ d dlGmZmZmZmZmZmZmZmZmZmZmZmZ d dlHmZ d dlIm*Z*m)Z)m+Z+mZm,Z,m'Z' d dlJm4Z4 d dlKm5Z5 d dlLm&Z& d ZMg dZNdS )    NUSE_SYMENGINE0)1ttrue)3SymbolIntegersympifySSympifyErrorexploggammasqrtIEpiMatrixsincostancotcscsecasinacosatanacotacscasecsinhcoshtanhcothasinhacoshatanhacothlambdifysymarraydiffzeroseyediagonesexpandFunctionsymbolsvarAddMul
DerivativeImmutableMatrix
MatrixBaseRationalBasic)gcd)AppliedUndef)r4   )r:   )r+   r1   r<   r0   r6   )r5   )igcdr   r   r	   r9   r   )r   )r   r3   r2   )r   r
   )r   r   )r$   r!   r&   r(   r#   r%   r'   r"   )r   )r   r    r   r   r   r   r   r   r   r   r   r   )r   )r-   r,   r.   r   r/   r*   )r7   )r8   )r)   c                     t          | t          t          f          sJ |                                 }|                                 t          | t                    r|                                }|S )z(Return a simplified copy of the matrix M)
isinstancer   r7   
as_mutablesimplifyas_immutable)MMnews     2lib/python3.11/site-packages/sympy/core/backend.py_simplify_matrixrF   B   s_    a&/233333<<>>DMMOOO!_%% #  ""K    )5r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r=   r<   )Oosgetenvr   lower	symenginer   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   symengine.lib.symengine_wrapperr;   r=   r<   sympy.core.addsympy.core.basicsympy.core.functionsympy.core.mulsympy.core.numberssympy.core.singletonsympy.core.symbolsympy.core.sympify&sympy.functions.elementary.exponential%sympy.functions.elementary.hyperbolic(sympy.functions.elementary.miscellaneous(sympy.functions.elementary.trigonometric'sympy.functions.special.gamma_functionssympy.matrices.densesympy.matrices.immutablesympy.matrices.matricessympy.utilities.lambdifyrF   __all__ rG   rE   <module>r`      sa   					/3//##%%);; 26 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 <;;;;;&&&&&&&""""""&&&&&&             """"""DDDDDDDDDDDDDDDD&&&&&&666666666688888888????????0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0======E E E E E E E E E E E E E E E E E E E E E E E E E E E E======               888888222222111111<    rG   