�
��g�� � � � d dl mZ d dlmZ d dlmZ d dlmZmZm Z m
Z
d dlmZm
Z d dlmZ d dlmZmZmZ d dlmZmZ d d lmZ d d
lmZ d dlmZ d dlmZm Z d d
l!m"Z" d dl#m$Z$m%Z% d dl&m'Z' d dl(m)Z) d� Z*d� Z+ G d� de"� � Z,dS )� )�Rational)�S)�is_eq)� conjugate�im�re�sign)�exp�log)�sqrt)�acos�asin�atan2)�cos�sin)�trigsimp�� integrate)�MutableDenseMatrix)�sympify�_sympify)�Expr)� fuzzy_not�fuzzy_or)�as_int)�prec_to_dpsc � � |�u|j rp|j du rt d� � �t d� | D � � � � }|r?t |dz t d� | D � � � � � � du rt d� � �dS dS dS dS )z$validate if input norm is consistentNFzInput norm must be positive.c 3 �6 K � | ]}|j o|j d u V � �dS )TN)� is_number�is_real��.0�is �i/home/asafur/pinokio/api/open-webui.git/app/env/lib/python3.11/site-packages/sympy/algebras/quaternion.py� <genexpr>z_check_norm.<locals>.<genexpr> s0 � � � �L�L�a���9�� �T�(9�L�L�L�L�L�L� � c 3 � K � | ] }|d z V � �
dS )r'