I have a couple problems with this “answer”, which roughly replace the 
transcendental function calls (which are indeed bijections) with symbols 
and solving for these symbols.

The most serious is that the transformed expressions are rational 
functions, and he proposed solution solves for their numerators. The author 
failed to note that for each proposed solution, the denominators are zero, 
meaning that the expressions are undefined at these points. Using those 
propôsed solutions require serious justifications (e. g. computing the 
limits of the (transformed) expressions at these points).

See my answer 
<https://github.com/sympy/sympy/issues/24824#issuecomment-1474975520>.
​
Le mardi 7 mars 2023 à 04:18:07 UTC+1, [email protected] a écrit :

> An answer is given in https://github.com/sympy/sympy/issues/24824
>
> On Sunday, March 5, 2023 at 1:26:50 PM UTC-6 [email protected] wrote:
>
>> I think you should   simplifythe equation and reduce the computational 
>> complexity as much as possible. It may also be helpful to check the 
>> implementation for errors or potential issues with the input parameters.
>>
>> On Tuesday, 28 February 2023 at 21:35:24 UTC+5:30 [email protected] 
>> wrote:
>>
>>> Hi all, 
>>> I try to solve a non linear equation but it conitnue runiing since 48 
>>> hours now.
>>> ``
>>> import sympy as sp
>>>
>>> X = sp.MatrixSymbol('X',2,2)
>>> W = sp.MatrixSymbol('W',2,2)
>>> Y = sp.MatrixSymbol('Y',1,2)
>>> W_X = sp.MatMul(W,X.T)
>>>
>>> liste = []
>>> for i in range(W_X.shape[0]):
>>>     row = []
>>>     for j in range(W_X.shape[1]):
>>>         row.append(1/(1+sp.exp(-W_X[i,j])))
>>>         
>>>     liste.append(row)
>>> sigmoid = sp.Matrix(liste)
>>>
>>> liste = []
>>> for i in range(Y.shape[0]):
>>>     row = []
>>>     for j in range(Y.shape[1]):
>>>         row.append(sp.log(Y[i,j]/(1-Y[i,j])))
>>>     liste.append(row)
>>> log_Y = sp.Matrix(liste)
>>>
>>> test = sigmoid.inv()
>>>
>>> W2 = sp.MatMul(log_Y,test).as_explicit()
>>>
>>> liste = []
>>> for index in range(W2.shape[1]):
>>>     for i in range(W.shape[0]):
>>>         for j in range(W.shape[1]):
>>>             liste.append(W2[index].diff(W[i,j]))
>>>             
>>>             
>>> p = sp.solve(liste,list(W),check=False,manual=True)
>>> ```
>>>
>>>
>>> Do someone have an idea where i am wrong or if it is from sympy ?
>>>
>>> Thanks a lot 
>>>
>>

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