Mike,

I'm the author of the referenced pull request (
https://github.com/sympy/sympy/pull/19479) for the equation type. There is 
a version you can try without having to set up SymPy for development (see 
https://github.com/gutow/Algebra_with_Sympy, which I try to keep roughly 
equivalent to the developing SymPy update). As you have interest in this, I 
would appreciate you trying it and providing feedback about behavior in the 
pull request. I am hoping to work on this some more as soon as I get things 
lined up for my Fall classes. I will be trying the Algebra_with_Sympy code 
with one of my classes this Fall.

Regards,
Jonathan

On Sunday, July 26, 2020 at 1:19:20 PM UTC-5 mikhae...@umontpellier.fr 
wrote:

> Thanks a lot for your answer. I belived "Eq" was a reduction for 
> "Equation" and not for "Equality".
> I started to do something similar to what you mention, but your way to do 
> it is smarter and I did and I will use your way.
> Thanks a lot,
>     Mike.
>
> Question : As you answerd nicely my question I require to close  this 
> request. How may I do it ?
>
>
> Le dimanche 26 juillet 2020 20:13:11 UTC+2, Davide Sandona' a écrit :
>
>> Hello Mike,
>> sadly, what you are trying to do is not easily possible! You are thinking 
>> of Eq as an equation, instead in Sympy it is an alias for the class 
>> Equality. They are conceptually different and the behaviour you are trying 
>> to represent is not possible: you can not apply the same mathematical 
>> operation to both sides simultaneously. If you happen to have objects of 
>> type Equality, it is better to convert them to an expression and perform a 
>> manipulation, for example:
>>
>> eq.rewrite(sp.Add).collect(a) / a
>>
>> Alternatively:
>>
>> sp.Eq(*[arg / a for arg in eq.args])
>>
>> If you absolutely need an object to represent an equation, take a look at 
>> the source code of this pull-request [1]. It's not perfect, but it is a 
>> starting point; with that class Equation, you can apply the same 
>> mathematical operation to both sides simultaneously.
>>
>> [1] https://github.com/sympy/sympy/pull/19479
>>
>> Davide.
>>
>>
>> Il giorno dom 26 lug 2020 alle ore 19:39 Mikhael Myara <
>> mikhae...@umontpellier.fr> ha scritto:
>>
> a simple code :
>>>
>>> import sympy as sp 
>>> sp.var('a b c',nonzero=True) 
>>> eq = Eq(a*b,a*c) 
>>> display(eq) 
>>> display(eq.simplify())
>>>
>>> Both display exhibit : ab = ac
>>>
>>> I would have liked sympy to simply remove 'a', which is possible because 
>>> I mentioned 'a' is nonzero.
>>>
>>> What's wrong ?
>>>
>>> Best regards, Mike
>>>
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