Use subclasses of sympy.Expr to replace the Mv class about galgebra

[meuns]

I wrote a very hacky thing following the same approach but it was quite clear sympy was useless manipulating the resulting expressions (very large polynomials expressions). I'm interested to follow this work, maybe you will find nice ways to tie GA and sympy together. On the other hand, I started to read a lot of papers about doing geometric proofs using computers. Most of them are wrote by Hongbo Li, he also wrote a nice book (https://www.amazon.com/Invariant-Algebras-Geometric-Reasoning-Hongbo/dp/9812708081). I'm still trying to find an implementation.

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[utensil]

I finally read the gist and find it quite neat. One concern, should we use the private _sympifyit?

[eric-wieser]

One concern, should we use the private

Sympy has not been built for ease of writing extension algebras - we have little choice but to call private methods if we want to actually integrate with rather than just depend on sympy

[utensil]

If we're going to use private methods (as an important design dependency) in SymPy, it's better to bring the discussion to SymPy and possibly submit PRs to make it part of the API.

[eric-wieser]

Found a useful part of the (private) sympy API, _constructor_postprocessor_mapping (example here)

https://github.com/sympy/sympy/blob/master/sympy/core/basic.py#L1793-L1822

This would allow us to overload Add(mv, mv).

[utensil]

I believe the equivalence of this is happening already, only in a different approach: https://github.com/pygae/galgebra/commits/master/galgebra/atoms.py . Should we close this? @eric-wieser