On Wed, Feb 10, 2021 at 6:47 AM David Bailey <d...@dbailey.co.uk> wrote:

> On 10/02/2021 00:53, Oscar Benjamin wrote:
>
> On Tue, 9 Feb 2021 at 23:58, S.Y. Lee <sylee...@gmail.com> 
> <sylee...@gmail.com> wrote:
>
>
> And we would also arrive in questions like: If equation brings its own 
> algebra system, there should be an equation of equations? How should we solve 
> them?
>
> It's not an "algebra system": it's just a few convenience operations.
> It should not be confused with allowing Equation to be used in places
> where Expr is expected.
>
> Might it be an idea to introduce functions such as AddSides,
> SubtractSides, etc that Mathematica has? Not only would these avoid any
> confusion with the normal arithmetic operations,  but I think using these
> functions would clarify what is going on. After all, when people do such
> operations by hand, they don't write (a=b)*k,or whatever, they typically
> write "Multiplying equation 4 by k we get..."
>

Is there a need to have an unevaluated version of AddSides? + already works
for an evaluated version.

It might be worth thinking about inequalities in the design here. We've
been ignoring them because it's simpler to do equalities first, but
inequalities have some restrictions that might clarify what design we want.
For a > b, things like function application or even multiplication aren't
straightforward. What should x*(a > b) do if x is only known to be real?
One option is a Piecewise, but then things get hairy if you start doing
other operations. Maybe a MultiplySides does actually make sense for this.

Aaron Meurer

David
>
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