Parse tower

[Aras14HD]

This adds parsing for Towers, Tetration and more intuitive numbers with exponent like 5.4 ⨉ 10^6.

This is a breaking change for the library, as we add a new constant to control, how deep towers should be displayed for inputs.

Two questions:

• Should Tetration and the new exponents only be accepted in parens? (no post op, and neither post nor pre op) (maybe also something for towers)
• Should we keep in the max tower depth or just give them as large as possible? (maybe keep only for value, not result)

[tolik518]

• Should Tetration and the new exponents only be accepted in parens? (no post op, and neither post nor pre op) (maybe also something for towers)
• Should we keep in the max tower depth or just give them as large as possible? (maybe keep only for value, not result)

I don't have a hard opinion on those topics as I feel like I can't really picture the consequences right now to be honest

[Aras14HD]

So as it currently stands, it would interpret

• ^(50)10! rendered ⁵⁰10! as (^(50)10)!
• 5.2 ⨉ 10^(50)! rendered 5.2 ⨉ 10⁵⁰! as (5.2 ⨉ 10^(50))!
• 10^50! rendered 10⁵⁰ꜝ as (10^50)!
• !10^50 rendered !10⁵⁰ as !(10^50)

Instead it should probably reject (some of) these examples (skipping just enough) and see this instead

• ^(50)10! as 10! (ignoring the later tetration)
• 5.2 ⨉ 10^(50)! as 10^(50)! (ignoring the later multiplication)
• 10^50! as 50! (ignoring the later exponentiation)
• !10^50 as !10 (ignoring the later power)

The second and third ones seem clear to me, that they should change, as factorial comes before multiplication and in the second one it is rendered (on at least some platforms) with the factorial in the exponent.

The first and fourth I feel should also be changed, as I think (sub-)factorial comes before power/tetration/etc.

[Aras14HD]

As I was pretty much completely sure, I should fix that, I did.

Now just max tower depth to figure out. It looks a lot better with, but we technically lose some info. (Maybe check for 1 in top exponent?)

[tolik518]

Yeah I think i'm too far away from math at the time to have a strong opinion tbh :D

Maybe check for 1 in top exponent?

This sounds a bit hacky, but I think that would suffice

[Aras14HD]

Just adds one check to formatting towers and is by definition of tetration equal. And for that, we don't have a major version change in the lib now. (Kept minor version change as it is a new minor feature)

[Aras14HD]

Also added parsing of complex infinity (like a constant) as I just saw somebody try to use it again.

[tolik518]

I have only one small suggestion, but I can also merge it as it is :)

[tolik518]

Thank you, I'll merge that soon