superscripts & subscripts for science/mathematics?

[David Melik via Unicode]

On 01/21/2018 02:27 PM, Frédéric Grosshans wrote:
> Le 21/01/2018 à 07:15, David Melik via Unicode a écrit :
>> I don't know if this was discussed, but it'd help 
>>scientists/mathematicians if all Greek and Hebrew were available as 
>>superscript & subscript.  Mathematicians use certain such letters in 
>>standard notation of important expressions/formulae (superscript π in 
>>Euler's Identity, subscript base π, superscript א in cardinality of 
>>real numbers, etc.)... actually we use all Greek letters, and since a 
>>few Hebrew (since 1800s) have standard mathematical meanings, more 
are >>used for variables.  After any such alphabets' letters are used, 
the >>rest are considered normal/standard to use in standard script, 
 >>superscript, and subscript, for any educational usage, and future 
 >>standard notation.
>
>> Mathematics superscript and substript are supposed to be rich text, 
>not plain text. Furthermore, “completing the set of mathematical 
>superscripts” is an impossible task, since one would need double 
>superscripts for e^(-x²) and even more exotic combinations for stuff 
as >common as e^x₁

On 01/22/2018 01:20 PM, Murray Sargent wrote:
> Subscripts and superscripts are more complicated in mathematics than 
>in ordinary text in that they can be nested and can include arbitrary 
>operators, e.g., a superscripted superscript  as in e^(-x^2). 
>Accordingly, encoding more Unicode subscripts and superscripts for 
>mathematics isn't general enough to be worthwhile and it can 
complicate >math input methods. In plain text, one can use a linear 
format such as >LaTeX or UnicodeMath. Ideally these formats can drive 
math display >engines that display elegant mathematical typography with 
arbitrary >combinations of subscripts, superscripts and other 
mathematical >constructs.

‘The intended use was to allow chemical and algebra formulas to be 
written without 
markup’--https://en.wikipedia.org/wiki/Unicode_subscripts_and_superscripts. 
  Unless wrong, apart from  disagreement, it's clear mathematics word 
processing software is useful, but not a reason to not finish 
almost-complete set of basic superscripts & subscripts 
((super|sub)scripts) for relevant alphabets used (English, Greek, 
perhaps Hebrew, latter two which were in my original post subject line, 
but I likely accidentally used link I received to delete pre-moderated 
post.)  Before rich-text, people used plain-text centuries, still do, 
such as plain-text files that may be about simpler topics, or 
informal/notes, and Internet areas predating all websites, such as 
standard (such as this non-HTML) email, NNTP/Usenet (still hundreds of 
mathematics posts/day,) Internet Relay Chat (IRC, still dozens of 
science & mathematics rooms, one math one with around 1000 people, busy 
all the time) etc., but the latter at least has Unicode (none are 
rich-text.)
     This shows how much of English has superscripts, and which letter 
doesn't: ᵃᵇᶜᵈᵉᶠᵍʰⁱʲᵏˡᵐⁿᵒᵖqʳˢᵗᵘᵛʷˣʸᶻ.  However, there are simple 
mathematics situations people use any/every letter, lowercase & 
uppercase, superscript & subscript (not sure about ‘overscript.’)
     It's up to each science/math fan, student, writer, instructor what 
type of text they want (not just what you say is ‘supposed to be,’ ‘can 
complicate.’)  I never said
make Unicode like super-complicated stuff math formatting software... 
only a small percentage of where people write math, which of course, 
writing isn't just advanced books, but also simple & informal/notes, and 
plain-text isn't just in text-editors, but also graphics editors.
     If not clearer now, all I was requesting was adding/completing 
Greek (super|sub)scripts, though had forgotten not all English ones 
exist, so those too, and I was suggesting Hebrew (super|sub)scripts... 
never mentioned supersuperscripts & subsubscripts, etc., which one of 
you showed then argued against (doesn't refute what I actually said.) 
I'm just talking about completing relevant alphabets for usage described 
‘chemical and algebra formulas,’ which as I took algebra before high 
school, wasn't seeing super-complicated stuff that may or not be in 
college/university algebra texts, or are in derived fields with some 
algebra-type formulae.  I'm only talking about simple, one-level 
(super|sub)scripts for largest variety of simple formulae, not 
‘completing the set’ (in relation to all math) nor 
(super|sub)(super|sub)scripts as in replies with mixed style.
     The biggest problem for me is Euler's Formula & Identity, which 
through high school math of analysis/calculus (and on through several 
years to applied & abstract analysis) are usually considered the most 
important & beautiful formula & identity in mathematics (the formula 
modelling basis of all current physics, and the identity having the most 
important numbers, symbols/operations in math.)  It's easy to write his 
formula plain-text, as below.

     eⁱˣ=cos x+i sin x

Almost every day in my plain-text notes/to-do-list, I read these, and 
discuss most weeks in math discussion areas (as mentioned) and ‘in real 
life,’ so thanks for i,x superscripts.  However, writing his identity 
has a problem: must say it definitively has π but am replacing with 
English letter that came from π and is equivalent, p, as below.

     eⁱᵖ+1=0

So, I can only write that in standard from with a word processor, TeX, 
MathML, or (technical jargon, even ambiguous to many computer 
programmers/scientists, CS) graphing calculator notiation, ‘e^(iπ)+1=0.’ :(

It's not just for mathematics research (what one of you were talking 
about,) but (in)formal use by math fans, students, instructors when they 
use plain-text (which I and many I know use.)  For example, For years I 
couldn't write Euler's Identity into graphics programs such as the 
Free/Libre Software (FL/S) one called GIMP (which doesn't have 
(super|sub)scripts (don't know about proprietary Adobe Photoshop 
graphics,) though it finally worked with Inkscape FL/S.  So, that's 
another problem... people using the most widely-used graphics FL/S need 
these in plain-text, otherwise may learn a trick to make 
(super|sub)scripts in GIMP by moving (not resizing) the text 
(personally, I spent days reading about standard (super|sub)script sizes 
and more hours making three text layers) so if 100 people each make an 
image about Euler for educational uses, or for a t-shirt, in GIMP, all 
100 are going to have varying, non-standard text appearance... unless 
the proper (super|sub)scripts are added.
     Of course, I've been aware of graphing calculator notation you used 
above like e^x, x_1, but punctuation there mean different things in much 
of CS (many CS whom didn't use graphing calculators, forgot, or started 
in school with newer math software) so it'd be helpful to have the 
proper superscripts for .TXT, email (and NNTP/Usenet?,) IRC.
     That's all I'm saying... not additional 
(super|sub)(super|sub)script levels... just, if you have some 
(super|sub)scripts in an alphabet, have a *basic* set of all (or all 
considered important)... particularly π, maybe φ, ...
     Also, the problem isn't just these classic formats (.TXT, NNTP, 
IRC) not all you necessarily use (many scientists do)... still, some 
web-forums are plain-text-only (or have text forum formatting code, some 
which has major (super|sub)script bugs... others allow in HTML, which 
seems to have disadvantage of increasing line height.)  Many have been 
‘dying’ while sites like Facebook & Twitter are growing... which also 
have... plain-text.  So, try to write about or discuss easy-to-read 
science/mathematics (in short posts) where most people are on the 
Internet, and you still run into the problem of Unicode currently being 
inadequate.   On those biggest sites, they can still post various emojis 
about poop and ideological cults... maybe that's going to help people 
discuss ideas how to advance science for a better world?  Not as much, I 
think...

Sincerely,
David