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Re: Subscripts And Superscripts In Gemtext
en

[In reply to: Curiouser gemini://gemi.dev/gemlog/2022-06-06-unicode-sub-sup.gmi]

Curiouser wrote:
	Math formulas are especially challenging, not only because they can have so many symbols (such as sigma 'Σ'), but those symbols must be rendered in a certain layout (e.g. Σ used to sum a series has the variable and its starting value, as well as the value its going to, arranged in 2 different rows to the right of the Σ).

As a further example, sigma notation only behaves that way when it’s inline.
‘Block-level’ sigma notation places one row above the sigma and the other below,
and makes the sigma like twice as large as the rest of the text.
This holds true for a lot of other operations as well,
such as integrals (∫), sequential products (∏), and sometimes unions (∪).
Limits also follow the same rules,
except they’re not extra-large because they don’t have their own symbol.

	In fact, text layout of formulas and symbols is such a complicate domain that Donald Knuth literally created TeX, an entire digital typesetting system, while he was writing "The Art of Computer Programming."

	Given all this complexity, I didn't even try to represent math formulas in gemtext.

This is what made me reply to this post.
You see, I quite like math, so I envision writing some here at times.
So as part of working on the back-end,
I needed to think about how to typeset math in Gemtext,
and I think I’ve come up with a workable solution.

Basically, we can use preformatted blocks to approximate block-level mathematics
and put plaintext math using unicode’s extensive set of math symbols
in the alt-text as a accessible fallback.

== Examples ==

For these examples,
%!gmi: try collapsing the preformatted blocks to see the alt-text
%!gmi: if your client supports that.
%!html: I have written the alt-text in //italics//

%!gmi: '''
%!gmi: ``` Σᵢ₌₃⁷ i²
%!html: //Σᵢ₌₃⁷ i²//
%!html: ```
 ₇
 Σ 𝑖²
ᶤ⁼³

%!gmi: '''

--------------------

%!gmi: '''

%!gmi: ``` ∫ _(π/6) ^π sin θ dθ = [−cos θ] _(π/6) ^π = 1 + (√3)/2

%!html: //∫ _(π/6) ^π sin θ dθ = [−cos θ] _(π/6) ^π = 1 + (√3)/2//

%!html: ```

π

⌠ ⎡ ⎤ π

⌡ sin 𝜃 d𝜃 = ⎢ − cos 𝜃 ⎥

π/6 ⎣ ⎦ π/6

√3

= 1 + ──

2

%!gmi: '''

--------------------

%!gmi: '''
%!gmi: ``` Dₓ cos(xy)  =  Dₓ (1 + sin y)
%!html: //Dₓ cos(xy)  =  Dₓ (1 + sin y)//
%!html: ```
     Dₓ cos(𝑥𝑦)  =  Dₓ (1 + sin 𝑦)

%!gmi: '''

%!gmi: '''

%!gmi: ``` −sin(xy)yy' = y' cos y

%!html: //−sin(xy)yy' = y' cos y//

%!html: ```

−sin(𝑥𝑦)𝑦𝑦′ = 𝑦′ cos 𝑦

%!gmi: '''

%!gmi: '''
%!gmi: ``` - [sin(xy)yy'] / (y' cos y)  =  1
%!html: //- [sin(xy)yy'] / (y' cos y)  =  1//
%!html: ```
     sin(𝑥𝑦)𝑦𝑦′
   − ──────────  =  1
      𝑦′ cos 𝑦

%!gmi: '''

%!gmi: '''

%!gmi: ``` - [sin(xy)y / cos y] (y'/y') = 1

%!html: //- ""[sin(xy)y / cos y]"" (y'/y') = 1//

%!html: ```

sin(𝑥𝑦)𝑦 𝑦′

− ──────── ── = 1

cos 𝑦 𝑦′

%!gmi: '''

%!gmi: '''
%!gmi: ``` y' (1 × 1¹)  =  − cos y / [sin(xy)y]
%!html: //y' (1 × 1¹)  =  − cos y / [sin(xy)y]//
%!html: ```
                       cos 𝑦
    𝑦′ (1 × 1¹)  =  - ────────
                      sin(𝑥𝑦)𝑦

%!gmi: '''

%!gmi: '''

%!gmi: ``` y' = − cos y / [sin(xy)y]

%!html: //y' = − cos y / [sin(xy)y]//

%!html: ```

cos 𝑦

𝑦′ = - ────────

sin(𝑥𝑦)𝑦

%!gmi: '''