Mathup: Easy MathML authoring tool with a quick to write syntax

TeX's design was finalised in 1982, when the computational resources were different by a few orders of magnitude. There is a very strong culture of backward compatibility (search for "A torture test for TeX") and there are so many equations written in TeX documents that it would be impossible to change the parsing now.

That said, something like MathJax would be free to create their own TeX-like syntax where parentheses are automatically paired.

I for one often find myself wanting more control, writing `\bigr]` or `\biggr]` instead of `\right]` to get the rendered equation to look good.

> And while rendering `(a+b)/a` as a `\frac` is opinionated, honestly, the only reason why this occurs in my notes is when I was too lazy to type `\frac{}{}`.

Plain TeX has the much nicer syntax `{a+b \over a}` but for some obscure reason LaTeX recommends against that.

When your write LaTeX you maintain some structure for complex equations, while here you kind of take the quickest route possible and very quickly loose your footing in the equation’s complexity. In LaTeX you can very easily write out a very complex equation with nothing but your text editor, but here once you are maybe 6 or 7 terms deep you loose your place and will probably need to see a visual rendering to find your footing and continue. Mathup makes this problem worse than in AsciiMath proper, because in AsciiMath proper you are forced to at least parenthesize many of your sub-expressions, while here you are free to go wild with the whitespace.

The whitespace grouping is actually even more powerful than just for fractions, e.g. you can use it group terms around any infix (incl. sub- and superscripts) as well as after any prefix (such as sqrt): `e ^ -x^2/2 / sqrt 2pi` will give you the standard normal distribution. The rule is that if there is space between the operator and the operand it will operate on everything until the next applicable whitespace, the space between sqrt and 2pi applies the the sqrt prefix, and is not applicable to the fraction, but the space before slash is applicable to the ^ so the sqrt 2pi term are not apart of the superscript. I actually don’t recommend relying on this and just use parentheses for all but the simplest expressions (it is fine in sub-expressions though).

But like I said the target usecase is quick and easy expressions, so people that write a+b / c+d are favored over the ones that write `(e^(-(x^2)/2))/sqrt(2pi)` - but honestly I would write this as `e^(-(x^2)/2) / sqrt(2pi)`.

1: https://github.com/runarberg/markdown-it-mathblock

2: https://github.com/runarberg/markdown-it-mathspan

3: https://github.com/runarberg/temml-custom-element

This space is pretty dominated by LaTeX whom almost all professionals use, but is pretty verbose and not exactly easy to use for beginners (or even non-frequent users). Other than LaTeX we have Office Math, which is a GUI, and AsciiMath. This tool is a dialect of AsciiMath[1] and builds on top of that. If you know AsciiMath, you know this. There is also UnicodeMathML[2], but that has another goal than this or AsciiMath, where the focus is on readability of authored expressions, rather than writability here.

1: https://asciimath.org/

2: https://github.com/doersino/UnicodeMathML

Aside, I love this expression that you landed on. The Gamma distribution is one of the reason I started writing this library 10 years ago. The way the original AsciiMath can’t have arbitrary identifiers (only texts) was a deal breaker for me. The Gamma distribution is a very nice showcase for capabilities of an authoring tool like this because the name is usually written using latin letters `Gamma` while its density function also includes the gamma function which is usually written with a greek capital gamma (Γ). In the original AsciiMath writing Gamma just gives you the greek letter. The gamma distribution is also just a very cool distribution, or rather it contains some very cool distributions (in particular the Chi-squared distribution).

1: https://temml.org/#%5Cbeta%5E%5Calpha

Second difference is with supported MathML target output. Mathup is far more expressive (we even have tensor index notation in mathup). In mathup you can target your preferred MathML output in a way you can’t in AsciiMath. For example in mathup you can purposefully write any token element you want except <ms>. (`<mi>`, \`<mo>`, "<mtext>", and #`<mn>`), in AsciiMath if you want to wrote Gamma as an identifier (as opposed having it turn into the greek letter) or int as an operator (as opposed to an integral) you have to do it with <mtext>. Here you can do `Gamma` for <mi>Gamma</mi> or \int for <mo>int</mo>.

Thirdly is some differences in syntax. Most noticeable is matrix notation, in AsciiMath you write [(row, one), (row, two)], while in mathup you write [row, one; row, two]. Another major syntax difference is how whitespace works. In mathup you can group pars of your expression together with whitespace, so a+b / c+d is not the same as a + b/c + d. In AsciiMath, you have to use parenthesis to do this.