+Nicolas Richard +Nicolas Richard i haven't used LuaTeX. I think at least it improve TeX by basing it on a more workable programing language.

XeTeX improves TeX in that it reduces TeX's complexity, by using unicode directly, so symbols can be set up in editors to be typed by just simple keystrokes and makes the source code much more readable.

but yes these 2 don't address the main point. Namely, TeX doesn't embody the structure of math formulas.

what i think is far much better is one that embodies the math structure. There are 2 that i know of. Mathematica and MathML.

For Mathematica, see example here at the top of the page. e.g.

Sum[1/n, {n,1,k}] ≻ Integrate[ 1/x ,{1,k+1}] = Log[k + 1]

Sum[ (-1)^n/(2*n + 1), {n, 0, ∞}] = 1 - 1/3 + 1/5 + 1/7 + … = π/4

Integrate[ f[x] ,{x,a,b}] = F[b] - F[a]

f'[a] = Limit[ (f[a+h]-f[a])/h,{h,0}]

Overbar[z/w] = Overbar[z]/Overbar[w]

r = Abs[z] = Sqrt[x^2+y^2]

{{1,2},{3,4}} * {{0,1},{0,0}} = {{0,1},{0,3}}

there are so many advantages.

• preserving the syntactic structure of math expressions

• the syntax also works as a executable programing language. (the above in M actually return answers, and the expression components can be manipulated just as in a programing language. (the symbols are actually variables and functions))

• much easier to type, and is readable, and can also use Unicode chars directly.

for MathML, it suffers from verbosity.