A few comments about my short experience writing math with TeXmacs. 

The most important is this : I am already more efficient with TeXmacs than I ever was with LaTeX, so obviously, TeXmacs power at writing math is a given.

I am sometimes a bit surprised though, so here is a list of a few quirks (so they seem to me, but I might, or will just have to, get used to...)

- I use left exponent a lot with the transpose symbol for matrices. I would have supposed it to work like this :

hit the matrix name, say A, then Ctrl-L ^, then the symbol such as t for the transposition. Instead, I get the exponent to the right of A when I proceed like this. Second try : I enter the name of the matrix, then selects it with shift-left, then hit ctrl-L ^ and A gets transformed into a left exponent. So I learned that instead you put the left exponent, then the matrix and everything is good. Actually I encoutered a situation when going out of the exponent put me out of formula editing, but I can't reproduce it. If I encounter it again, I'll post here.

- when writing a big sum with indices directly under and over, which is automatic when big centered formulas, it is a bit weird to have to hit twice the right key for the focus to go back to "normal" or maybe I should say that what is weird is what happens if you don't ! Not a big issue of course, the cursor being a good hint of what the focus is, but still something uncanny for newcomers when you go from :

to

just hitting a.

- Something I didn't understand, but by writing this mail and experimenting at the same time, I think I just did... Sometimes I want to write the product |x| |y| with no multiplication symbol, just the space that TeXmacs puts automatically by hitting * with no alternate version. In that case, TeXmacs only enters the left part of the absolute part when I hit the | symbol, whereas usually it gives me both. I am pretty sure now it is by design, as it allows to obtain quickly the semidirect product symbol as an alternate, which makes sense, but still something to get accustomed to.

Regards,

Pierre-Henri