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LyX uses LaTeX as its backend typesetting mechanism.

TeXmacs implements its own typesetting system.

I think this is the main differences.



Let's add also: as a software system (that is independent from TeX), TeXmacs is programmable on its own (using Scheme). Of course if you want to add functionalities to LyX you have to do it in the LyX way (and possibly in the TeX way).




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