How to handle for example \asin or \sin ^{-1}(a) in LatTeX.

That sounds like a LaTeX question you probably want a connection to
FriCAS. No?

No. Think of jFriCAS and )set output tex on.

I would claim, that ")set output tex on" in jFriCAS is not a very good idea.

Why not outputting LaTeX output via FormatLaTeX, if you want the LaTeX representation. OK FormatLaTeX is maybe too over-flexible, you would need fricasmath.sty
https://github.com/fricas/fricas/blob/master/src/doc/fricasmath.sty#L41
for the respective .tex file to compile.
But it allows to redefine anything you like. For example, you could (inside the fricasmath environment) define \sqrt like this.

\def\sqrt##1{\left(##1\right)^1/2}

(Note the double ##, since that definition appears inside a definition.)

In LaTeX you can prefer 1D or 2D for fraction also. That's possible in
the interpreter, ')set output fraction' for pure OutputForm. For the
texfomat I have not tested. In fact I am thinking about a more general
way of outputting objects/elments.

I would also like to see an expression handling as it was started in the Algebra library of Aldor (look for ExpressionTree and friends).

Ralf

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