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> If anyone has links to suitable packages please share, I don't
> remember from last discussions maybe the number crunchers here can
> help you, but slightly recall also like usual the Lua library
> ecosystem wasn't that satisfactory.
>
…
> * Have a "rationals" package. Most useful if you do not use irrational
> things like sin(), PI or so, want precission, and don't run into the
> big numbers problem. This kind of packages make out of numbers a
> package that stores divisor and divident as seperate numbers. Clojure
> comes to mind as a language that has this entities in the language
> base package already.

 http://www.ntg.nl/maps/42

has this reference:

Luigi Scarso
    Extending CTX with PARI/GP (English), MAPS 42, 2011, 34-42

CTX is Context, a TeX system with embedded Lua.  Pari/GP is
a simple scripting interface to a powerful library that can do
arbitrary-precision floating point, exact rational arithmetic,
multivariate polynomials, truncated power series, and some
number-theoretical stuff (including p-adic arithmetic).

Luigi brings in Pari/GP via a Lua binding made with swig-2.0.0.

Dirk