With RhinoLink you can:
This packages is for interfacing with the Singular computer algebra system. Singular is an open-source computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.
Makes it easy to write Mathematica packages in Haskell. Just write some functions and provide a package specification in a simple DSL that mimics that of Mathematica's mprep utility.
This package provides access to Mathematica's MathLink library from Julia, with convenient wrappers for import Mathematica functions, seamless data conversion etc. It is used as the bases of the Mathematica.jl Julia package.
NetLogo is a modelling environment for agent-based modelling using the Logo programming language. It comes with a Mathematica link that makes it possible to run and analyse models directly from Mathematica.