Implement solving polynomial equation systems symbolically. (I.e. finding the variety of a set of polynomials). This involves first computing the Groebner basis for a set of polynomials. Groebner basis computation is NP complete so it is essential that the implementation is practical. It should start by studying the literature on state-of-the art Groebner basis solvers.
Recommended Skills: Calculus and discrete mathematics. Prior knowledge of computational algebra and ring theory is preferred.
Expected Results: Working Groebner basis and rootfinding algorithms to be deployed in the Symbolics.jl package, along with documentation and tutorials.
Mentors: Shashi Gowda, Yingbo Ma, Mason Protter
Implement the heuristic approach to symbolic integration. Then hook into a repository of rules such as RUMI
Recommended Skills: Calculus
Expected Results: A working implementation of symbolic integration in the Symbolics.jl library, along with documentation and tutorials demonstrating its use in scientific disciplines.
Mentors: Shashi Gowda, Yingbo Ma, Mason Protter