Symbolic computation project ideas

Groebner basis and Symbolic root finding

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

Symbolic Integration

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