07-11, 10:10–10:20 (Europe/Amsterdam), For Loop (3.2)
A lot of knowledge about algorithms is hidden in old academic texts and may only have been implemented in now-defunct CAS systems. Here I share my experience writing ParametricGrobnerBases.jl for computing parametric Gröbner bases in Julia, and why I think Julia could be a secret weapon for researchers in computational algebra.
This talk is about implementing an algorithm for computing parametric/comprehensive Gröbner bases, which are Gröbner bases over a parameterized family of ideals. Gröbner bases are a crucial tool for almost every computation involving multivariate polynomials. This algorithm doesn't seem to be very well-known, but in this talk I outline why Julia is uniquely well-suited to implementing such algorithms, as well as give some examples of problems, that can be efficiently solved using this algorithm. All of this will be available in the package ParamtetricGrobnerBases.jl.
This talk can be seen both by computer scientists for its mathematical content and by mathematicians as an inspiration to use Julia in their research.
Danish mathematician, interested in bringing ideas from algebra and algebraic geometry to the world of software.