I'm a mathematician, researcher in geometric group theory at KIT (Karlsruhe, Germany); I received my PhD in pure mathematics in 2014 and since then changed my scientific focus to aspects including more computational problems. I've been coding in julia since 2016, mostly around group theory, mathematical optimization and certified computation.
In this talk we discuss a symmetry reduction approach relying on the invariance of the polynomial under a group of actions. From the algebraic properties of the group, the SymbolicWedderburn package determines a change of basis that enables the decomposition of the constraints into smaller bases, some of them being equal which further reduces the problem. We show how to specify the group symmetry to allow SumOfSquares to perform this reformulation automatically.