Why You Should Stop Using the Monomial Basis

Explore the innovative design of StarAlgebras.jl for computing with arbitrary basis in this 24-minute talk from The Julia Programming Language. Discover how to compute symmetry adapted bases using the group algebra of the symmetric group and rewrite problems into this symmetry adapted basis. Learn to work with different bases as conveniently as the monomial basis, including better-conditioned orthogonal bases like the Chebyshev basis. Understand how this approach can improve conditioning and complexity through block diagonalization and low-rank structure identification. Examine practical applications and benchmarks for polynomial optimization using both Sum-of-Squares and Macaulay frameworks.

Why you should stop using the monomial basis