Guide users to formulate problems as noncommutative polynomial optimization using NCTSSoS.jl — choose the right algebra, build objective/constraints, configure sparsity, solve, and extract results via GNS reconstruction. Use this skill whenever the user mentions: polynomial optimization, SOS relaxation, ground state energy, Bell inequality, quantum correlations, semidefinite relaxation, moment-SOS hierarchy, Hamiltonian optimization, NCTSSoS, noncommutative optimization, or wants to optimize over quantum operators/observables. Also trigger when the user describes a physics problem (spin chains, fermionic systems, bosonic modes, entanglement witnesses) that could be cast as polynomial optimization, even if they don't use those words.
2026-04-09