Benoît Legat

See section 3.1.6 of > Blekherman, G., Parrilo, P. A., & Thomas, R. R. (Eds.). > Semidefinite optimization and convex algebraic geometry SIAM 2013

- [x] Multipartite (done in SOSTools): https://github.com/JuliaOpt/SumOfSquares.jl/pull/69 - [ ] Exact with V-representation -> H-representation conversion (done in SOSTools with CDD), we can use [Polyhedra](https://github.com/JuliaPolyhedra/Polyhedra.jl) for that - [ ]...

Implement constraint on semialgebraic set

2

Let's check the different way we can implement the SOS constraint ``` julia @polyconstraint q(x) >= 0 domain=[f_1(x) = 0, ..., f_m(x) = 0, g_1(x) >= 0, ..., g_p(x) >=...

For SOS constraints on varieties, it would be faster in some case to use the sampling method of: ["Sampling algebraic varieties for sum of squares programs" by D Cifuentes, P...

See #4

It is easy to compute the standard monomials for those varieties, we should have something faster in that case

The function ```julia f{T}()::Vector{T} = T[] ``` should be updated to ```julia (f()::Vector{T}) where {T} = T[] ``` but FemtoCleaner update it to ```julia f()::Vector{T} where {T} = T[] ```...