jump-dev / jump-dev/SumOfSquares.jl

Unclear Documentation on Creating SOS Polynomials

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Dominant language
Julia
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Description

The [documentation](https://jump.dev/SumOfSquares.jl/stable/variables/#Nonnegative-polynomial-variables) says creating SOS polynomials is the same as creating free polynomials but replacing Poly(basis) with SOSPoly(basis), but that doesn't seem to be true. The constraint seems to create a GramMatrix rather than a polynomial, and while the documentation claims a polynomial p is set to x'Qx, I can't find how to access that polynomial.
I tried manually creating the polynomial as x'*Q*x, but in my case, I need x to be a Chebyshev basis. I tried using the MultivariateBases package for that, but I get an error saying ChebyshevBasisFirstKind doesn't support adjoint.

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Research direction

Start with the Nonnegative-polynomial variables section of the linked documentation and reproduce the SOSPoly and ChebyshevBasisFirstKind examples from the issue. Trace whether the constraint creates a GramMatrix or an accessible polynomial, then document the supported Chebyshev-basis workflow and the adjoint limitation. Done means the documentation matches the actual API and explains how to obtain or represent the polynomial.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
documentation
Issue type
Documentation
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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