Use WeightedSOSCone by default

[blegat]

This requires

• [x] https://github.com/JuliaAlgebra/StarAlgebras.jl/pull/21
• [x] https://github.com/JuliaAlgebra/StarAlgebras.jl/pull/51
• [x] https://github.com/JuliaAlgebra/StarAlgebras.jl/pull/52
• [x] https://github.com/JuliaAlgebra/StarAlgebras.jl/pull/53
• [x] https://github.com/JuliaAlgebra/MultivariateBases.jl/pull/35
• [x] https://github.com/JuliaAlgebra/MultivariateBases.jl/pull/39
• [x] https://github.com/JuliaAlgebra/MultivariateBases.jl/pull/40
• [x] https://github.com/JuliaAlgebra/MultivariateBases.jl/pull/42
• [x] https://github.com/jump-dev/PolyJuMP.jl/pull/128
• [x] https://github.com/jump-dev/PolyJuMP.jl/pull/129
• [x] https://github.com/jump-dev/PolyJuMP.jl/pull/130

[kalmarek]

I was also thinking that we have two different approaches here to accomplish something very similar:

1. You're using polynomials (free objects) and quotient basis (reducing them modulo an ideal).
2. I use words over an alphabet (free objects) to represent group elements (e.g. as words rewritten to their ~canonical forms) which then end up in the Dirac basis (generic w.r.t. the type of elements)

Your approach seems a bit more "lazy" but I have some doubts if this could be applied to my case as I want to eagerly reduce the number of words as soon as possible to avoid duplication.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 85.47009% with 68 lines in your changes missing coverage. Please review.

Project coverage is 80.06%. Comparing base (c4f7e9a) to head (66e8e51). Report is 12 commits behind head on master.

Files	Patch %	Lines
src/Certificate/newton_polytope.jl	90.28%	17 Missing :warning:
src/constraints.jl	75.00%	8 Missing :warning:
src/Bridges/Constraint/sos_polynomial.jl	84.09%	7 Missing :warning:
src/Certificate/Symmetry/wedderburn.jl	0.00%	6 Missing :warning:
.../Constraint/sos_polynomial_in_semialgebraic_set.jl	68.75%	5 Missing :warning:
src/Certificate/ideal.jl	91.83%	4 Missing :warning:
src/attributes.jl	60.00%	4 Missing :warning:
src/Bridges/Bridges.jl	40.00%	3 Missing :warning:
src/Certificate/Certificate.jl	82.35%	3 Missing :warning:
src/sosdec.jl	89.65%	3 Missing :warning:
... and 5 more

:exclamation: There is a different number of reports uploaded between BASE (c4f7e9a) and HEAD (66e8e51). Click for more details.

HEAD has 1 upload less than BASE

| Flag | BASE (c4f7e9a) | HEAD (66e8e51) | |------|------|------| ||2|1|

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #355 +/- ## ========================================== - Coverage 85.10% 80.06% -5.04% ========================================== Files 41 38 -3 Lines 2222 2162 -60 ========================================== - Hits 1891 1731 -160 - Misses 331 431 +100 ```

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[kalmarek]

Holy crap! all those fixes will make SOS great again! 🎉