[blegat]

It's been a request form @kalmarek for a while. This follows the approach of https://github.com/kalmarek/SymbolicWedderburn.jl/blob/master/examples/sos_problem.jl
This will create less equality constraints as it only adds constraints on some invariant basis. This also allows us to just request simple basis from SymbolicWedderburn (not semi-simple), so it needs

• Move the Linear Algebra diagonalization from SumOfSquares kalmarek/SymbolicWedderburn.jl#106
• Add parent for simple basis JuliaAlgebra/MultivariateBases.jl#83
• Update to PrettyTable v3 JuliaAlgebra/KnuthBendix.jl#99

[codecov]

Codecov Report

❌ Patch coverage is 10.16949% with 53 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (main@a3908f8). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/Certificate/Symmetry/invariant_basis.jl	0.00%	26 Missing ⚠️
src/Certificate/Symmetry/wedderburn.jl	0.00%	25 Missing ⚠️
src/Bridges/Constraint/sos_polynomial.jl	66.66%	2 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #445   +/-   ##
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  Coverage        ?   85.03%           
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  Files           ?       45           
  Lines           ?     2887           
  Branches        ?        0           
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  Hits            ?     2455           
  Misses          ?      432           
  Partials        ?        0           

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