SymbolicWedderburn v0.3 -> v0.4

[blegat]

Closes #352

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (c4f7e9a) 85.10% compared to head (d33d510) 85.32%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #341      +/-   ##
==========================================
+ Coverage   85.10%   85.32%   +0.22%     
==========================================
  Files          41       41              
  Lines        2222     2222              
==========================================
+ Hits         1891     1896       +5     
+ Misses        331      326       -5     

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[kalmarek]

@blegat how to turn MonomialBasis{Monomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}}, MonomialVector{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}}} into an actual vector?

[kalmarek]

also something is rather odd here:

    basis = SumOfSquares.Certificate.gram_basis(cert.certificate, poly)
    @info eltype(basis)

shows Any ?

[blegat]

Maybe we could define eltype I think I didn't do it since it's not an AbstractVector. By the way, an StarAlgebras.AbstractBasis is also not an AbstractVector so probably that will remain the case right ?

julia> basis = MonomialBasis(monomials([x, y], 2))
MonomialBasis([y², xy, x²])

julia> generators(basis)
3-element MonomialVector{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}}:
 y²
 xy
 x²

julia> generators(basis) isa AbstractVector
true

julia> eltype(generators(basis))
Monomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}}

You could also let me know the API you need the basis to implement and we could make sure StarAlgebra.AbstractBasis subtypes such as MonomialBasis do implement it.

[kalmarek]

at the moment it's enough for basis to get an honest vector that's it.

We'll overhaul the whole thing in the near future, so there's no need to define the API for the old version, right?

[blegat]

No, no need, this PR can sit here and wait for StarAlgebras

[blegat]

I bumped in #355 even if it's not working but I'll wait for kalmarek/SymbolicWedderburn.jl#79