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StarAlgebras bases #79

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blegat opened this issue Jul 3, 2024 · 0 comments
Open

StarAlgebras bases #79

blegat opened this issue Jul 3, 2024 · 0 comments

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@blegat
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blegat commented Jul 3, 2024

We should have a feature that returns ConstraintBasis, GramBases and a structure that can be use to simplify examples/sos_problem.jl as well as SumOfSquares
Something like:

struct ConstraintBasis <: SA.ExplicitBasis
    invariant_vectors
    mstruct # gram_basis x gram_basis -> invariant_vector coefficients
end
struct GramBasis <: SA.ExplicitBasis
    U
    character_id
end

function mstructure(basis::ConstraintBasis, g1::GramBasis, g2::GramBasis)
    @assert g1 == g2
    return basis.mstruct[g1.character_id]
end

This will not assume that the gram basis is a subset of the constraint basis

Needs JuliaAlgebra/StarAlgebras.jl#55

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