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This point is related to #101 #126. Future versions of Alpine can leverage the https://github.com/JuliaOpt/MINLPTests.jl repo for testing core JuMP features and edge cases (e.g. feasibility problems).
I would also recommend to add a new category of polynomial problems to https://github.com/JuliaOpt/MINLPTests.jl (see jump-dev/MINLPTests.jl#1). Specifically for testing global solvers that support polynomials but not other floating point functions like exp,sin, etc...