MathOptInterface says that Interval and GreaterThan constraints aren't supported by CDDLib

[nsajko]

import MathOptInterface, CDDLib
const MOI = MathOptInterface

function powers(degree::Int, x::F) where {F <: Real}
        local ret = F[1 for _ in 0:degree]
        for i in 1:degree
                ret[i + 1] = x * ret[i]
        end
        ret
end

sets(pts::Vector{Tuple{F, F}}) where {F <: Real} =
        map(p -> MOI.GreaterThan(p[2]), pts)

saf(cs::Vector{F}, vars::T) where {F <: Real, T <: Any} =
        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(cs, vars), zero(F))

safs(degree::Int, pts::Vector{Tuple{F, F}}, vars::T) where {F <: Real, T <: Any} =
        map(p -> saf(powers(degree, p[1]), vars), pts)

constrain(lp::Opt, degree::Int, pts::Vector{Tuple{F, F}}) where
  {Opt <: MOI.AbstractOptimizer, F <: Real} =
        MOI.add_constraints(lp,
                            safs(degree, pts, MOI.add_variables(lp, degree + 1)),
                            sets(pts))

constrain(::Type{F}) where {F <: Real} =
        constrain(CDDLib.Optimizer{F}(), 5, Tuple{F, F}[(0, 1//2), (1, 7//3)])

With this example code constrain(Float64) and constrain(Rational{BigInt}) both lead to MOI errors about the model not supporting the constraint:

MathOptInterface.UnsupportedConstraint{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}}: `MathOptInterface.ScalarAffineFunction{Float64}`-in-`MathOptInterface.GreaterThan{Float64}` constraint is not supported by the model.

Using Interval instead of GreaterThan results in a similar error, but LessThan seems to work. Not sure whether this is intended behavior.

[blegat]

The only supported constraints are EqualTo and LessThan. See
https://github.com/JuliaPolyhedra/Polyhedra.jl/blob/728c80a64ffc2ecadc58138ac0415dbac1df5a6c/src/opt.jl#L84-L88
This is intended behavior as the CDD library only supports these two.
Replace CDDLib.Optimizer{F}() by MOI.instantiate(CDDLib.Optimizer{F}, with_bridge_type=F)
See https://jump.dev/MathOptInterface.jl/stable/reference/models/#MathOptInterface.instantiate

[odow]

This can be closed

[odow]

Closing as won't fix.

[blegat]

To complement my above comment, you should add a bridge layer when calling MOI.instantiate and then it will be supported by bridging