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This is an attempt to fix the modelling toolkit extension, and reintroduce support for the mtk_to_si function, which was removed in the last update.

Changes:

• mtk_to_si is no longer exported from the extension. But instead created in the main package (without methods) and methods then added in the extension.
• I have removed the export statements in the extension as these should not be there.
• I have renamed the extension to ModelingToolkitSIExt. Motivation: extensions should (ideally) have names unique to both packages involved. If two packages both created extensions called ModelingToolkitExt (no unthinkable), these will overwrite each other, causing errors if loaded simultaneously.

Unfortunately this does not work fully. This code:

using StructuralIdentifiability, ModelingToolkit

@parameters r1, r2, c1, c2, beta1, beta2, chi1, chi2
@variables t, x1(t), x2(t), y(t), u(t)

D= Differential(t)

eqs = [
    D(x1) ~ r1 * x1 * (1 - c1 * x1) + beta1 * x1 * x2 / (chi1 + x2) + u,
    D(x2) ~ r2 * x2 * (1 - c2 * x2) + beta2 * x1 * x2 / (chi2 + x1),
]

measured_quantities = [y ~ x1]

ode_mtk = ODESystem(eqs, t, name = :mutualist)

local_id_1 = assess_identifiability(ode_mtk, measured_quantities = measured_quantities)
global_id_1 = assess_local_identifiability(ode_mtk, measured_quantities = measured_quantities)


si_model = mtk_to_si(ode_mtk, measured_quantities)
global_id_2 = assess_identifiability(si_model)

generates a

ERROR: MethodError: no method matching assess_identifiability(::Tuple{ODE{Nemo.QQMPolyRingElem}, Dict{SymbolicUtils.BasicSymbolic{…}, Nemo.QQMPolyRingElem}})

Closest candidates are:
  assess_identifiability(::ODESystem; measured_quantities, funcs_to_check, prob_threshold, loglevel)
   @ ModelingToolkitSIExt ~/.julia/dev/StructuralIdentifiability/ext/ModelingToolkitSIExt.jl:349
  assess_identifiability(::ODE{P}; funcs_to_check, prob_threshold, loglevel) where P<:AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}
   @ StructuralIdentifiability ~/.julia/dev/StructuralIdentifiability/src/StructuralIdentifiability.jl:98

Stacktrace:
 [1] top-level scope
   @ ~/Desktop/Julia Playground/Catalyst playground/Environment - Temporary/temproary_playground.jl:24
Some type information was truncated. Use `show(err)` to see complete types.

error.

This, however, works:

ode = @ODEmodel(
    x1'(t) = -(a01 + a21) * x1(t) + a12 * x2(t) + u(t),
    x2'(t) = a21 * x1(t) - a12 * x2(t) - x3(t) / b,
    x3'(t) = x3(t),
    y(t) = x2(t)
)
assess_identifiability(ode)

mtk_to_si resturns not only an MTK model but also a correspondence between the SI and MTK models. So I think just replacing si_model = mtk_to_si(ode_mtk, measured_quantities) with si_model, _ = mtk_to_si(ode_mtk, measured_quantities) should work

Ahh, that makes sense. Yes, that worked, thanks a lot :)

Ok, I have added some tests to ensure that mtk_to_si is exported and works as well. Feel free to merge/ignore/use any part of this PR.

@TorkelE Thank you very much!