`structural_simplify` elimiantes differently for `ODESystem` and `NonlinearSystem`s

[TorkelE]

Something popped up while going through the Catalyst tests. Simple example. Here, I'd imagine that we could eliminate A in both cases. However, structural_simplify does it only for NonlinearSystems, but not for ODESystems. Seems odd that the two systems have different behaviours here?

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@parameters p d a b
@variables X(t) A(t)
eqs1 = [
    D(X) ~ p - d * X
    a*A^2 ~ X + b
]
eqs2 = [
    0 ~ p - d * X
    a*A^2 ~ X + b
]
@mtkbuild osys = ODESystem(eqs1, t) 
@mtkbuild nlsys = NonlinearSystem(eqs2)
unknowns(osys) # [X(t) A(t)]
unknowns(nlsys) # [A(t)]

[AayushSabharwal]

It's not eliminating A in either system? The NonlinearSystem eliminates X because it's linearly solvable. In the ODE, it's a differentiated variable and thus can't be linearly solved for.

[AayushSabharwal]

For clarity, what would you expect the equations and observed of the ODESystem to be?

[TorkelE]

Actually, you might be right, I was thinking A could be computed from X, but I guess the square root means this won't be the case?

[AayushSabharwal]

Yeah, the square root has two solutions and MTK has no way of knowing which one to use

[TorkelE]

makes sense, thanks for the help!