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Systems definitions in Julia

Results 30 MathematicalSystems.jl issues
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I would expect the following to fail: ```julia julia> using MathematicalSystems julia> f(u) = 1; # irrelevant, just needs to be defined julia> U0 = [1]; # irrelevant, just needs...

macros
fix

from [Zulip,](https://julialang.zulipchat.com/#narrow/stream/278609-juliareach) ```julia p = @ivp(x' = Interval(-11,-2)*x, x(0) ∈ Interval(1, 2)) ERROR: MethodError: no method matching LinearContinuousSystem(::Interval{Float64}) ```

`@map` can only read unconstrained maps so far. But we can read constraints in `@system`. It should be rather easy to share that code (I hope).

enhancement
macros

```julia julia> b = [1.0] 1-element Array{Float64,1}: 1.0 julia> @system(x' = x + b) LinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64}}([1.0], [1.0]) ``` The answer is OK but I would expect an `AffineContinuousSystem` instead. This way...

macros

This is a follow up of https://github.com/JuliaReach/MathematicalSystems.jl/pull/223 ```julia julia> b = rand(1); @system(x' = x + b) AffineContinuousSystem{Float64,IdentityMultiple{Float64},Array{Float64,1}}([1.0], [0.4376218479701559]) julia> b = rand(10); @system(x' = x + b, dim=10) ERROR:...

macros

It would be nice to have an `Examples` or a "How to use?" section to the documentation to showcase the features. I can give it a go, once the `@system`...

documentation

Handle equality sign for the initial states, as in: `@system(x' = -x, x(0) = x0)`. _Originally posted by @mforets in https://github.com/JuliaReach/MathematicalSystems.jl/pull/147_

macros