Delay differential equation handling

[ChrisRackauckas]

Delay differential equations are going to be really really hard, but this is how we can get there. We probably just want to build it onto ODESystem, and just add a DDEProblem lowering. "Just" doesn't do it justice, because there's a list of issues:

• [ ] Overriding syntax
• [ ] Automatic detection of which terms are delay terms.
• [ ] Lower delay term calculations to interpolations of history https://diffeq.sciml.ai/stable/tutorials/dde_example/
• [ ] Opt the history terms out of structural transformations
• [ ] Construct the RHS function

Building such a build_function will likely want to start by swapping out x(t-5) directly to h(p,t-5)[1], but we will need to make that so we "CSE" the history calculations if there's many at the same time. We can leave that optimization to a later issue.

[asprionj]

Can only state variables be delayed or also arbitrary intermediate, i.e. algebraic, variables? The latter would be useful in many "engineering" models, think e.g. a transport delay applied to some property of a volumetric flow that is (algebraically) mixed out of several sources (which could be state variables or algebraic relations themselves...).

[ChrisRackauckas]

If states can be delayed then algebraic variables would be able to be through the same design.

[slwu89]

@ChrisRackauckas are the delays for difference equations in the tests here (https://github.com/SciML/ModelingToolkit.jl/blob/master/test/discretesystem.jl#L87) and use of DelayDiffEq in other tests here (https://github.com/SciML/ModelingToolkit.jl/blob/master/test/odesystem.jl#L536) indicative of significant progress on this front?

[ChrisRackauckas]

There's at least symbolic interfaces for it now, though the codegen is lacking.

[ChrisRackauckas]

This is handled via System