feat: add pass which removes equations incident on a single variable

[AayushSabharwal]

This avoids cases where pantelides ends up choosing a bad matching and unnecessarily differentiates the kind of equations removed by this pass.

[oscardssmith]

would this be more readable if it was while !isnothing(v)?

[AayushSabharwal]

I was hoping isa Int would help type inference better. And iirc since v::Union{Int, Nothing}, codegen will union-split the call to isnothing whereas isa is a builtin, so there's only ever one thing to call.

[AayushSabharwal]

Also this is just personal preference but I like reading var === nothing over isnothing(var).

[oscardssmith]

I'd also be fine with !(isa Nothing). isa Int just feels kind of fragile (e.g. it would break if we changed incidence to Int32)

[AayushSabharwal]

Ah, I see your point.

[oscardssmith]

is this needed to prevent needing to recompute the neighbors after each variable removal? IMO it could use a comment if so.

[AayushSabharwal]

Will add a comment (and just spam some more in general)

[AayushSabharwal]

I also just realized that this pass doesn't need to substitute, since if the eliminated variable is removed from fullvars we'll end up treating it like a parameter. The perfect aliases pass needs to substitute because we change incidence for the eliminated variable to its alias, so the alias needs to be symbolically present in the equation.

[oscardssmith]

That's a very nice simplification!

[AayushSabharwal]

Addressed the comments

[AayushSabharwal]

A multibody model is now simplifying to 25 variables instead of 17 because of the latest changes on this PR.

[oscardssmith]

any idea what the difference is?

[AayushSabharwal]

A bunch of algebraic equations that should have been torn but weren't.

[oscardssmith]

We also need to make sure to deal with #4458 for this (and add a test)

[AayushSabharwal]

Okay, we do need to substitute. If we eliminate a variable v, and var_to_diff[v] !== nothing, that means the symbolic expression D(fullvars[v]) is present in some equation. Observed equations can't have D(...) on the LHS, so we need to substitute to handle this case. Substitution time complexity doesn't scale with the number of entries in the Dict, so if we need to substitute derivatives we might as well substitute the entire thing.

[AayushSabharwal]

The problematic multibody system is handled by changing the tearing algorithm to the old ModiaTearing. It's possible I implemented the new tearing algorithm wrong? Will double check, but I don't think I did.

[AayushSabharwal]

Weirdly either CarpanzanoTearing without this pass, or ModiaTearing with this pass works.

[AayushSabharwal]

I'm certain though, there was a point where this pass + CarpanzanoTearing was perfectly fine.