Yingbo Ma

Don't merge these PRs just yet. I am still testing them locally.

This might be fixed by https://github.com/SciML/OrdinaryDiffEq.jl/pull/1168. I saw the same issue last night.

Ah never mind, there is a deeper issue here. We don't handle an overdetermined/underdetermined system yet.

One difficulty I can see is the sparsity pattern has to be recomputed for the split problem, as nz pattern of `f1` and `f2` might differ. This would invalidate `f1.jac`...

Remember to use `Dict`s when using `merge`.

I tried it on the latest MTK, but the initialization of the DAE then fails just like https://github.com/SciML/SciMLBenchmarks.jl/pull/372

Woah, Jung's theory of collective unconscious confirmed.

But, what is the expected behavior when adding another algebraic equation `0 ~ 1 - (A + C)`? Do we assume that's true and eliminate differential equations? I am not...

We reduce them if the system is actually consistent.

```julia Differential(t)(A(t)) ~ k2*C(t) - (k1*A(t)*B(t)) Differential(t)(B(t)) ~ k2*C(t) - (k1*A(t)*B(t)) Differential(t)(C(t)) ~ k1*A(t)*B(t) - (k2*C(t)) ``` already uniquely define `A`, `B`, and `C`. If `0 ~ 1 - A(t)...