#1524 broke MTK reference tests

[AayushSabharwal]

Before:

$$\begin{align} \frac{\mathrm{d} u\left( t \right)_{1}}{\mathrm{d}t} &= p_{3} \left( - u\left( t \right)_{1} + u\left( t \right)_{2} \right) \\\ 0 &= - u\left( t \right)_{2} + \frac{1}{10} \left( p_{1} - u\left( t \right)_{1} \right) p_{2} p_{3} u\left( t \right)_{1} \\\ \frac{\mathrm{d} u\left( t \right)_{3}}{\mathrm{d}t} &= \left( u\left( t \right)_{2} \right)^{\frac{2}{3}} u\left( t \right)_{1} - p_{3} u\left( t \right)_{3}\\ \end{align}$$

After:

$$\begin{align} \\ \frac{\mathrm{d} u\_{1}\left( t \right)}{\mathrm{d}t} &= p_{3} \left( - u\_{1}\left( t \right) + u\_{2}\left( t \right) \right) \\\ 0 &= - u\_{2}\left( t \right) + \frac{1}{10} \left( p_{1} - u\_{1}\left( t \right) \right) p_{2} p_{3} u\_{1}\left( t \right) \\\ \frac{\mathrm{d} u\_{3}\left( t \right)}{\mathrm{d}t} &= u\_{2}\left( t \right)^{\frac{2}{3}} u\_{1}\left( t \right) - p_{3} u\_{3}\left( t \right)\\\ \end{align}$$

Is this intentional? It's incredibly inconsistent

[TorkelE]

Out of curiosity, why did we previously do e.g. u(t)_1. WOuldn't u_1(t) look better?

[AayushSabharwal]

Might be an artifact of how array symbolics print

julia> x[1]
(x(t))[1]

[TorkelE]

Sounds like a likely explanation. Long-term it seems like a thing it would be nice to improve.

[isaacsas]

It was broken before with where the index was being placed, and now it is broken differently. I did explicitly mention this in my PR, but at least on my end I don't think this is any worse

The difference is the bug is no longer in Symbolics incorrectly forming the Expr that is passed to Latexify, but now in Latexify: korsbo/Latexify.jl#331

If Symbolics wants to turn off snakecase = true I believe this issue would go away as that is what leads to u[1] becoming u\_1 instead of u_1 with that bug. Basically, Symbolics is using too many Latexify options, which are a bit of a mess in how they interact, see the issue above and korsbo/Latexify.jl#332

[isaacsas]

Also, in the PR all the MTK tests reported as passed? Only Catalyst tests failed and it was due to the other issues we were having this week there that were unrelated. Are the MTK LaTeX tests not actually being run from Symbolics?

[isaacsas]

If we want a simple temporary fix here until Latexify fixes the deeper issue, but don't want to drop snakecase = true, we could drop printing of the the argument for array Symbolics, i.e. instead of trying to generate u_1(t) just generate u_1. That would work fine currently.

[AayushSabharwal]

Also, in the PR all the MTK tests reported as passed?

Yeah I forgot to add the latex tests to downstream.

[isaacsas]

@ChrisRackauckas what do you think about dropping the argument in all these expressions? Generally I find the MTK-generated DAEs are too verbose because of all the (t)'s that appear anyways, and it also looks not-so-great when combined with the use of \mathtt. If the function argument was just dropped I think this issue would be fixed and the general display of DAEs would look better.

i.e. I wouldn't normally typeset an ODE as

$$\frac{dX(t)}{dt} = -\lambda X(t) + (X(t))^2$$

but as

$$\frac{dX}{dt} = -\lambda X + X^2$$

[isaacsas]

But maybe that isn't a great idea since in other contexts keeping the arguments is important.

[ChrisRackauckas]

That's fine with me. It's the standard convention.

But maybe that isn't a great idea since in other contexts keeping the arguments is important.

I'm not entirely sure how to make it switchable though.