Accessors for differential and algebraic erquations

[TorkelE]

Creates 10 different general purpose accessors for handling differential and algebraic functions within systems:

is_alg_equation
is_diff_equation
alg_equations
diff_equations
has_alg_equations
has_diff_equations
get_alg_eqs
get_diff_eqs
has_alg_eqs
has_diff_eqs

Examples:

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@parameters p d
@variables X(t)
eq1 = D(X) ~ p - d*X
eq2 = 0 ~ p - d*X
@named osys1 = ODESystem([eq1], t)
@named osys2 = ODESystem([eq2], t)
osys12 = compose(osys1, [osys2])
osys21 = compose(osys2, [osys1])

is_alg_equation(eq1) # returns `false`.
is_alg_equation(eq2) # returns `true`.
is_diff_equation(eq1) # returns `true`.
is_diff_equation(eq2) # returns `false`.

has_alg_equations(osys1) # returns `false`.
has_alg_equations(osys2) # returns `true`.
has_diff_equations(osys1) # returns `true`.
has_diff_equations(osys2) # returns `false`.

alg_equations(osys1) # returns `Equation[]`.
alg_equations(osys2) # returns `[ 0 ~ p - d*X(t)]`.
diff_equations(osys1) # returns `[Differential(t)(X(t)) ~ p - d*X(t)]`.
diff_equations(osys2) # returns `Equation[]`.

get_alg_eqs(osys12) # returns `Equation[]`.
get_alg_eqs(osys21) # returns `[0 ~ p - d*X(t)]`.
get_diff_eqs(osys12) # returns `Differential(t)(X(t)) ~ p - d*X(t)`.
get_diff_eqs(osys21) # returns `Equation[]`.

has_alg_eqs(osys12) # returns `true`.
has_alg_eqs(osys21) # returns `false`.
has_diff_eqs(osys12) # returns `true`.
has_diff_eqs(osys21) # returns `false`.

There are docstrings and tests for all functions.

These are needed in Catalyst v14 to handle equations when you convert to ODESystems that may (or may not) contain algebraic equations. Sincet hey are general-purpose, I figured it was better to put them here than in Catalyst.

[ChrisRackauckas]

Format and document

[TorkelE]

Got docstrings, so can link them in the docs, where would you want them? In the long term (as part of this PR or not), would it be useful to have an "API" page on the docs which just lists functions like these and their docstrings?

[ChrisRackauckas]

No, API dumps are always bad. Make a proper manual page on equations. Add the has_algebraic and such to the right system docs pages (ODESystem, SDESystem, etc.)

[TorkelE]

Ok, I have added docs and run the formater.

[ChrisRackauckas]

We should use the new non-canonical, but we can handle that in a future PR

[TorkelE]

Sounds good

[TorkelE]

thanks for helping getting this one sorted out quickly!