fix: record array elements in collect_operator_variables

[ChrisRackauckas-Claude]

Note

Draft — please ignore until reviewed by @ChrisRackauckas.

The bug

collect_operator_variables records arguments(v)[1] for each operator application. When
the operator is applied to an array variable or a slice — D(u[2:4]) — that argument is
the array, not its elements. Every caller tests membership of the scalar unknowns, so
nothing ever matches.

The visible consequence is in DAEProblem, which builds

diffvars = collect_differential_variables(sys)
differential_vars = map(Base.Fix2(in, diffvars), unknowns(sys))

so a system whose equations differentiate an array slice reports every variable as
algebraic, and DAE initialization then has nothing to work from.

Failing before, passing after

@variables w(t)[1:4]
collect_differential_variables(D(w[2:3]) ~ w[1:2])

	result	membership map over unknowns
before	Set([w[2:3]])	[0, 0, 0, 0]
after	Set([w[2], w[3]])	[0, 1, 1, 0]

Measured downstream on a real system (a MethodOfLines finite-difference discretization
that emits its interior as one array equation), DAEProblem's differential_vars goes
from 0/21 to 19/21 at one grid size and 0/81 to 79/81 at another — 19 and 79 being
the interior points, with the two boundary points genuinely algebraic.

The change

One function. When the operator's argument is array-valued, scalarize it and record the
elements; otherwise behave exactly as before, so scalar operators take an identical path.

Tests

lib/ModelingToolkitBase/test/variable_utils.jl gains a testset covering a whole array
variable, a slice, an unaffected scalar derivative, and the differential_vars-style
membership test that motivated the fix. It fails on unpatched code with the
[0, 0, 0, 0] map shown above.

Test Summary:  | Pass  Total      Time
variable_utils |  145    145  11m03.2s

(145 = 141 pre-existing + 4 added.)

Not verified

I ran the variable_utils file, not the full ModelingToolkitBase suite — the change is
additive and confined to one branch of one function, but a full run has not been done
locally. Other callers of collect_operator_variables (collect_applied_operators,
Shift-based discrete paths) are unaffected for scalar arguments and now see elements
rather than arrays for array ones, which is the intended correction but is worth a
reviewer's eye.

Context

Found while making finite-difference PDE discretizations emit array (slice-form) equations
instead of one scalar equation per grid point — see SciML/MethodOfLines.jl#428. This is one
of several places where array equations lose their shape; the others (equation counting,
implicit-DAE codegen row indexing) are more invasive and will be proposed separately.

🤖 Generated with Claude Code

https://claude.ai/code/session_01S1dxUEPGysx27SSSpxtiQ9

[AayushSabharwal]

The comments in #4982 on this part of the code apply here.