fix: drop equations from scc_eqs whose matched variable is outside the SCC

[baggepinnen]

Summary

Fixes the "Tearing internal error: lowering DAE into semi-implicit ODE failed!" thrown at reassemble.jl:499 for systems where the dummy-derivative pass leaves stale entries in full_var_eq_matching that cause get_sorted_scc to pull equations into an SCC's scc_eqs whose eq_var_matching value points at a variable outside that SCC. When this happens, two distinct SCCs end up emitting differential equations for the same state-variable index (via push!(var_ordering, diff_to_var[iv])), tripping the duplicate-state-var assertion.

The fix filters scc_eqs in get_sorted_scc to keep only equations whose matched variable is either Unassigned or inside the SCC. This drops the spurious cross-SCC overlap without affecting well-formed systems.

Root cause

In generate_system_equations!, var_ordering is filled from two push sites:

• reassemble.jl:460 (linear-SCC inline path): push!(var_ordering, ∫iv) with ∫iv = diff_to_var[iv]
• reassemble.jl:837 (general codegen_equation! derivative-variable branch): push!(var_ordering, diff_to_var[iv])

For a duplicate to occur in var_ordering[is_diff_eq], two distinct matched ivs must satisfy diff_to_var[iv₁] == diff_to_var[iv₂]. In the failing case this happens because the same iv = D(angles[2]) is processed twice — once in a singleton SCC matched to the joint's der_angles[2] ~ D(angles[2]) equation, and once again in a separate (large, linsol-able) SCC whose vscc was populated by get_sorted_scc pulling in that joint equation through full_var_eq_matching[v] for some v in the larger SCC's scc list.

Concretely, with the rolling-wheel reproducer below, get_sorted_scc produces:

• scc = [1, 47, 8, 29, 45, 69, 71, 72, 73, 74, 75, 76, 138, …] (24 entries, no 2)
• scc_eqs(final) of size 25 including eq 14
• eq_var_matching[14] = 2, so scc_vars ends up with 2 injected at position 17 even though 2 ∉ scc

The big SCC and the singleton SCC for var 2 then both push diff_to_var[2] = 20 into var_ordering.

Reproducer

Repo: JuliaComputing/MultibodyComponents.jl, branch rolling_wheel, HEAD f531433.

using ModelingToolkit, MultibodyComponents
import DyadCompilerPasses

@named model = MultibodyComponents.tests.WheelInWorld()
ssys = MultibodyComponents.multibody(model)   # ← Tearing internal error before this PR

Stack of the failing pre-PR error:

Tearing internal error: lowering DAE into semi-implicit ODE failed!
  [2] generate_system_equations!(...) @ ModelingToolkitTearing reassemble.jl:499
  [4] DefaultReassembleAlgorithm(...)  @ ModelingToolkitTearing reassemble.jl:1184
  [6] dummy_derivative                 @ ModelingToolkit symbolics_tearing.jl:84
 [19] multibody(model::System, ...)    @ MultibodyComponents

After this PR, multibody(model) completes; the sibling SlipWheelInWorld test (which already compiled) continues to compile and integrate to t_end = 3.0 with retcode = Success.

Regression test

Not included here. The bug only surfaces with the dummy-derivative alias pattern produced by the multibody port; minimal 2D rolling-disk MTK-only models (with and without acceleration-level kinetics) compile cleanly both with and without this fix, so they don't witness the bug. The rolling-wheel reproducer above is the smallest known trigger; happy to backport a regression test if a smaller MTK-only MWE is found.

Test plan

• mtkcompile(MultibodyComponents.tests.WheelInWorld()) succeeds (previously threw Tearing internal error).
• MultibodyComponents.tests.SlipWheelInWorld still compiles + integrates to t_end = 3.0, retcode = Success.
• Pkg.test("ModelingToolkitTearing") shows the same 2 pre-existing trivial_tearing! failures with and without this change — no regression.

🤖 Generated with Claude Code

[AayushSabharwal]

This is an interesting bug. While the diagnosis is correct, I don't think the solution is. scc_eqs will have fewer elements than it should. The correct fix is to probably update full_var_eq_matching in state selection/tearing so that it is not stale.

[AayushSabharwal]

This is very incorrect and as such I'm closing the PR