Combining systems compares the variables, and a loaded system holds the live ones

[ofloveandhate]

Stacked on #483 (chore/housekeeping-for-4.0), so the diff shows only this work; it retargets to develop when #483 merges.

A loaded system holds the live variables. Variable::Make interns variables by name, and the whole symbolic engine relies on that: making x here and x there gives one node. Boost deserialization bypassed Make, so a System or Slice that came through an archive, which is what copy.deepcopy, copy.copy and pickle do, held variables equal by name but distinct as objects. A System and a Slice now re-intern their nodes as the last step of a load (the loader for records already did this through ReinternNodes), so a copied or unpickled system combines with its original. ADR-0068 records the decision; a new archivable class that holds nodes needs the same step.

Combining systems makes one check. Concatenate compared variable orderings by object and refused the un-interned copies. MakeHomotopy and MakeMovingHomotopy compared counts only and accepted anything with the right number of variables, then blended block operands by position: a target over (x, y) and a start over (y, x) produced a homotopy that evaluated y - 3 at (7, 11) to 4. All four combining operations (Concatenate, MakeHomotopy, MakeMovingHomotopy, operator+=) now go through CheckVariableStructuresMatch, which compares the ordering, the affine and projective groups, the ungrouped variables and the homogenizing variables, and says which kind of difference it found: the same variables in a different order, a different grouping, different variables, or the same names as different objects. A system that declares no variables adopts the other's structure, so building a system from functions alone and combining it still works.

Python nodes compare by identity of the node. __eq__, __ne__ and __hash__ on the node base compare the underlying pointer, so Variable('x') == Variable('x') holds and nodes can be dictionary keys; comparing with a non-node returns NotImplemented.

A latent bug the work exposed. System::swap omitted the auxiliary variable groups and auxiliary coordinates. It surfaced when MakeHomotopy gained a second return value and the move stopped being elided. Fixed, with a test.

Tests: core/test/classes/system_identity_test.cpp, core/test/classes/auxiliary_coordinates_test.cpp, python/test/classes/clone_concatenate_test.py. The concatenate tutorial and the changelog describe the rule. Verified: all C++ suites, the Python suite (1160), the tutorial doctests (198), and the three lints. The cellular decomposition port, the most intensive user of the library, combines systems at dozens of sites and was refused nowhere.

🤖 Generated with Claude Code

[ofloveandhate]

this PR brings an imporatnt ability in Python -- x made twice, is the same x. and, systems that are loaded from pickel etc are combineable with those already in memory, when they use the same symbols. this is the hashconsing work i did in June and July coming back in winning form. I used Claude Fable to do that work, and it has made some UI issues in this library ... disappear. Verschwinden.

[ofloveandhate]

The interning work is admittedly the part i least understand of this work. I am accepting it -- it clearly works correctly. I am doing my best to be diligent, and I accept responsibility for the correctness of this code. If it is incorrect in any way, I will do my best to promptly fix it. My dreams are big. I am reaching for them.