Tabulate high-order expansion derivatives by recurrence

[pbrubeck]

Fixes firedrakeproject/firedrake#4152

Summary

• Tabulate arbitrary-order Dubiner expansion derivatives by applying Leibniz to the recurrence factors.
• Default simplex expansion tabulation to the recurrence path instead of dense differentiation matrices.
• Add order-4 triangle/tetrahedron coverage for orthonormal and bubble variants.

Tests

• python -m py_compile FIAT/expansions.py test/FIAT/unit/test_polynomial.py
• python -m pytest test/FIAT/unit/test_polynomial.py test/FIAT/unit/test_hierarchical.py::test_hierarchical_sparsity test/FIAT/regression/test_regression.py::test_expansions_jet -q

AI tool used: Codex.

[pbrubeck]

Updated verification after the HCT degree-14 follow-up.

What changed:

• Stabilized high-order Ck vertex supersmoothness constraints by imposing each constraint block on the current nullspace, instead of burying high-order vertex constraints in one large SVD.
• Added high-order HCT regression coverage for degrees 13 and 14.

Verification:

• python -m py_compile FIAT/expansions.py FIAT/macro.py test/FIAT/unit/test_hct.py test/FIAT/unit/test_polynomial.py
• python -m pytest test/FIAT/unit/test_hct.py test/FIAT/unit/test_macro.py -q
• python -m pytest test/FIAT/unit/test_polynomial.py::test_high_order_expansion_derivatives test/FIAT/regression/test_regression.py::test_expansions_jet -q
• Firedrake exact issue command for HCT degree 13: passed, V.dim() = 803
• Firedrake HCT degree 14: passed, V.dim() = 923
• Firedrake HCT degree sweep 13..17: passed with dimensions 803, 923, 1051, 1187, 1331

AI tool used: Codex.

[rckirby]

After we resolve the comments, I think this makes sense to do. The derivative matrices are kind of clunky and tend to go unstable at high order.

[rckirby]

Thanks, I think this makes a lot of sense.