feat(ga): add Cl(p,q,r) kingdon-like interface for Clifford algebras

[utiberious]

Summary

Adds a Cl(p, q, r) convenience function that creates a geometric algebra from its signature, following the convention popularized by ganja.js and kingdon. This provides an intuitive entry point for users coming from those libraries.

Fixes #524

Changes

• galgebra/ga.py: Add Cl(p, q=0, r=0) function that:
  • Builds basis names e_1, e_2, ...
  • Constructs diagonal metric from signature (+1, -1, 0)
  • Returns (Ga, *basis_vectors) tuple
• galgebra/__init__.py: Export Cl
• test/test_test.py: Add tests for Cl(3), Cl(1,3), Cl(2,0,1) with metric verification

Example

from galgebra import Cl

ga, e1, e2, e3 = Cl(3)          # 3D Euclidean
ga, e1, e2, e3, e4 = Cl(1, 3)   # Spacetime
ga, e1, e2, e3 = Cl(2, 0, 1)    # 2D PGA

Test plan

• Unit tests pass
• Full CI with nbval notebooks passes

[utensil]

Thanks for this! A few things before merging:

1. Move Cl to galgebra/interop.py: ga.py is core algebra; Cl is a compatibility shim. Keeping them separate makes the purpose clear.

2. Namespace-based conventions instead of a parameter: rather than convention='kingdon' as an argument, provide Cl via namespaces:

   • galgebra.interop.Cl — galgebra defaults (no surprises for existing users)
   • galgebra.interop.kingdon.Cl — kingdon convention (dual mode 'Iinv+', etc.)

   The import path is the documentation — from galgebra.interop.kingdon import Cl is self-explanatory. A string argument is harder to discover, harder to type-check, and silently changes behavior mid-code. Conventions are better expressed as namespaces.

   Default stays galgebra so existing users aren't affected.

3. Docstring: mention ganja.js popularized Cl(p,q,r), kingdon adopted it; and document the known incompatibilities:

   • Basis naming: galgebra numbers from 1 (e_1, e_2, ...); kingdon defaults to 0-indexed for PGA (e0, e1, e2, e3)
   • Dual convention: galgebra's default is 'I+' (dual(A) = I * A); kingdon uses 'Iinv+' (dual(A) = A * I⁻¹) via codegen_polarity — see fix(ga): change default dual mode to Iinv+ for correct B*dual(B)=I #544 for why this matters

[utiberious]

Restructured per review. Pushed in 35026b6:

1. Moved Cl to galgebra/interop/: ga.py is now core-only.

2. Namespace-based conventions:

   • from galgebra.interop import Cl -- galgebra defaults (1-indexed basis, I+ dual)
   • from galgebra.interop.kingdon import Cl -- kingdon conventions (0-indexed basis, Iinv+ dual)
   • from galgebra import Cl still works (re-exported from interop)

3. Docstrings updated with:

   • ganja.js/kingdon attribution
   • Known incompatibilities: basis naming (1-indexed vs 0-indexed) and dual convention (I+ vs Iinv+)

4. Tests added for both test_Cl (interop) and test_Cl_kingdon (0-indexed, Iinv+ dual mode verified and restored).

[utensil]

Thanks for the clean refactor! One note: galgebra.interop.kingdon.Cl sets Ga.dual_mode('Iinv+') globally — this is a session-wide side effect. Worth adding a note in the docstring that callers should save/restore Ga.dual_mode_value if mixing conventions in the same session (as the test already shows). Otherwise good to merge.

[utiberious]

Added a warning block in the kingdon.Cl docstring about the session-wide side effect and the save/restore pattern. Pushed in 524e3f2.