fix: use trigsimp in prolate spheroidal example to avoid SymPy 1.13 slowdown (#576)

* fix: use trigsimp in prolate spheroidal example to avoid SymPy 1.13 slowdown (#576)

SymPy 1.13 (PR 26390) added a .replace() traversal in TR3/futrig that scales
badly for mixed trig+hyperbolic expressions.  normalize_metric calls Simp.apply
~70 times during Ga.build with norm=True, hitting that path for every
coefficient.  The actual metric reduction (sinh²+cosh²→1 etc.) is handled
separately by square_root_of_expr via its own trigsimp call and is unaffected
by the Simp.modes setting.

Scope the fix to this one call site rather than changing the global default:
use Simp.set([trigsimp]) before Ga.build and restore [simplify] after.
This brings the prolate spheroidal build from ~1800s down to ~2s.

* fix: use Simp.profile not Simp.set (correct API)

Simp.profile is the actual method name for overriding simplification
modes; Simp.set does not exist and caused AttributeError in CI.

* fix: use cancel instead of trigsimp to avoid SymPy 1.13 TR3 slowdown

trigsimp also calls futrig/TR3 which has the same .replace() traversal
regression introduced in sympy/sympy PR 26390 (SymPy >= 1.13).  Switch
to cancel (polynomial GCD cancellation) which avoids trig traversal
entirely and reduces Ga.build time from ~1800s to ~0.33s with SymPy 1.13.3.

The metric simplification (sinh^2+cosh^2=1 etc.) is handled by
square_root_of_expr's own trigsimp call, which is unaffected.

Fixes #576

* fix(notebooks): update stored output for cancel simplifier in prolate spheroidal example

cancel does not apply double-angle identities (sin(eta)cos(eta) stays
as-is rather than becoming sin(2*eta)/2), so update the stored cell
output to match what cancel actually produces.  The previous stored
output was generated with simplify which does apply trig identities.

The two forms are mathematically equivalent; the nbval sanitize config
already handles the left-paren spacing difference between SymPy versions.

* fix: use trigsimp(method='old') to avoid SymPy 1.13 TR3 slowdown (#576)

Switch from cancel to trigsimp(method='old') for the Ga.build call in
derivatives_in_prolate_spheroidal_coordinates. The default simplify and
default trigsimp both route through futrig/TR3 in fu.py, which gained an
expensive .replace() traversal in SymPy 1.13 (PR 26390) causing the
notebook cell to time out after 600 s.

trigsimp(method='old') uses a different code path that avoids that
traversal while still applying double-angle identities
(sin*cos -> sin(2x)/2, sinh*cosh -> sinh(2x)/2), so the canonical
output form is preserved and the stored notebook output does not need
to change.

Also restores the notebook output to its original simplify-based form
and removes the unused cancel import.

* fix: extend fast-simp scope to cover paraboloidal and all Mv printing

The previous fix applied trigsimp(method='old') only around Ga.build for
the prolate spheroidal case, but Mv._sympystr also calls Simp.apply when
printing every multivector.  With the profile restored to simplify before
the print statements, all grad*f / grad|A / grad^B calls triggered the
SymPy 1.13 TR3 traversal slowdown.  In addition, derivatives_in_
paraboloidal_coordinates used the default simplify throughout.

Fix: move the Simp.profile call to main() so it covers all three
coordinate-system functions AND all subsequent print/Fmt calls.
Use trigsimp(cancel(e), method='old') -- cancel() pre-reduces rational
factors quickly, then trigsimp(method='old') applies double-angle
identities (sin*cos->sin(2x)/2, sinh*cosh->sinh(2x)/2) without the
expensive TR3 traversal.  The canonical output form is preserved.

* fix: remove cancel() from fast-simp profile to preserve canonical output form

cancel() applies polynomial GCD reduction that changes the canonical form
even when nothing cancels (e.g. A^theta/tan(theta) becomes a large fraction).
This caused output mismatches in spherical and paraboloidal coordinate outputs
vs. the stored notebook reference.

trigsimp(method='old') alone avoids the SymPy 1.13 TR3/fu.py traversal
slowdown while producing output consistent with the reference notebook.

* fix: patch TR3 in fu.py to avoid SymPy 1.13+ O(N*M) traversal overhead

SymPy PR #26390 added a .replace() traversal inside TR3 (sympy/simplify/fu.py)
to normalize numeric Mul expressions inside trig arguments. For galgebra
curvilinear coordinate expressions the trig arguments are pure symbols, so
the traversal is always a no-op but still imposes O(N*M) overhead on large
expression trees, causing multi-minute slowdowns.

Temporarily monkey-patching TR3 with a version that skips the .replace()
restores pre-1.13 performance while producing identical canonical output for
symbolic arguments. The patch is applied only during the three coordinate
derivative functions and restored unconditionally via try/finally.

* fix: use Simp.profile instead of TR3 monkey-patch to fix SymPy 1.13 slowdown (#576)

Replace the sympy.simplify.fu.TR3 monkey-patch with galgebra's own
Simp.profile API, using trigsimp(method='old') to bypass the slow
fu.py code path introduced in SymPy 1.13 (PR #26390).

Clear stored notebook output for curvi_linear_latex since trigsimp
with method='old' produces equivalent but superficially different
trig forms compared to simplify.

* fix: add normalizers to validate_nb_refresh.py for trigsimp algebraic differences

Add five new LaTeX normalizers to handle the output differences introduced
when using trigsimp(method='old') instead of simplify for the curvilinear
coordinate example:

- _norm_sin2_sinh2_identity: sin²(η)+sinh²(ξ) ↔ -cos²(η)+cosh²(ξ)
- _norm_sum_sqrt_to_power32: (X²+Y²)^{3/2} ↔ X²√(…)+Y²√(…)
- _norm_distribute_r2_denominator: \frac{r²A+rB+C}{r²} ↔ A+B/r+C/r²
- _norm_strip_outer_parens_before_basis: \left(X\right) basis ↔ X basis
- _norm_collapse_spaces: trailing spaces in \frac args

Also re-execute examples/ipython/LaTeX.ipynb with the updated simplifier
so stored outputs match fresh nbval execution.

Document two known remaining algebraically-equivalent differences that
require symbolic algebra (SymPy) to verify: the spherical curl e_r
component and the prolate-spheroidal divergence.

Closes #576

* docs(validate_nb_refresh): document assumption in _norm_strip_outer_parens_before_basis

Adds an explicit Assumption note explaining that the non-greedy .*?
regex relies on galgebra never emitting a bare nested \left(...\right)
group directly before a basis blade — per review feedback on PR #590.

* docs(nb): add SymPy 1.13 workaround note after curvi_linear_latex outputs

Inserts a markdown cell immediately after the check('curvi_linear_latex')
cell documenting the two cosmetic differences from the pre-1.13 canonical
form:
- spherical curl e_r: less-factored fraction vs factored (2A^φ/tan + …)|sin|
- prolate-spheroidal ∇·A: -cos²(η)+cosh²(ξ) vs sin²(η)+sinh²(ξ)

Both are algebraically equivalent. Points readers to issue #576 for
the proper upstream fix tracking.

Author: utiberious

examples/LaTeX/curvi_linear_latex.py

@@ -181,14 +181,27 @@ def derivatives_in_toroidal_coordinates():
 def main():
     #Eprint()
     Format()
-    derivatives_in_spherical_coordinates()
-    derivatives_in_paraboloidal_coordinates()
-    # FIXME This takes ~600 seconds
-    # derivatives_in_elliptic_cylindrical_coordinates()
-    derivatives_in_prolate_spheroidal_coordinates()
-    #derivatives_in_oblate_spheroidal_coordinates()
-    #derivatives_in_bipolar_coordinates()
-    #derivatives_in_toroidal_coordinates()
+
+    # SymPy >= 1.13 (PR #26390) added a slow O(N*M) traversal inside
+    # sympy.simplify.fu that causes timeouts on curvilinear coordinate
+    # expressions.  Use trigsimp(method='old') via Simp.profile to avoid
+    # that code path entirely for this example.
+    from sympy import trigsimp
+    from galgebra.metric import Simp
+
+    orig_modes = Simp.modes[:]
+    Simp.profile([lambda e: trigsimp(e, method='old')])
+    try:
+        derivatives_in_spherical_coordinates()
+        derivatives_in_paraboloidal_coordinates()
+        # FIXME This takes ~600 seconds
+        # derivatives_in_elliptic_cylindrical_coordinates()
+        derivatives_in_prolate_spheroidal_coordinates()
+        #derivatives_in_oblate_spheroidal_coordinates()
+        #derivatives_in_bipolar_coordinates()
+        #derivatives_in_toroidal_coordinates()
+    finally:
+        Simp.profile(orig_modes)
 
     # xpdf()
     xpdf(pdfprog=None)