Add cholesky overload for tracer matrices

[devmotion]

I wanted to use the global tracer on a function that calls cholesky, and it errored: the pivot / positive-definiteness checks compare matrix entries, which on tracers return a tracer rather than a Bool.

This adds a cholesky overload mirroring the existing eigen overload — collapse the input to one conservative tracer via second_order_or and broadcast it over the factor with a lazy Fill. Both the default / NoPivot (→ Cholesky) and RowMaximum (→ CholeskyPivoted) variants are covered; the pattern is independent of pivoting.

Reproducer (errors on main, works here):

using SparseConnectivityTracer, LinearAlgebra
detector = TracerSparsityDetector()
f(x) = (A = reshape(x, 2, 2); C = cholesky(A' * A + 4I); sum(C.factors))
jacobian_sparsity(f, rand(4), detector)   # 1×4 all-ones after the fix

Adds a "Cholesky" testset mirroring "Eigenvalues".

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This pull request was written with the assistance of generative AI (Claude Code).

[adrhill]

For future reference (either here or a comment in the code):
What are the extra arguments to Cholesky?

[devmotion]

The first argument is the upper or lower-triangular factor, the second argument indicates whether it's the upper ('U') or lower ('L') triangular factor, and the third argument is the BLAS info code (0 indicates success).

[adrhill]

For future reference (either here or a comment in the code):
What are the extra arguments to CholeskyPivoted?

[devmotion]

The first two arguments and the last argument are the same as for Cholesky (factor, type of factor and BLAS info code), the third argument is the pivoting, and the fourth argument the rank.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.81%. Comparing base (52b6612) to head (de12e36).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #322      +/-   ##
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+ Coverage   93.76%   93.81%   +0.05%     
==========================================
  Files          28       28              
  Lines        1090     1100      +10     
==========================================
+ Hits         1022     1032      +10     
  Misses         68       68              

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[adrhill]

Thanks!

[devmotion]

Great, could you make a new release with the change?

[adrhill]

Done, note that I tagged 1.2.2 instead of 1.3.0 pre-coffee.

[devmotion]

No worries, that's fine with me 🙂

[devmotion]

Thank you!