Rewrite det(inv(X)) → 1/det(X)

[alessandrogentili001]

Description

Related Issue

• Closes Rewrite det(inv(X)) → 1/det(X) #2083
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

[jessegrabowski]

These aren't related to linalg, the name is wrong

Each of these should be a separate rewrite, and we should be using the new scalar Op properties. We have monotonic_increasing and monotonic_decreasing, which imply sign(f(x)) -> sign(x) and sign(f(x)) -> sign(-x) if the op is also zero_preserving.

We just have to be careful about strict montonicity vs non-strict. I can't remember if ceil(x) is marked as monotonic for example. We might need a separate flag for the strict variety and check it in this rewrite.

[jessegrabowski]

Suggested change

Since det(inv(X)) = 1/det(X), we avoid computing the inverse.

[alessandrogentili001]

Hi jesse, thanks for the feedback! I've refactored the implementation to address your points regarding modularity and property-based rewriting.

1. Decoupling Linalg from Math: I've moved the non-linalg rewrites (like log(reciprocal(x))) out of pytensor/tensor/rewriting/linalg/summary.py and into pytensor/tensor/rewriting/math.py.
2. Property-Based sign(f(x)) Rewrite: I implemented a generic local_sign_of_monotonic rewriter in math.py. Instead of hardcoding special cases, it now queries ScalarOp properties.
3. Strict Monotonicity Flags: To handle the edge cases you mentioned (like ceil), I've added strictly_monotonic_increasing and strictly_monotonic_decreasing flags to the UnaryScalarOp base class and applied them to all relevant strictly monotonic Ops across basic.py and math.py (including Log, Exp, Tanh, Sigmoid, Erf, etc.). The sign rewrite now specifically checks for strict monotonicity to ensure correctness.
4. Atomic Rewrites: I've separated the logic into atomic rewriters (local_log_reciprocal, local_sign_reciprocal, and local_sign_of_monotonic) and registered them across canonicalize, stabilize, and specialize to ensure they trigger reliably.
5. Docstring Cleanup: Simplified the det_of_inv docstring as suggested.
6. Expanded Testing: Added comprehensive tests in tests/tensor/rewriting/test_math.py to verify these generic rewrites, including a negative test case for ceil to confirm it is not incorrectly optimized.

Let me know if you have any further suggestions!