[codex] add gaussian multiplication example

[FlorianPfaff]

Summary

• Added examples/basic/gaussian_multiplication.py to demonstrate multiplying Gaussian distributions and checking the result against the closed-form information representation.
• Fixed GaussianDistribution.multiply() to compute the Gaussian product in information form instead of using backend dot() for matrix products.
• Added a regression test for multiplying multiple Gaussian factors.

Validation

• PYTHONPATH=src python examples/basic/gaussian_multiplication.py
• PYTHONPATH=src python -m pytest tests/distributions/test_gaussian_distribution.py
• PYTHONPATH=src PYRECEST_BACKEND=pytorch python examples/basic/gaussian_multiplication.py
• PYTHONPATH=src PYRECEST_BACKEND=pytorch python -m pytest tests/distributions/test_gaussian_distribution.py
• PYTHONPATH=src PYRECEST_BACKEND=jax python examples/basic/gaussian_multiplication.py
• PYTHONPATH=src PYRECEST_BACKEND=jax python -m pytest tests/distributions/test_gaussian_distribution.py

[github-actions]

✅MegaLinter analysis: Success

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[github-actions]

Test Results

    12 files  ± 0      12 suites  ±0   4h 26m 48s ⏱️ - 14m 35s
 1 172 tests + 1   1 172 ✅ + 1      0 💤 ±0  0 ❌ ±0 
14 356 runs  +12  10 840 ✅ +12  3 516 💤 ±0  0 ❌ ±0 

Results for commit 317ea32. ± Comparison against base commit 1c808e2.