PyTensor workflows

Express the intended calculation, then verify its values, shapes, derivatives, and state transitions.

Establish the contract

1. Use the project's existing environment. Check installed PyTensor and relevant backend versions before choosing an API; development builds may differ.
2. State input/output shapes, axis meanings, dtypes, support, and mutable or random state. Named axes are not automatically coordinate-indexed arrays.
3. Choose the simplest supported graph operation. Prefer existing tensor primitives to an unnecessary custom Op. Preserve the scientific calculation when diagnosing compiler or backend limitations.
4. Check version-appropriate official documentation and installed source when a signature or backend limitation is uncertain.
5. Define an independent numerical or analytic reference and meaningful failure cases before executing the example.