Add heat kernel

[inducer]

Squashed from #185

To do:

• Look at review comments in Add heat kernel #185.

[ShawnL00]

This is now ready for review.

[inducer]

Thanks! Squashed and tweaked a bit. LGTM, I'll just wait for the copilot review and then likely merge.

[Copilot]

Pull request overview

This PR adds a new HeatKernel (heat-equation Green’s function) to sumpy.kernel and extends the test suite to validate PDE consistency and translation behavior for heat-kernel expansions. It also adjusts toy-context expansion formation to consistently use the “no target-derivative” kernel variant and updates M2L translation code to account for translation preprocessing.

Changes:

• Add HeatKernel as an ExpressionKernel, including PDE operator support and kernel-mapper integration.
• Extend existing kernel PDE-check tests to include the heat kernel and add a dedicated translation convergence test module.
• Refactor expansion-to-expansion (M2L-with-dependent-data) codegen to handle preprocessed source expansion sizes and tighten typing/structure in a few places.

Reviewed changes

Copilot reviewed 6 out of 7 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
sumpy/kernel.py	Introduces HeatKernel, its PDE operator, and mapper hooks.
sumpy/e2e.py	Adds typing/property refactors and updates M2L-dependent-data codegen to support preprocessing.
sumpy/toys.py	Ensures P2E formation in toy context uses the target-transformation-removed kernel.
sumpy/test/test_misc.py	Adds heat-kernel coverage to the PDE-check test and adjusts sampling for time-forward evaluation.
sumpy/test/test_kernels.py	Refactors P2E/E2P convergence tests to use toy expansion helpers and updates convergence thresholds/logic.
sumpy/test/test_heat_translations.py	New tests for heat-kernel M2M/L2L/M2L translation convergence.

Comments suppressed due to low confidence (1)

sumpy/e2e.py:77

• The E2EBase.init docstring no longer matches the actual parameters (it references expansion and strength_usage, which are not accepted here). This makes the public API documentation misleading and can confuse users/readers.

            name: str | None = None):
        """
        :arg expansion: a subclass of :class:`sympy.expansion.ExpansionBase`
        :arg strength_usage: A list of integers indicating which expression
            uses which source strength indicator. This implicitly specifies the

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