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feat: add PartialDerivative#341

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feat: add PartialDerivative#341
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feat/add-partial-derivative

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Introduces the PartialDerivative. This structure enables the computation of partial derivatives of 0-forms defined over a CartesianGeometry, while preserving the form rank.

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dccabanas requested a review from J15525 March 20, 2026 09:19
@dccabanas dccabanas self-assigned this Mar 20, 2026
@dccabanas dccabanas added the enhancement 🔥 New feature or request label Mar 20, 2026
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dccabanas changed the base branch from main to dev March 20, 2026 09:19
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dccabanas force-pushed the feat/add-partial-derivative branch from 72a3469 to 65cbc99 Compare March 20, 2026 09:24
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dccabanas marked this pull request as draft March 23, 2026 08:13
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dccabanas force-pushed the feat/add-partial-derivative branch from 54925fa to dbc8ce4 Compare March 23, 2026 08:20
@dccabanas
dccabanas force-pushed the feat/add-partial-derivative branch from dbc8ce4 to 4603c83 Compare April 17, 2026 09:12
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dccabanas force-pushed the feat/add-partial-derivative branch 2 times, most recently from 7951962 to 7a45b23 Compare May 15, 2026 10:11
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dccabanas force-pushed the feat/add-partial-derivative branch 2 times, most recently from fb429f3 to b7b30a7 Compare June 5, 2026 15:52
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dccabanas force-pushed the feat/add-partial-derivative branch 2 times, most recently from 638f805 to 00d3529 Compare June 9, 2026 12:37
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dccabanas force-pushed the feat/add-partial-derivative branch 4 times, most recently from 47cd8e7 to ea8760f Compare June 24, 2026 10:16
dccabanas added 11 commits June 29, 2026 12:32
The feature is limited to 0-forms defined on Cartesian geometries.
The previous version was not correct for `FormField`s.
Change from an error to a warning if geometry is not Cartesian.
Summary of changes:
- introduce a new structure `PartialOrder`; allows dispatching on the
  total derivative order, which is useful for logic and optimisation.
- introduce general method for arbitrary geometries if the total
  derivative order is 1.
- specialise computations for `CartesianGeometry`.
@dccabanas
dccabanas force-pushed the feat/add-partial-derivative branch from ea8760f to 07604d0 Compare June 29, 2026 10:32
Summary of changes:

- Throw error for the geometric scaling of an abstract geometry; the
  implementation is not correct. A correct implementation would
  requiring mixing derivatives, which is not done currently. Requires a
  vector field structure.
- Allow bypass of incorrect method for `HierarchicalGeometry`, if said
  geometry is built only on `CartesianGeometry`.
@dccabanas
dccabanas force-pushed the feat/add-partial-derivative branch from 07604d0 to ce263df Compare June 29, 2026 11:54
@dccabanas
dccabanas force-pushed the feat/add-partial-derivative branch from ce263df to 23632a5 Compare June 29, 2026 12:08
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