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Diff — Hodge star operator

Revision #3187 → #3688 · back to history

modifiedHodge star operator5e07b2cd8fc9
FieldFrom #3187To #3688
noteNo Hodge star operator is defined anywhere in Mathlib4 (no `hodgeStar`/`Hodge` results in `Mathlib/`).Grep for `Hodge`, `hodgeStar`, `HodgeStar` in `Mathlib/` returns no definition of a Hodge star operator.
modifiedCodifferential (lead)2f4fd6a0430d
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noteThe codifferential as Hodge-adjoint of the exterior derivative is not defined in Mathlib.No `codifferential` decl exists in Mathlib and no Hodge-adjoint of the exterior derivative is defined.
modifiedLaplace–de Rham operator (lead)4b8d7db43fd3
FieldFrom #3187To #3688
noteThe Laplace–de Rham (Hodge) Laplacian is not formalized in Mathlib.No `LaplaceRham`/`HodgeLaplacian`/`deRham` Laplacian appears in Mathlib.
modifiedInduced inner product on k-vectorsc7e46dcc6439
FieldFrom #3187To #3688
mathlib.declexteriorPower.inner_ιMulti_ιMulti
mathlib.match_kindexact
mathlib.moduleMathlib.Analysis.InnerProductSpace.ExteriorPower
noteMathlib has `ExteriorPower` and inner product spaces but no induced inner product on the exterior power of an inner product space.`Mathlib.Analysis.InnerProductSpace.ExteriorPower` builds an `InnerProductSpace ℝ (⋀[ℝ]^n E)` instance with `inner_ιMulti_ιMulti` giving exactly the Gram determinant formula on decomposables.
statusnot_formalizedformalized
addedHodge star maps k-vectors to (n−k)-vectors7315ec1d97ed
addedGram matrix of an inner product on k-vectors7f5b62d544b2
addedHodge star on 2-forms in Minkowski space06ab21d2a28a