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Diff — Curl (mathematics)

Revision #1139 → #1978 · back to history

modifiedStokes' theorem (curl form)bcef3e8d0890
FieldFrom #1139To #1978
mathlib.declMeasureTheory.integral_divergence_of_hasFDerivWithinAt_off_countable
mathlib.moduleMathlib.MeasureTheory.Integral.DivergenceTheorem
noteMathlib has the divergence theorem for Henstock–Kurzweil/Bochner integrals and a Poincaré lemma for 1-forms, but no Stokes theorem stated in curl form.Mathlib has the divergence theorem on Euclidean boxes but no Stokes/Kelvin–Stokes theorem stated in curl form.
provenanceaiai-moderated
statuspartialnot_formalized
modifiedCurl operator93c665fe31e9
FieldFrom #1139To #1978
noteNo declaration named `curl` (or analog) on vector fields exists in Mathlib.No declaration named `curl` (or analog) on vector fields exists in Mathlib; a grep over `Mathlib/` returns no curl operator.
modifiedKelvin–Stokes theorem7baa4e6bbeff
FieldFrom #1139To #1978
noteMathlib does not contain a Kelvin–Stokes theorem; only the divergence theorem and a Poincaré lemma for 1-forms exist.Mathlib does not contain a Kelvin–Stokes theorem; only the divergence theorem on Euclidean boxes exists.
modifiedCurl via surface integral over a shellca29f7844d7e
FieldFrom #1139To #1978
noteNo surface-integral-over-a-shell definition of curl is present.No surface-integral-over-a-shell definition of curl is present in Mathlib.
modifiedCurl via exterior derivative9552d0e1e02f
FieldFrom #1139To #1978
mathlib.match_kindgeneralization
provenanceaiai-moderated
modifiedCurl of rotating disk velocity field7367abdfef2c
FieldFrom #1139To #1978
noteNo formalization of the rotating-disk velocity field example.No formalization of the rotating-disk velocity field example; in particular, the identity vorticity = curl(velocity) = 2·(angular velocity) is not formalized.
provenanceaiai-moderated
modifiedDifferential k-forms in 3 dimensionsbbb1f108aac5
FieldFrom #1139To #1978
mathlib.moduleMathlib.Analysis.Calculus.DifferentialForm.BasicMathlib.Topology.Algebra.Module.Alternating.Basic
noteMathlib represents differential `n`-forms as `E → E [⋀^Fin n]→L[𝕜] F`, generalizing the 3D 0/1/2/3-form classification.Mathlib represents differential `n`-forms via `ContinuousAlternatingMap` (notation `E [⋀^Fin n]→L[𝕜] F`), generalizing the 3D 0/1/2/3-form classification.
addedAngular speed equals half the curl magnitudef436f25d49ae
addedMagnetic vector potentialf273e733714d
addedGeneralized Stokes' theorem (for differential forms)8723026273de