Generic TangentGroup TG from action-parameterized ProductLieGroup#2570
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AlessandroFornasier wants to merge 30 commits into
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Generic TangentGroup TG from action-parameterized ProductLieGroup#2570AlessandroFornasier wants to merge 30 commits into
AlessandroFornasier wants to merge 30 commits into
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Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Tangent Lie group
TG = G ⋉ 𝔤on top of the action-parameterized ProductLieGroup.Stacked on #2494, will be rebased once #2494 is merged.
Adds the tangent group of a Lie group,
TangentLieGroup<G>, built as a semidirectProductLieGroup<G, g, AdjointAction<G>>whereGacts on its own Lie algebragby the adjoint actionφ(g,ξ) = Ad_g·ξ.Changes
TangentLieGroup.h:AdjointAction<G>and theTangentLieGroup<G>alias. Element(g, ξ), group law(g₁,ξ₁)·(g₂,ξ₂) = (g₁g₂, ξ₁ + Ad_{g₁}ξ₂), dimension2·dim(G).ProductLieGroup: static algebra adjointadjointMap(ξ)for semidirect products. It recurses through the base group'sadjointMap, so tangent groups of products work as expected.Tests
testTangentLieGroup: group axioms/concepts, Exp/Log round-trip and Jacobians, the left-Jacobian transport block, and theAd/adblock structure, onTG(SO3),TG(SE3),TG(Gal3).testActionProductLieGroup: anSE(3) ⋉ ℝ⁴example (defined inline in the test) reconstructingGal(3), cross-checked against the nativeGal3compose/between/inverse/Exp/Log/Adjoint, retract/local, and the static algebra adjoint.