docs: geometry - #869
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Maps the four-operation toolkit (Lift, ad, Poisson, ∂ₜ) that moved from CTFlows to CTLie in v2.1.0-beta, and demonstrates the bridge identity Poisson(Lift(X), Lift(Y)) ≈ Lift(ad(X, Y)) on a genuinely nonlinear pair of vector fields. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Lift(f::Function) returns an OptimalControl.LiftedHamiltonianFunction, not an AbstractHamiltonian — a silent behavior change from v2.0 flagged with its own warning. Lift(X::AbstractVectorField) still returns a real Hamiltonian; only the plain-function overload changed. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
ad(X, f)/ad(X, Y) — Lie derivative or Lie bracket depending on whether the second argument is scalar- or vector-valued. Covers typed nesting, ∂ₜ's always-NonAutonomous result, and every error the old ⋅/Lie/autonomous= spelling now triggers. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Poisson(H, G), its bridge to Lie brackets, and the singular-control application (H01, H001, H101, u_sing = -H001/H101). Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Bracket notation for ad/Poisson: [X, Y], {H, G}, nesting, arithmetic at
an evaluation point, and the keyword-parenthesization gotcha. Verified
the nested-brace examples in the actual rendered VitePress HTML, not
just a clean Documenter exit code.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
New page: dg_ad_backend/dg_ad_backend!, the ad_backend= keyword shared by ad/Poisson/∂ₜ/@lie, and the CPU/GPU DifferentiationInterface split. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
…rk board Full julia --project=docs docs/make.jl rebuild and npx vitepress build, both clean except pre-existing unrelated warnings (missing sibling inventory files, and CTLie's own internal @ref targets in the auto-generated API reference — neither introduced by this PR). Ticked all 7 acceptance criteria in 06-geometry.md against that build, with an "Also found and fixed" section recording the BoundsError caught by the build, the non-existent examples-singular-control anchor, and the ad/Lift shared-guard message wart. Confirmed no src/ or test/ change was needed — src/imports/ctlie.jl already re-exports the full surface. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
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Summary
docs/src/geometry/) covering CTLie'sdifferential-geometry toolkit:
Lift,ad,Poisson,∂ₜ,@Lie, and the AD-backendcontrols (
dg_ad_backend/dg_ad_backend!). Spec:docs/reports/06-geometry.md.docs/attic/manual-differential-geometry.mdis built entirely on
Lie,⋅, andHamiltonianLift, none of which exist any more, plus afalse claim that
Hamiltonian/VectorField/HamiltonianVectorFieldaren't exported. Everycode example is new or rewritten and verified live against CTLie 0.1.5-beta (the version
docs/Manifest.tomlactually resolves), not trusted from the attic or the spec's own prose.src//test/change — unlike PR 8,src/imports/ctlie.jlalready re-exports the fullsurface the spec calls for, confirmed live before writing a single page.
BoundsErrorvia the actualmake.jlbuild (a dimension mismatch in a@Liearithmetic example), a broken forward-link to a not-yet-existing
examples-singular-controlanchor (PR 10 hasn't started), and three bare
LiftedHamiltonianFunctionreferences missingthe required
OptimalControl.prefix (it's import-only, not exported).Test plan
julia --project=docs docs/make.jl— full rebuild, clean except pre-existing/unrelatedwarnings (missing sibling inventory files; CTLie's own internal
@reftargets in theauto-generated API reference).
npx vitepress build— clean; nested Poisson-bracket notation (@Lie {{H, K}, L}-style)checked in the actual rendered HTML, not just the build log.
grep -rn 'Lie(\| ⋅ \|HamiltonianLift\|autonomous=\|OptimalControl\.VectorField' docs/src/geometry/— only intentional "coming from v2.0" mentions and the deliberate rejection demo remain.
docs/reports/06-geometry.mdticked against the real build.typosclean.Branched off
docs/flows(#868, not yet merged) since PR 9 depends on PR 8 per the work board— temporary stacking, same pattern used for PRs 6/7/8.
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