OAI/GroupTheory/PolycyclicRecognition/Geometry/CartanPolarTiledChains.lean

GitHub source file

2 declarations, 0 contain sorry, 0 declared as axioms

The three actual chains for the polar flow partition

  1. def OAI.PolycyclicRecognition.normalizedPolarTemplates line 12

    Source documentation

    Normalized templates ordered as source, reverse anchor, within-tile.

    def normalizedPolarTemplates {W : Type*} [NormedAddCommGroup W] [NormedSpace ℝ W]
        (K : ProperCone ℝ (StrongDual ℝ W)) (ε : ℝ) (j : Fin 3) : Set W :=
    …
  2. theorem OAI.PolycyclicRecognition.CartanWordModel.exists_polar_tiled_probe_chains line 44

    Source documentation

    The same maximal polar ideal basis from the flow tiling supplies all three actual measurable chain families. Their common ambient basis and amplitude envelope are constructed from the largest polar radius.

    theorem exists_polar_tiled_probe_chains
        (hExp : IsGroupExponential Exp)
        (realize : ExponentialLinearRealizationInput (EG := EG) (G := G))
    …

    Mentions: OAI.PolycyclicRecognition.ExponentialLinearRealizationInput