OAI/Geometry/Convex/GeneralMahler/Reduction.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

Cone-volume identities.

  1. theorem OAI.GeneralMahler.Body.vol_pos line 12
  2. theorem OAI.GeneralMahler.Body.chi_axis line 18

    Source documentation

    Slice integral of a cone at a vertical dual vector.

    theorem chi_axis (K : Body n) (r : ℝ) (hr : 0 < r) :
        chi K.cone (pair r 0) =
          (r⁻¹ ^ (n+1)) * n.factorial * (volume (K : Set (Rn n))).toReal := by
    …

    Mentions: OAI.GeneralMahler.Body, OAI.GeneralMahler.chi, OAI.GeneralMahler.pair, OAI.GeneralMahler.Rn

  3. def OAI.GeneralMahler.Body.shear line 81

    Source documentation

    Shear of cone coordinates for translations.

    def shear (z : Rn n) : (LiftSpace n) ≃ₗ[ℝ] LiftSpace n where
    …

    Mentions: OAI.GeneralMahler.Rn, OAI.GeneralMahler.LiftSpace

  4. theorem OAI.GeneralMahler.Body.shear_off line 92
  5. theorem OAI.GeneralMahler.Body.cone_volume line 110