OAI/Geometry/Convex/GeneralMahler/Reduction.lean
5 declarations, 0 contain sorry, 0 declared as axioms
Cone-volume identities.
- theorem
OAI.GeneralMahler.Body.vol_posline 12 - theorem
OAI.GeneralMahler.Body.chi_axisline 18Source 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
- def
OAI.GeneralMahler.Body.shearline 81Source 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
- theorem
OAI.GeneralMahler.Body.shear_offline 92 - theorem
OAI.GeneralMahler.Body.cone_volumeline 110