OAI/GroupTheory/PolycyclicRecognition/Geometry/TemplateWeightRays.lean
1 declarations, 0 contain sorry, 0 declared as axioms
Template symmetries preserve the positive generator-weight rays
- theorem
OAI.PolycyclicRecognition.templateSymmetry_weight_rayline 21Source documentation
The cap argument from the support-symmetries lemma: pullback of every nonzero generator weight is a positive multiple of another generator weight. It uses preservation of all compact convex templates, not only segments.
theorem templateSymmetry_weight_ray (D : SupportDatum W I B) (A : templateSymmetryGroup D) (j : I) (hj : D.weight j ≠ 0) : ∃ (i : I) (r : ℝ), 0 < r ∧ (D.weight j).comp A.val.toLinearMap = r • D.weight i := by …Mentions: OAI.PolycyclicRecognition.SupportDatum, OAI.PolycyclicRecognition.templateSymmetryGroup