OAI/GroupTheory/PolycyclicRecognition/Geometry/TemplateWeightRays.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

Template symmetries preserve the positive generator-weight rays

  1. theorem OAI.PolycyclicRecognition.templateSymmetry_weight_ray line 21

    Source 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