coxeterWeight — Mathlib

English

The Coxeter weight of a pair is defined by coxeterWeight i j = pairing i j · pairing j i; it is interpreted as 4 cos^2 θ in a finite diagram.

Русский

Вес Коцитора пары задаётся как coxeterWeight i j = pairing i j · pairing j i; он, при конечном диаграмме, равен 4 cos^2 θ.

LaTeX

$$$$ \\operatorname{coxeterWeight}(i,j) = \\; \\operatorname{pairing}(i,j) \\cdot \\operatorname{pairing}(j,i). $$$$

Lean4

/-- The Coxeter Weight of a pair gives the weight of an edge in a Coxeter diagram, when it is
finite.  It is `4 cos² θ`, where `θ` describes the dihedral angle between hyperplanes. -/
def coxeterWeight : R :=
  pairing P i j * pairing P j i

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