Theorems · Theorem · nonassociative algebras

RootPairing.chainTopCoeff_if_one_zero

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {P : RootPairing ι R M N} [inst_5 : Finite ι]
  [inst_6 : CharZero R] [inst_7 : IsDomain R] {i j : ι} [inst_8 : P.IsNotG2],
  P.root i - P.root j ∈ Set.range ⇑P.root → RootPairing.chainTopCoeff i j = if P.pairingIn ℤ i j = 0 then 1 else 0

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

0 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteCharZeroIsDomainRootPairing.IsNotG2