Theorems · Theorem · nonassociative algebras
RootPairing.rootForm_anisotropic
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup N] [inst_3 : CommRing R] [inst_4 : LinearOrder R] [IsStrictOrderedRing R] [inst_6 : Module R M]
[inst_7 : Module R N] (P : RootPairing ι R M N) [P.IsRootSystem],
(LinearMap.BilinMap.toQuadraticMap P.RootForm).Anisotropic- Cited by
- 0 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- IsStrictOrderedRingstatement and proof · cited by 2,490
- RootPairingstatement and proof · cited by 710
- LinearMap.BilinMap.toQuadraticMapstatement · cited by 53
- RootPairing.IsRootSystemstatement and proof · cited by 50
- RootPairing.RootFormstatement · cited by 41
- QuadraticMap.Anisotropicstatement · cited by 13
- RootPairing.IsRootSystem.span_root_eq_topproof · cited by 11
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