Theorems · Theorem · nonassociative algebras
RootPairing.coroot_eq_polarizationEquiv_apply_root
∀ {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 : Field R] [inst_4 : Module R M] [inst_5 : Module R N] (P : RootPairing ι R M N)
[inst_6 : P.IsAnisotropic] [inst_7 : P.IsRootSystem] (i : ι),
P.coroot i = (2 / (P.RootForm (P.root i)) (P.root i)) • P.PolarizationEquiv (P.root i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- LinearEquivstatement · cited by 3,317
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- LinearMap.BilinFormstatement · cited by 501
- smul_smulproof · cited by 360
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.polarizationEquiv_symm_apply_corootproof · cited by 0
- RootPairing.coroot_mem_or_neg_mem_closure_of_rootproof · cited by 0