Theorems · Theorem · nonassociative algebras
RootPairing.Base.toCoweightBasis_apply
∀ {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} (b : P.Base)
[inst_5 : P.IsRootSystem] (i : ↥b.support), b.toCoweightBasis i = P.coroot ↑i- Defined in
- Mathlib.LinearAlgebra.RootSystem.Base
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Module.Basisstatement · cited by 1,477
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.Basestatement and proof · cited by 148
- RootPairing.Base.supportstatement and proof · cited by 139
- RootPairing.corootstatement · cited by 123
- RootPairing.IsRootSystemstatement and proof · cited by 50
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.Base.toCoweightBasis_repr_corootproof · cited by 0