Theorems · Theorem · nonassociative algebras
RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs
∀ {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 : P.EmbeddedG2] [Finite ι] [CharZero R] [IsDomain R],
RootPairing.EmbeddedG2.allRoots P =
List.map (⇑(Fintype.linearCombination ℤ ![RootPairing.EmbeddedG2.shortRoot P, RootPairing.EmbeddedG2.longRoot P]))
RootPairing.EmbeddedG2.allCoeffs- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- IsDomainstatement and proof · cited by 2,196
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.EmbeddedG2.allRoots_nodupproof · cited by 1
- RootPairing.EmbeddedG2.mem_span_of_mem_allRootsproof · cited by 1