Theorems · Definition · commutative algebra
AdjoinRoot.powerBasisAux
{K : Type u_5} → [inst : Field K] → {f : Polynomial K} → f ≠ 0 → Module.Basis (Fin f.natDegree) K (AdjoinRoot f)The elements 1, root f, ..., root f ^ (d - 1) form a basis for AdjoinRoot f,
where f is an irreducible polynomial over a field of degree d.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- Module.Basisstatement · cited by 1,477
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.leadingCoeffproof · cited by 498
- minpolyproof · cited by 439
- AdjoinRootstatement · cited by 177
- AdjoinRoot.rootproof · cited by 77
- Module.Basis.mkproof · cited by 29
- AdjoinRoot.minpoly_rootproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AdjoinRoot.powerBasisproof · cited by 9
- AdjoinRoot.powerBasisAux.congr_simpstatement and proof · cited by 0