Theorems · Theorem · commutative algebra
IsAdjoinRootMonic.basis_apply
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRootMonic S f) (i : Fin f.natDegree), h.basis i = h.root ^ ↑i- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Module.Basisstatement · cited by 1,477
- Polynomial.natDegreestatement and proof · cited by 1,105
- Finsupp.singleproof · cited by 943
- AddMonoidAlgebra.coeffproof · cited by 365
- Polynomial.toFinsuppproof · cited by 64
- IsAdjoinRootMonicstatement and proof · cited by 35
- IsAdjoinRoot.rootstatement and proof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- IsAdjoinRootMonic.powerBasisproof · cited by 5
- IsAdjoinRootMonic.coeff_root_powproof · cited by 2
- IsAdjoinRootMonic.basis_oneproof · cited by 0