Theorems · Theorem · commutative algebra
AdjoinRoot.aeval_eq
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} (p : Polynomial R),
(Polynomial.aeval (AdjoinRoot.root f)) p = (AdjoinRoot.mk f) p- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.mapproof · cited by 806
- Polynomial.aevalstatement · cited by 615
- AdjoinRootstatement and proof · cited by 177
- AdjoinRoot.rootstatement · cited by 77
- AdjoinRoot.mkstatement and proof · cited by 50
- Polynomial.map_idproof · cited by 15
- Algebra.algebraMap_selfproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- AdjoinRoot.eval₂_rootproof · cited by 10
- AdjoinRoot.adjoinRoot_eq_topproof · cited by 4
- AdjoinRoot.minpoly_rootproof · cited by 3
- Polynomial.Monic.exists_splits_mapproof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.map_mkproof · cited by 2
- Polynomial.irreducible_compproof · cited by 1
- PowerBasis.quotientEquivQuotientMinpolyMap_apply_mkproof · cited by 0
- Irreducible.natDegree_dvd_iff_dvd_X_pow_card_pow_sub_Xproof · cited by 0
- Polynomial.isCoprime_iff_aeval_ne_zeroproof · cited by 0
- AdjoinRoot.coe_algHomOfDvdstatement · cited by 0