Theorems · Theorem · field theory
eval_minpolyDiv_self
∀ {R : Type u_2} {S : Type u_1} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {x : S},
Polynomial.eval x (minpolyDiv R x) = (Polynomial.aeval x) (Polynomial.derivative (minpoly R x))- Defined in
- Mathlib.FieldTheory.Minpoly.MinpolyDiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xproof · cited by 1,639
Cited by1
Results whose statement or proof uses this declaration.
- eval₂_minpolyDiv_of_eval₂_eq_zeroproof · cited by 2