Theorems · Theorem · field theory
minpoly.neg
∀ {A : Type u_1} [inst : Field A] {B : Type u_3} [inst_1 : Ring B] [inst_2 : Algebra A B] (x : B),
minpoly A (-x) = (-1) ^ (minpoly A x).natDegree * (minpoly A x).comp (-Polynomial.X)- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xstatement and proof · cited by 1,639
- map_mulproof · cited by 1,137
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- neg_negproof · cited by 960
Cited by2
Results whose statement or proof uses this declaration.
- minpoly_neg_splitsproof · cited by 1
- IsConjRoot.negproof · cited by 0