Theorems · Theorem · field theory
Algebra.normalizedTrace_minpoly
∀ (F : Type u_1) {K : Type u_2} [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra F K] [inst_3 : CharZero F]
[inst_4 : Algebra.IsIntegral F K] (a : K),
(Algebra.normalizedTrace F K) a = (↑(minpoly F a).natDegree)⁻¹ • -(minpoly F a).nextCoeffNormalized trace defined purely in terms of the degree and the next coefficient of the minimal polynomial. Could be an alternative definition but it is harder to work with linearity.
- Defined in
- Mathlib.FieldTheory.NormalizedTrace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Polynomial.natDegreestatement · cited by 1,105
- CharZerostatement and proof · cited by 932
- minpolystatement · cited by 439
- IsIntegralproof · cited by 427
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.IsIntegral.isIntegralproof · cited by 86
- Polynomial.nextCoeffstatement · cited by 46
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.normalizedTrace_algebraMap_of_liftsproof · cited by 1