Theorems · Theorem · field theory
Polynomial.nextCoeff_map_eq_of_isUnit_leadingCoeff
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] [Nontrivial S] (f : R →+* S),
IsUnit p.leadingCoeff → (Polynomial.map f p).nextCoeff = f p.nextCoeff- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringSemiringNontrivial
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- IsUnitstatement and proof · cited by 1,602
- Polynomial.mapstatement · cited by 806
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.nextCoeffstatement · cited by 46
- IsUnit.ne_zeroproof · cited by 36
- RingHom.isUnit_mapproof · cited by 14
- Polynomial.nextCoeff_map_of_leadingCoeff_ne_zeroproof · cited by 1
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