Theorems · Theorem · field theory
Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {p : Polynomial R} (f : R →+* S),
f p.leadingCoeff ≠ 0 → (Polynomial.map f p).leadingCoeff = f p.leadingCoeff- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.natDegree_map_of_leadingCoeff_ne_zeroproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- RingHom.isIntegralElem_localization_at_leadingCoeffproof · cited by 2
- Polynomial.leadingCoeff_le_mapMahlerMeasureproof · cited by 1
- Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeffproof · cited by 1
- Polynomial.integralNormalization_mapproof · cited by 1