Theorems · Theorem · field theory
Polynomial.degree_map_eq_of_injective
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {f : R →+* S},
Function.Injective ⇑f → ∀ (p : Polynomial R), (Polynomial.map f p).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- WithBotstatement · cited by 1,498
- Polynomial.mapstatement · cited by 806
- Polynomial.degreestatement · cited by 643
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_map_eq_of_injectiveproof · cited by 11
- IsAlgebraic.extendScalarsproof · cited by 10
- Polynomial.degree_mapproof · cited by 10
- IsSepClosed.exists_eval₂_eq_zero_of_injectiveproof · cited by 2
- Polynomial.IsPrimitive.isUnit_iff_isUnit_map_of_injectiveproof · cited by 2
- IsAlgClosed.exists_eval₂_eq_zero_of_injectiveproof · cited by 2
- Polynomial.IsUnitTrinomial.irreducible_of_coprime'proof · cited by 1
- Polynomial.cyclotomic_dvd_of_mahlerMeasure_eq_oneproof · cited by 0