Theorems · Theorem · field theory
Polynomial.degree_map
∀ {R : Type u} {S : Type v} [inst : Ring R] [IsSimpleRing R] [inst_2 : Semiring S] [Nontrivial S] (p : Polynomial R)
(f : R →+* S), (Polynomial.map f p).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- WithBotstatement · cited by 1,498
- Polynomial.mapstatement · cited by 806
- Polynomial.degreestatement · cited by 643
- RingHom.injectiveproof · cited by 187
- IsSimpleRingstatement and proof · cited by 39
- Polynomial.degree_map_eq_of_injectiveproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- splits_X_pow_sub_one_of_X_pow_sub_Cproof · cited by 1
- Polynomial.Irreducible.natDegree_dvd_finrankproof · cited by 1
- Polynomial.Gal.prime_degree_dvd_cardproof · cited by 1
- Polynomial.Gal.splits_in_splittingField_of_compproof · cited by 1
- IntermediateField.Lifts.exists_lift_of_splits'proof · cited by 1
- Polynomial.isUnit_mapproof · cited by 1
- Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosedproof · cited by 0
- Polynomial.lift_of_splitsproof · cited by 0
- IsAlgClosed.of_denseRangeproof · cited by 0
- IsAlgClosed.of_ringEquivproof · cited by 0