Theorems · Theorem · field theory
Polynomial.natDegree_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).natDegree = p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 113 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.
- 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
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.mapstatement · cited by 806
- RingHom.injectiveproof · cited by 187
- IsSimpleRingstatement and proof · cited by 39
- Polynomial.natDegree_map_eq_of_injectiveproof · cited by 11
Cited by21
Results whose statement or proof uses this declaration.
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.card_rootSet_eq_natDegreeproof · cited by 3
- AlgHom.natCard_of_powerBasisproof · cited by 2
- RatFunc.natDegree_minpolyXproof · cited by 2
- Polynomial.natDegree_removeFactorproof · cited by 1
- IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_elementproof · cited by 1
- spectralNorm.spectralNorm_pow_natDegree_eq_prod_rootsproof · cited by 1
- Polynomial.exists_aroots_norm_sub_lt_of_norm_coeff_sub_ltproof · cited by 1
- minpoly.map_algebraMapproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- minpoly.map_eq_of_isSeparable_of_isPurelyInseparableproof · cited by 1
- Algebra.normalizedTrace_algebraMap_of_liftsproof · cited by 1