Theorems · Theorem · field theory
Polynomial.natDegree_map_le
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {f : R →+* S} {p : Polynomial R},
(Polynomial.map f p).natDegree ≤ p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 108 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.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.mapstatement · cited by 806
- Polynomial.natDegree_le_natDegreeproof · cited by 12
- Polynomial.degree_map_leproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.Monic.natDegree_mapproof · cited by 21
- Polynomial.card_roots_map_le_natDegreeproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- RatFunc.irreducible_minpolyXproof · cited by 1
- Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegreeproof · cited by 1
- Polynomial.IsWeaklyEisensteinAt.mapproof · cited by 1
- isIntegral_of_isIntegralElem_of_monic_of_natDegree_ltproof · cited by 1
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1
- Polynomial.Gal.splits_in_splittingField_of_compproof · cited by 1
- sum_smul_minpolyDiv_eq_X_powproof · cited by 1
- IsPrimitiveRoot.totient_le_degree_minpolyproof · cited by 1
- Polynomial.aeval_sumIDeriv_of_posproof · cited by 1