Theorems · Theorem · field theory
Polynomial.degree_X_pow_sub_C
∀ {R : Type u} [inst : Ring R] [Nontrivial R] {n : ℕ},
0 < n → ∀ (a : R), (Polynomial.X ^ n - Polynomial.C a).degree = ↑n- Cited by
- 14 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHomstatement · 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.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- WithBotstatement and proof · cited by 1,498
- sub_eq_add_negproof · cited by 1,023
- Polynomial.degreestatement and proof · cited by 643
- map_negproof · cited by 378
- Polynomial.degree_X_pow_add_Cproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- pow_ne_of_irreducible_X_pow_sub_Cproof · cited by 4
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- Polynomial.card_nthRootsproof · cited by 3
- X_pow_sub_C_irreducible_of_primeproof · cited by 2
- rootOfSplitsXPowSubC_powproof · cited by 2
- minpoly_algEquiv_toLinearMapproof · cited by 2
- IsAlgClosed.exists_pow_nat_eqproof · cited by 2
- ZMod.sq_add_sqproof · cited by 2
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- irreducible_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- splits_X_pow_sub_one_of_X_pow_sub_Cproof · cited by 1
- IsSepClosed.exists_pow_nat_eqproof · cited by 1