Theorems · Theorem · field theory
Polynomial.monic_X_pow_sub_C
∀ {R : Type u} [inst : Ring R] (a : R) {n : ℕ}, n ≠ 0 → (Polynomial.X ^ n - Polynomial.C a).MonicX ^ n - a is monic.
- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.Monicstatement and proof · cited by 461
- map_negproof · cited by 378
- Polynomial.monic_X_pow_add_Cproof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.isIntegralproof · cited by 15
- IsPurelyInseparable.elemExponent_le_of_pow_memproof · cited by 3
- IsCyclotomicExtension.finite_of_singletonproof · cited by 2
- root_X_pow_sub_C_ne_zeroproof · cited by 2
- minpoly_algEquiv_toLinearMapproof · cited by 2
- IsCyclotomicExtension.integralproof · cited by 2
- IsIntegrallyClosed.pow_dvd_pow_iffproof · cited by 2
- Polynomial.X_pow_sub_one_eq_prodproof · cited by 1
- X_pow_mul_sub_C_irreducibleproof · cited by 1
- irreducible_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRootproof · cited by 1
- Polynomial.not_isUnit_X_pow_sub_oneproof · cited by 0