Theorems · Theorem · field theory
Polynomial.monic_X_sub_C
∀ {R : Type u} [inst : Ring R] (x : R), (Polynomial.X - Polynomial.C x).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 109 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.
Cites10
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
- sub_eq_add_negproof · cited by 1,023
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.C_negproof · cited by 25
- Polynomial.monic_X_add_Cproof · cited by 9
Cited by41
Results whose statement or proof uses this declaration.
- Polynomial.dvd_iff_isRootproof · cited by 15
- RingHom.isIntegralElem_mapproof · cited by 8
- Polynomial.modByMonic_X_sub_C_eq_C_evalproof · cited by 7
- Polynomial.finiteMultiplicity_X_sub_Cproof · cited by 7
- Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardproof · cited by 6
- minpoly.eq_X_sub_C_of_algebraMap_injproof · cited by 4
- Polynomial.monic_multisetProd_X_sub_Cproof · cited by 4
- Matrix.charpoly_degree_eq_dimproof · cited by 4
- Polynomial.resultant_X_sub_C_leftproof · cited by 3
- Polynomial.pow_mul_divByMonic_rootMultiplicity_eqproof · cited by 3
- Polynomial.cyclotomic'.monicproof · cited by 3
- Polynomial.rootMultiplicity_mul_X_sub_C_powproof · cited by 3