Theorems · Theorem · field theory
Polynomial.roots_X_sub_C
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (r : R), (Polynomial.X - Polynomial.C r).roots = {r}- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.countproof · cited by 302
- Polynomial.rootsstatement · cited by 264
- Multiset.ext'proof · cited by 31
- Polynomial.count_rootsproof · cited by 19
Cited by14
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesproof · cited by 4
- LinearMap.IsSymmetric.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Polynomial.roots_multiset_prod_X_sub_Cproof · cited by 3
- Polynomial.roots_Xproof · cited by 3
- Polynomial.roots_X_pow_char_pow_sub_Cproof · cited by 2
- Polynomial.roots_prod_X_sub_Cproof · cited by 2
- Polynomial.roots_quadratic_eq_pair_iff_of_ne_zeroproof · cited by 2
- Polynomial.aroots_X_sub_Cproof · cited by 2
- Polynomial.roots_C_mul_X_sub_C_of_IsUnitproof · cited by 2
- Polynomial.roots_X_add_Cproof · cited by 2
- Polynomial.splits_X_sub_C_mul_iffproof · cited by 1
- Polynomial.roots_countP_pos_le_signVariationsproof · cited by 0