Theorems · Theorem · field theory
Polynomial.roots_C
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (x : R), (Polynomial.C x).roots = 0- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 9 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.
Cites17
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 and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.countproof · cited by 302
- Polynomial.rootsstatement and proof · cited by 264
- Polynomial.rootMultiplicityproof · cited by 79
- Polynomial.C_0proof · cited by 40
- Polynomial.count_rootsproof · cited by 19
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.roots_C_mulproof · cited by 9
- Polynomial.roots_oneproof · cited by 8
- Polynomial.nthRoots_zeroproof · cited by 5
- Polynomial.aroots_Cproof · cited by 3
- Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succproof · cited by 3
- Polynomial.roots_quadratic_eq_pair_iff_of_ne_zeroproof · cited by 2
- IsAlgClosed.roots_eq_zero_iffproof · cited by 1
- Polynomial.Splits.roots_map_of_ne_zeroproof · cited by 1
- IsSepClosed.roots_eq_zero_iffproof · cited by 0