Theorems · Theorem · field theory
Polynomial.roots_one
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R], Polynomial.roots 1 = ∅- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.rootsstatement · cited by 264
- Polynomial.roots_Cproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.roots_powproof · cited by 4
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.Chebyshev.roots_T_realproof · cited by 2
- Polynomial.Chebyshev.roots_U_realproof · cited by 2
- Polynomial.Splits.roots_map_of_ne_zeroproof · cited by 1
- Polynomial.roots_list_prodproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1