Theorems · Theorem · field theory
Polynomial.roots.congr_simp
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (p p_1 : Polynomial R), p = p_1 → p.roots = p_1.roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.rootsstatement and proof · cited by 264
Cited by31
Results whose statement or proof uses this declaration.
- Polynomial.count_rootsproof · cited by 19
- Polynomial.Splits.natDegree_eq_card_rootsproof · cited by 16
- Polynomial.Splits.eq_prod_rootsproof · cited by 16
- Polynomial.roots_C_mulproof · cited by 9
- Polynomial.card_roots'proof · cited by 9
- Polynomial.nthRoots_zeroproof · cited by 5
- Polynomial.natSepDegree_expandproof · cited by 4
- Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_rootsproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · 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