Theorems · Theorem · field theory
Polynomial.count_roots
∀ {R : Type u} {a : R} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : DecidableEq R] (p : Polynomial R),
Multiset.count a p.roots = Polynomial.rootMultiplicity a p- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainDecidableEq
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.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Multisetproof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Multiset.countstatement and proof · cited by 302
- Polynomial.rootsstatement and proof · cited by 264
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- Polynomial.roots.congr_simpproof · cited by 31
- Multiset.count_eq_zero_of_notMemproof · cited by 27
- Multiset.count.congr_simpproof · cited by 22
- Polynomial.roots_zeroproof · cited by 19
- Polynomial.rootMultiplicity_zeroproof · cited by 11
Cited by19
Results whose statement or proof uses this declaration.
- Polynomial.roots_X_sub_Cproof · cited by 14
- Polynomial.roots_mulproof · cited by 12
- Polynomial.roots_Cproof · cited by 9
- Polynomial.mem_roots'proof · cited by 8
- Polynomial.map_roots_leproof · cited by 3
- Polynomial.roots_expand_powproof · cited by 3
- Polynomial.map_roots_comp_C_mul_X_add_Cproof · cited by 2
- Polynomial.roots_expand_pow_map_iterateFrobenius_leproof · cited by 2
- Polynomial.count_roots_le_oneproof · cited by 1
- Polynomial.nodup_roots_iff_of_splitsproof · cited by 1
- Polynomial.roots_scaleRootsproof · cited by 1
- Polynomial.eq_centerMass_of_eval_derivative_eq_zeroproof · cited by 1