Theorems · Theorem · field theory
Polynomial.card_roots
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {p : Polynomial R}, p ≠ 0 → ↑p.roots.card ≤ p.degree- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 7 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.
Cites9
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
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Multiset.cardstatement and proof · cited by 375
- Polynomial.rootsstatement · cited by 264
- Polynomial.exists_multiset_rootsproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.card_roots'proof · cited by 9
- Polynomial.card_nthRootsproof · cited by 3
- Polynomial.roots_eq_of_degree_le_card_of_ne_zeroproof · cited by 2
- Polynomial.card_roots_sub_Cproof · cited by 1
- Polynomial.card_roots_X_pow_sub_Cproof · cited by 0
- Polynomial.card_roots_map_le_degreeproof · cited by 0
- Cubic.card_roots_leproof · cited by 0