Theorems · Theorem · field theory
Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] (p : Polynomial R) {ι : Type u_2} [inst_2 : Fintype ι] {f : ι → R},
Function.Injective f → (∀ (i : ι), Polynomial.eval (f i) p = 0) → p.natDegree < Fintype.card ι → p = 0- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Set.rangeproof · cited by 4,705
- Finset.univproof · cited by 3,473
- Finset.cardproof · cited by 2,327
- IsDomainstatement and proof · cited by 2,196
- Fintype.cardstatement and proof · cited by 1,386
- Polynomial.natDegreestatement and proof · cited by 1,105
- Finset.imageproof · cited by 910
- Polynomial.evalstatement and proof · cited by 796
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero'proof · cited by 2
- Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_cardproof · cited by 2
- Polynomial.eq_of_natDegree_lt_card_of_eval_eqproof · cited by 1
- sum_smul_minpolyDiv_eq_X_powproof · cited by 1