Theorems · Theorem · field theory
Polynomial.roots_zero
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R], Polynomial.roots 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 19 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 · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.rootsstatement · cited by 264
Cited by19
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_Cproof · cited by 9
- Polynomial.card_roots'proof · cited by 9
- Polynomial.roots_powproof · cited by 4
- Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_rootsproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succproof · cited by 3
- IntermediateField.AdjoinSimple.norm_gen_eq_prod_rootsproof · cited by 2
- IntermediateField.AdjoinSimple.trace_gen_eq_sum_rootsproof · cited by 1
- Polynomial.map_roots_le_of_injectiveproof · cited by 1