Theorems · Theorem · field theory
Polynomial.exists_max_root
∀ {R : Type u} [inst : CommRing R] [IsDomain R] [inst_2 : LinearOrder R] (p : Polynomial R),
p ≠ 0 → ∃ x₀, ∀ (x : R), p.IsRoot x → x ≤ x₀- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainLinearOrder
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Cites8
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
- LinearOrderstatement and proof · cited by 8,572
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.evalproof · cited by 796
- Polynomial.IsRootstatement · cited by 152
- Polynomial.finite_setOfPred_isRootproof · cited by 7
- Set.exists_upper_bound_imageproof · cited by 1
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