Theorems · Theorem · field theory
Polynomial.eval_rootOfSplits
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} (hf : f.Splits) (hfd : f.degree ≠ 0),
Polynomial.eval (Polynomial.rootOfSplits hf hfd) f = 0- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement · cited by 1,498
- Polynomial.evalstatement · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.Splits.exists_eval_eq_zeroproof · cited by 14
- Polynomial.rootOfSplitsstatement · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- rootOfSplitsXPowSubC_powproof · cited by 2
- Polynomial.Gal.prime_degree_dvd_cardproof · cited by 1
- Polynomial.natSepDegree_ne_zeroproof · cited by 1
- IntermediateField.Lifts.exists_lift_of_splits'proof · cited by 1
- IsAlgClosed.of_denseRangeproof · cited by 0