Theorems · Definition · field theory
Polynomial.Splits
{R : Type u_1} → [inst : Semiring R] → Polynomial R → PropA polynomial Splits if it is a product of constant and monic linear polynomials.
- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 290 results in Mathlib
- Foundations
- Depth 101 from the axioms, rests on 1,822 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Set.ofPredproof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Submonoid.closureproof · cited by 167
Cited by319
Results whose statement or proof uses this declaration.
- IsAlgClosed.splitsstatement · cited by 29
- Polynomial.Splits.of_dvdstatement and proof · cited by 21
- Polynomial.SplittingField.splitsstatement · cited by 21
- Polynomial.Splits.mapstatement and proof · cited by 19
- Polynomial.Splits.mulstatement and proof · cited by 18
- Polynomial.Splits.natDegree_eq_card_rootsstatement and proof · cited by 16
- IsGalois.card_aut_eq_finrankproof · cited by 16
- Polynomial.Splits.eq_prod_rootsstatement and proof · cited by 16
- Polynomial.Splits.exists_eval_eq_zerostatement and proof · cited by 14
- Polynomial.IsSplittingField.splitsstatement · cited by 14
- Polynomial.splits_iff_card_rootsstatement and proof · cited by 11
- Polynomial.Splits.roots_mapstatement and proof · cited by 10
Showing the 200 most cited of 319.