Theorems · Definition · commutative algebra
Polynomial.monicEquivDegreeLT
{R : Type u} →
[inst : Semiring R] → [Nontrivial R] → (n : ℕ) → { p // p.Monic ∧ p.natDegree = n } ≃ ↥(Polynomial.degreeLT R n)The equivalence between monic polynomials of degree n and polynomials of degree less than
n, formed by adding a term X ^ n.
- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Equivstatement · cited by 8,337
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.eraseLeadproof · cited by 65
- Polynomial.degreeLTstatement and proof · cited by 47
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Field.realize_genericMonicPolyHasRootproof · cited by 1
- FirstOrder.Field.lift_genericMonicPolystatement · cited by 1
- Polynomial.monicEquivDegreeLT.congr_simpstatement and proof · cited by 0