Theorems · Definition · field theory
Polynomial.MonicDegreeEq
(R : Type u) → ℕ → [Semiring R] → Type u
The type of monic polynomials of degree n.
The implementation is slightly different because it is useful to still contain X ^ n when
R is trivial. See MonicDegreeEq.mk for the usual constructor.
- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Polynomialproof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
Cited by38
Results whose statement or proof uses this declaration.
- Polynomial.MonicDegreeEq.mapstatement and proof · cited by 12
- Polynomial.UniversalFactorizationRingstatement and proof · cited by 10
- MvPolynomial.mapEquivMonicstatement and proof · cited by 10
- Polynomial.UniversalCoprimeFactorizationRingstatement and proof · cited by 7
- Polynomial.MonicDegreeEq.map_coestatement and proof · cited by 6
- Polynomial.UniversalFactorizationRing.factor₁statement and proof · cited by 6
- Polynomial.UniversalFactorizationRing.factor₂statement and proof · cited by 6
- Polynomial.UniversalFactorizationRing.presentationstatement and proof · cited by 6
- Polynomial.MonicDegreeEq.freeMonicstatement · cited by 4
- Polynomial.UniversalCoprimeFactorizationRing.factor₁statement and proof · cited by 4
- Polynomial.UniversalCoprimeFactorizationRing.factor₂statement and proof · cited by 4
- Polynomial.UniversalFactorizationRing.fromTensorstatement and proof · cited by 4