Theorems · Theorem · commutative algebra
Polynomial.content_eq_gcd_range_of_lt
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] (p : Polynomial R) (n : ℕ),
p.natDegree < n → p.content = (Finset.range n).gcd p.coeff- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNormalizedGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finset.rangestatement and proof · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement · cited by 1,045
- NormalizedGCDMonoidstatement and proof · cited by 159
- Finset.gcdstatement · cited by 49
- Polynomial.contentstatement · cited by 41
- dvd_antisymm_of_normalize_eqproof · cited by 15
- Finset.dvd_gcd_iffproof · cited by 9
- Polynomial.normalize_contentproof · cited by 8
- Finset.normalize_gcdproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.gcd_content_eq_of_dvd_subproof · cited by 1
- Polynomial.content_eq_gcd_range_succproof · cited by 0