Theorems · Definition · commutative algebra
Polynomial.content
{R : Type u_1} → [inst : CommRing R] → [NormalizedGCDMonoid R] → Polynomial R → Rp.content is the gcd of the coefficients of p.
- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 60 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.
Cites6
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
- Polynomial.coeffproof · cited by 1,045
- Polynomial.supportproof · cited by 237
- NormalizedGCDMonoidstatement and proof · cited by 159
- Finset.gcdproof · cited by 49
Cited by41
Results whose statement or proof uses this declaration.
- Polynomial.eq_C_content_mul_primPartstatement and proof · cited by 14
- Polynomial.normalize_contentstatement · cited by 8
- Polynomial.content_eq_zero_iffstatement · cited by 7
- Polynomial.associated_content_mulstatement and proof · cited by 6
- Polynomial.IsPrimitive.content_eq_onestatement · cited by 5
- Polynomial.content_Cstatement · cited by 5
- Polynomial.content_zerostatement and proof · cited by 5
- Polynomial.associated_content_C_mulstatement and proof · cited by 4
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.isPrimitive_iff_content_eq_onestatement and proof · cited by 4
- Polynomial.isPrimitive_primPartproof · cited by 4
- Polynomial.IsPrimitive.mulproof · cited by 3