Theorems · Theorem · commutative algebra
Polynomial.eq_C_content_mul_primPart
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] (p : Polynomial R),
p = Polynomial.C p.content * p.primPart- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 107 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Polynomial.Cstatement and proof · cited by 1,598
- NormalizedGCDMonoidstatement and proof · cited by 159
- Polynomial.contentstatement and proof · cited by 41
- Polynomial.primPartstatement and proof · cited by 19
- Polynomial.content_zeroproof · cited by 5
- Polynomial.C_content_dvdproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.isPrimitive_primPartproof · cited by 4
- Polynomial.IsPrimitive.dvd_primPart_iff_dvdproof · cited by 2
- Polynomial.associated_primPart_mulproof · cited by 2
- Polynomial.natDegree_primPartproof · cited by 2
- Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPartproof · cited by 1
- Polynomial.isUnit_primPart_Cproof · cited by 1
- Polynomial.primPart_dvdproof · cited by 1
- Polynomial.IsPrimitive.primPart_eqproof · cited by 1
- Polynomial.eval₂_primPart_eq_zeroproof · cited by 0
- Polynomial.primPart_mulproof · cited by 0