Theorems · Definition · commutative algebra
Polynomial.primPart
{R : Type u_1} → [inst : CommRing R] → [NormalizedGCDMonoid R] → Polynomial R → Polynomial RThe primitive part of a polynomial p is the primitive polynomial gained by dividing p by
p.content. If p = 0, then p.primPart = 1.
- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 105 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.
Cites4
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
- NormalizedGCDMonoidstatement and proof · cited by 159
- Polynomial.C_content_dvdproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- Polynomial.eq_C_content_mul_primPartstatement and proof · cited by 14
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.isPrimitive_primPartstatement and proof · cited by 4
- Polynomial.primPart_zerostatement · cited by 3
- Polynomial.IsPrimitive.dvd_primPart_iff_dvdstatement and proof · cited by 2
- Polynomial.associated_primPart_mulstatement and proof · cited by 2
- Polynomial.primPart_ne_zerostatement · cited by 2
- Polynomial.natDegree_primPartstatement and proof · cited by 2
- Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPartstatement and proof · cited by 1
- Polynomial.isUnit_primPart_Cstatement and proof · cited by 1
- Polynomial.primPart_dvdstatement · cited by 1