Theorems · Theorem · field theory

Polynomial.rootMultiplicity_add

∀ {R : Type u} [inst : CommRing R] {p q : Polynomial R} (a : R),
  p + q ≠ 0 →
    min (Polynomial.rootMultiplicity a p) (Polynomial.rootMultiplicity a q) ≤ Polynomial.rootMultiplicity a (p + q)

The multiplicity of p + q is at least the minimum of the multiplicities.

Defined in: Mathlib.Algebra.Polynomial.Div
Cited by: 0 results in Mathlib
Foundations: Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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CommRingstatement and proof · cited by 17,173
Polynomialstatement and proof · cited by 5,681
Polynomial.rootMultiplicitystatement · cited by 79
Polynomial.le_rootMultiplicity_iffproof · cited by 10
Polynomial.pow_rootMultiplicity_dvdproof · cited by 9
min_pow_dvd_addproof · cited by 1

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