Theorems · Theorem · field theory

Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors

∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {t : R},
  p.IsRoot t →
    ↑(Polynomial.rootMultiplicity t p) ∈ nonZeroDivisors R →
      Polynomial.rootMultiplicity t (Polynomial.derivative p) = Polynomial.rootMultiplicity t p - 1

Defined in: Mathlib.Algebra.Polynomial.FieldDivision
Cited by: 1 results in Mathlib
Foundations: Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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DFunLike.coestatement and proof · cited by 62,936
RingHom.idstatement · cited by 18,349
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Submonoidstatement · cited by 3,086
mul_commproof · cited by 2,262
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map_zeroproof · cited by 1,614
Polynomial.Cproof · cited by 1,598

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Polynomial.derivative_rootMultiplicity_of_rootproof · cited by 3