Theorems · Theorem · field theory
Polynomial.rootMultiplicity_zero
∀ {R : Type u} [inst : Ring R] {x : R}, Polynomial.rootMultiplicity x 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- Polynomial.rootMultiplicitystatement · cited by 79
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.count_rootsproof · cited by 19
- Polynomial.pow_rootMultiplicity_dvdproof · cited by 9
- Polynomial.derivative_rootMultiplicity_of_rootproof · cited by 3
- Polynomial.rootMultiplicity_expand_powproof · cited by 2
- Polynomial.rootMultiplicity_eq_natTrailingDegree'proof · cited by 1
- Polynomial.rootMultiplicity_le_one_of_separableproof · cited by 1
- Polynomial.eq_rootMultiplicity_mapproof · cited by 1
- Polynomial.rootMultiplicity_scaleRootsproof · cited by 1
- Polynomial.rootMultiplicity_Cproof · cited by 1
- Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisorsproof · cited by 1
- Polynomial.count_map_roots_of_injectiveproof · cited by 0