Theorems · Theorem · commutative algebra
Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt
∀ {F : Type u_1} [inst : Field F] [CharZero F] {p : Polynomial F} {d : ℕ},
p ≠ 0 → Polynomial.rootMultiplicity 1 p < d → (p.hilbertPoly d).natDegree = d - Polynomial.rootMultiplicity 1 p - 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringproof · cited by 13,802
- AddCommMonoidproof · cited by 12,281
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- mul_assocproof · cited by 1,667
- Polynomial.Xproof · cited by 1,639
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_hilbertPoly_of_ne_zeroproof · cited by 0