Theorems · Theorem · field theory
Polynomial.degree_derivative
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} [IsAddTorsionFree R],
p.natDegree ≠ 0 → (Polynomial.derivative p).degree = ↑(p.natDegree - 1)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIsAddTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- le_antisymmproof · cited by 2,068
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotstatement · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- le_transproof · cited by 985
Cited by3
Results whose statement or proof uses this declaration.
- Irreducible.separableproof · cited by 6
- Polynomial.natDegree_derivativeproof · cited by 1
- Polynomial.degree_derivative_eqproof · cited by 0