Theorems · Theorem · field theory
Polynomial.leadingCoeff_derivative
∀ {R : Type u} [inst : Semiring R] [IsAddTorsionFree R] (p : Polynomial R),
(Polynomial.derivative p).leadingCoeff = p.leadingCoeff * ↑p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 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.
Cites15
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
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.derivativestatement and proof · cited by 331
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