Theorems · Definition · field theory
Polynomial.hasseDeriv
{R : Type u_1} → [inst : Semiring R] → ℕ → Polynomial R →ₗ[R] Polynomial RThe kth Hasse derivative of a polynomial ∑ a_i X^i is ∑ (i.choose k) a_i X^(i-k).
It satisfies k! * (hasse_deriv k f) = derivative^[k] f.
- Defined in
- Mathlib.Algebra.Polynomial.HasseDeriv
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- LinearMap.compproof · cited by 1,642
- Nat.chooseproof · cited by 494
- Polynomial.monomialproof · cited by 256
- DistribSMul.toLinearMapproof · cited by 50
- Polynomial.lsumproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- Polynomial.hasseDeriv_applystatement · cited by 6
- Polynomial.hasseDeriv_monomialstatement · cited by 5
- Polynomial.taylor_coeffstatement and proof · cited by 4
- Polynomial.hasseDeriv_coeffstatement · cited by 3
- Polynomial.hasseDeriv_zerostatement · cited by 2
- Polynomial.hasseDeriv_Cstatement and proof · cited by 1
- Polynomial.hasseDeriv_eq_zero_of_lt_natDegreestatement · cited by 1
- Polynomial.hasseDeriv_natDegree_eq_Cstatement and proof · cited by 1
- Polynomial.hasseDeriv_onestatement · cited by 1
- Polynomial.hasseDeriv_one'statement · cited by 1
- Polynomial.hasseDeriv_zero'statement · cited by 1
- Polynomial.natDegree_hasseDeriv_lestatement · cited by 1