Theorems · Theorem · field theory
Polynomial.hasseDeriv_monomial
∀ {R : Type u_1} [inst : Semiring R] (k n : ℕ) (r : R),
(Polynomial.hasseDeriv k) ((Polynomial.monomial n) r) = (Polynomial.monomial (n - k)) (↑(n.choose k) * r)- Defined in
- Mathlib.Algebra.Polynomial.HasseDeriv
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 100 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.
Cites16
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 · cited by 5,681
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- MulZeroClass.zero_mulproof · cited by 1,625
- Nat.choosestatement and proof · cited by 494
- Polynomial.monomialstatement and proof · cited by 256
- Polynomial.extproof · cited by 118
- Polynomial.coeff_monomialproof · cited by 40
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.taylor_coeffproof · cited by 4
- Polynomial.hasseDeriv_Cproof · cited by 1
- Polynomial.hasseDeriv_mulproof · cited by 0
- Polynomial.natDegree_hasseDerivproof · cited by 0
- Polynomial.hasseDeriv_Xproof · cited by 0