Theorems · Theorem · commutative algebra
bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt
∀ (R : Type u_1) [inst : CommRing R] (n : ℕ) {ν k : ℕ},
k < ν → Polynomial.eval 0 ((⇑Polynomial.derivative)^[k] (bernsteinPolynomial R n ν)) = 0- Defined in
- Mathlib.RingTheory.Polynomial.Bernstein
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
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- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- sub_zeroproof · cited by 938
- Polynomial.evalstatement and proof · cited by 796
- Nat.iteratestatement and proof · cited by 740
- LT.lt.trans_leproof · cited by 678
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.eval_mulproof · cited by 127
Cited by2
Results whose statement or proof uses this declaration.
- bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zeroproof · cited by 1
- bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_ltproof · cited by 1