Theorems · Definition · commutative algebra
bernsteinPolynomial
(R : Type u_1) → [inst : CommRing R] → ℕ → ℕ → Polynomial R
bernsteinPolynomial R n ν is (choose n ν) * X^ν * (1 - X)^(n - ν).
Although the coefficients are integers, it is convenient to work over an arbitrary commutative ring.
- Defined in
- Mathlib.RingTheory.Polynomial.Bernstein
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 98 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Nat.chooseproof · cited by 494
Cited by27
Results whose statement or proof uses this declaration.
- bernsteinproof · cited by 7
- bernstein_applyproof · cited by 4
- bernsteinPolynomial.derivative_succstatement and proof · cited by 2
- bernsteinPolynomial.eval_at_0statement · cited by 2
- bernsteinPolynomial.flip'statement and proof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0statement and proof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_ltstatement and proof · cited by 2
- bernsteinPolynomial.sumstatement and proof · cited by 2
- bernstein.probabilityproof · cited by 1
- bernstein.varianceproof · cited by 1
- bernsteinPolynomial.derivative_succ_auxstatement and proof · cited by 1
- bernsteinPolynomial.eq_zero_of_ltstatement · cited by 1