Theorems · Theorem · commutative algebra
bernsteinPolynomial.sum_mul_smul
∀ (R : Type u_1) [inst : CommRing R] (n : ℕ), ∑ ν ∈ Finset.range (n + 1), (ν * (ν - 1)) • bernsteinPolynomial R n ν = (n * (n - 1)) • Polynomial.X ^ 2
- Defined in
- Mathlib.RingTheory.Polynomial.Bernstein
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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.
Cites51
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- CommSemiringproof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialproof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
Cited by1
Results whose statement or proof uses this declaration.
- bernsteinPolynomial.varianceproof · cited by 1