Theorems · Theorem · linear algebra

Lagrange.eval_basis_not_at_node

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {v : ι → F} {i : ι} {x : F},
  i ∈ s →
    x ≠ v i →
      Polynomial.eval x (Lagrange.basis s v i) =
        Polynomial.eval x (Lagrange.nodal s v) * (Lagrange.nodalWeight s v i * (x - v i)⁻¹)

Defined in

Mathlib.LinearAlgebra.Lagrange

Cited by

1 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldDecidableEq