Theorems · Theorem · linear algebra

Lagrange.interpolate_eq_add_interpolate_erase

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {i j : ι} {v : ι → F}
  (r : ι → F),
  Set.InjOn v ↑s →
    i ∈ s →
      j ∈ s →
        i ≠ j →
          (Lagrange.interpolate s v) r =
            (Lagrange.interpolate (s.erase j) v) r * Lagrange.basisDivisor (v i) (v j) +
              (Lagrange.interpolate (s.erase i) v) r * Lagrange.basisDivisor (v j) (v i)

Defined in

Mathlib.LinearAlgebra.Lagrange

Cited by

0 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldDecidableEq