Bennett coeff mul trunc
ProvedD1Bound5.bennett_coeff_mul_truncdiophantine-tuplesnumber-theory
Truncating a multiplier preserves every coefficient below the truncation order, even when the other factor is an infinite series.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Degree.Operations import Mathlib.Algebra.Polynomial.Div import Mathlib.Algebra.Polynomial.PartialFractions import Mathlib.Algebra.Polynomial.RingDivision import Mathlib.LinearAlgebra.Matrix.Polynomial import Mathlib.RingTheory.PowerSeries.Binomial import Mathlib.RingTheory.PowerSeries.Trunc import Mathlib.Tactic.Ring
Formal statement
section
open Finset
namespace D1Bound5
variable {F : Type*} [Field F] [CharZero F]
section Nodes
variable {I : Type*} [Fintype I] [DecidableEq I]
theorem _root_.D1Bound5.bennett_coeff_mul_trunc (P θ : PowerSeries F) (D r : ℕ) (hr : r < D) :
PowerSeries.coeff r (P * (PowerSeries.trunc D θ : PowerSeries F)) =
PowerSeries.coeff r (P * θ) := by sorry
end Nodes
end D1Bound5
end
Source
D1Bound5/BennettResidualCancellation.lean, lines 106-117, SHA-256 0e8f4d1dac16aef29c7622ad8fa6e48d05646e38a9ebaf133da673991996797d. Project: https://github.com/tomislav-math/d1-bound5-lean