Homogeneous Multiset Sum singleton
ProvedD1Bound5.homogeneousMultisetSum_singletondiophantine-tuplesnumber-theory
A single variable has exactly one monomial in each degree.
Preamble
import Mathlib.Data.Finset.Insert import Mathlib.Data.Sym.Basic import Mathlib.LinearAlgebra.Lagrange import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Definitions.Def_D1Bound5_HomogeneousSymmetric_Definitions
Formal statement
section
open Polynomial Finset
namespace D1Bound5
theorem _root_.D1Bound5.homogeneousMultisetSum_singleton
{ι R : Type*} [DecidableEq ι] [CommSemiring R]
(a : ι → R) (t : ι) (n : ℕ) :
homogeneousMultisetSum (fun i : ({t} : Finset ι) => a i) n = (a t)^n := by sorry
end D1Bound5
end
Source
D1Bound5/LagrangeHomogeneous.lean, lines 36-49, SHA-256 b4a9130e2e09325e0a7c90a60c13433e1e3d45746589329d45719e084b45b442. Project: https://github.com/tomislav-math/d1-bound5-lean