Research proof index

The reduce of TenQuanta is a new TenQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.toCharges.dedup.map fun q10 => (q10, ((x.filter (fun f => f.1 = q10)).map (fun y => y.2)).sum) /-! ### B.1. The reduced TenQuanta has no duplicate elements -/ lem...

The reduce of TenQuanta is a new TenQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.toCharges.dedup.map fun q10 => (q10, ((x.filter (fun f => f.1 = q10)).map (fun y => y.2)).sum) /-! ### B.1. The reduced TenQuanta has no duplicate elements -/ lem...

Given a finite set of charges c the TenQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. This is defined to be as efficient as possible. -/ def liftCharge (c : Finset 𝓩) : Multiset (TenQuanta 𝓩) := /- The {(1, 0), (1, 0), (1, 0)} case. -/ /- The multisets of cardinality 3 containing 3 elements of c. -/ let...

A version of fundamental_theorem_of_variational_calculus' for Continuous f. The proof uses assumption that source of f is finite-dimensional inner-product space, so that a bump function with compact support exists via ContDiffBump.hasCompactSupport from Analysis.Calculus.BumpFunction.Basic. The proof is by contradiction, assume that there is `x₀...

A version of fundamental_theorem_of_variational_calculus' for Continuous f. The proof uses assumption that source of f is finite-dimensional inner-product space, so that a bump function with compact support exists via ContDiffBump.hasCompactSupport from Analysis.Calculus.BumpFunction.Basic. The proof is by contradiction, assume that there is `x₀...

G(1/s) = s^10 * (H₄(is))³ * (2(H₄(is))² + 5H₂(is)H₄(is) + 5(H₂(is))²)