_artin_braid_local for uniquefusion case

Author: borisdevos

src/fusiontrees/braiding_manipulations.jl

@@ -65,14 +65,7 @@ function artin_braid(f::FusionTree{I, N}, i; inv::Bool = false) where {I, N}
     c = inner_extended[i]
     e = inner_extended[i + 1]
     c′ = only(a ⊗ d)
-    coeff = oftype(
-        oneT,
-        if inv
-            conj(Rsymbol(d, c, e) * Fsymbol(d, a, b, e, c′, c)) * Rsymbol(d, a, c′)
-        else
-            Rsymbol(c, d, e) * conj(Fsymbol(d, a, b, e, c′, c) * Rsymbol(a, d, c′))
-        end
-    )
+    coeff = oftype(oneT, _artin_braid_local((a, b, c, d, e, c′), inv))
     inner′ = TupleTools.setindex(inner, c′, i - 1)
     f′ = FusionTree{I}(uncoupled′, coupled′, isdual′, inner′)
     return f′ => coeff