(* ::Package:: *)

(*******************************************************)
(*  This file contains the integrability relations for the      *)
(*  coproduct of a consistent hexagon function, denoted using   *)
(*  the following notation:                                     *)  
(*                                                              *)
(*       F[a_,b_] = F^{a,b}                                    *)
(*                                                              *)
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F[1-w,yu]==F[1-w,yv]+F[yu,1-w]-F[yv,1-w]


F[1-v,yv]==F[1-v,yw]-F[1-w,yv]+F[1-w,yw]+F[yv,1-v]+F[yv,1-w]-F[yw,1-v]-F[yw,1-w]


F[1-v,yu]==F[1-v,yw]+F[yu,1-v]-F[yw,1-v]


F[1-v,1-w]==F[1-w,1-v]+F[yu,yv]-F[yu,yw]-F[yv,yu]+F[yv,yw]+F[yw,yu]-F[yw,yv]


F[1-u,yv]==F[1-u,yw]+F[yv,1-u]-F[yw,1-u]


F[1-u,yu]==F[1-u,yw]-F[1-w,yv]+F[1-w,yw]+F[yu,1-u]+F[yv,1-w]-F[yw,1-u]-F[yw,1-w]


F[1-u,1-w]==F[1-w,1-u]-F[yu,yv]+F[yu,yw]+F[yv,yu]-F[yv,yw]-F[yw,yu]+F[yw,yv]


F[1-u,1-v]==F[1-v,1-u]+F[yu,yv]-F[yu,yw]-F[yv,yu]+F[yv,yw]+F[yw,yu]-F[yw,yv]


F[w,yw]==F[yw,w]


F[w,yv]==-F[1-u,yw]+F[yv,w]+F[yw,1-u]


F[w,yu]==-F[1-v,yw]+F[yu,w]+F[yw,1-v]


F[w,1-v]==F[1-v,w]-F[yu,yw]+F[yw,yu]


F[w,1-u]==F[1-u,w]-F[yv,yw]+F[yw,yv]


F[v,yw]==-F[1-u,yw]+F[yw,1-u]+F[yw,v]


F[v,yv]==F[yv,v]


F[v,yu]==-F[1-w,yv]+F[yu,v]+F[yv,1-w]


F[v,1-w]==F[1-w,v]-F[yu,yv]+F[yv,yu]


F[v,1-u]==F[1-u,v]+F[yv,yw]-F[yw,yv]


F[v,w]==F[w,v]-F[yv,yw]+F[yw,yv]


F[u,yw]==-F[1-v,yw]+F[yw,u]+F[yw,1-v]


F[u,yv]==-F[1-w,yv]+F[yv,u]+F[yv,1-w]


F[u,yu]==F[yu,u]


F[u,1-w]==F[1-w,u]+F[yu,yv]-F[yv,yu]


F[u,1-v]==F[1-v,u]+F[yu,yw]-F[yw,yu]


F[u,w]==F[w,u]-F[yu,yw]+F[yw,yu]


F[u,v]==F[v,u]-F[yu,yv]+F[yv,yu]
