(********************************************************************)
(*                                                                  *)
(*  Ancillary file to                                               *)
(*  "Bootstrapping a Five-Loop Amplitude from Steinmann Relations"  *)
(*  by S. Caron-Huot, L. Dixon, A. McLeod, and M. von Hippel        *)
(*  arXiv:1609.00669                                                *)
(*                                                                  *)
(*  This file contains expressions for the coefficients multiplying *)
(*  powers of log(u*w/v) in the multi-particle factorization limit  *)
(*  s_{345} -> 0, or u,w -> 0 with u/w and v fixed,                 *)
(*  for the NMHV quantity                                           *)
(*         U(u,v,w)                                                 *)
(*  defined in eqs. (5.15) and (5.23) of arXiv:1408.1505,           *)
(*  through five loops.                                             *)
(*                                                                  *)
(*  In the notation of arXiv:1609.00669, we have                    *)
(*         U(u,v,w) = log[E(u,v,w)]                                 *)
(*                                                                  *)
(*  We expand U in the loop counting parameter g^2,                 *)
(*  not in a = 2*g^2 as was done in arXiv:1408.1505.                *)
(*  So the L-loop results here are 2^L times larger than those      *)
(*  given in arXiv:1408.1505 and arXiv:1509.08127.                  *)
(*  The result is a polynomial in log(u*w/v) of degree L            *)
(*  (except at one loop where it has degree 2):                     *)
(*                                                                  *)
(*    U(u,v,w)  ->  \sum_{r=0}^L U_r^{(L)} [log(u*w/v)]^r ,         *)
(*                                                                  *)
(*  and we present the coefficient functions U, with                *)
(*                                                                  *)
(*                   U[r_,L_]  =  U_r^{(L)}.                        *)
(*                                                                  *)
(********************************************************************)

U[2, 1] = - 1/2;
U[1, 1] = 0;
U[0, 1] = - 2*zeta[2];

U[2, 2] = 3*zeta[2];
U[1, 2] = - 2*zeta[3];
U[0, 2] = 71/2*zeta[4];

U[3, 3] = 8/3*zeta[3];
U[2, 3] = - 75*zeta[4];
U[1, 3] = 56*zeta[5]+64*zeta[2]*zeta[3];
U[0, 3] = - 644*zeta[6] - 24*zeta[3]^2;

U[4, 4] = 4*zeta[4];
U[3, 4] = - 64*zeta[5] - 48*zeta[2]*zeta[3];
U[2, 4] = 3769/2*zeta[6] + 84*zeta[3]^2;
U[1, 4] = - 1570*zeta[7] - 2564*zeta[3]*zeta[4] - 1528*zeta[2]*zeta[5];
U[0, 4] = 62629/4*zeta[8] + 532*zeta[2]*zeta[3]^2 + 1156*zeta[3]*zeta[5];

U[5, 5] = 32/5*zeta[5];
U[4, 5] = - 328*zeta[6] - 32*zeta[3]^2;
U[3, 5] = 1920*zeta[7] + 2336*zeta[3]*zeta[4] + 1536*zeta[2]*zeta[5];
U[2, 5] = - 60548*zeta[8] - 2288*zeta[2]*zeta[3]^2 - 5008*zeta[3]*zeta[5];
U[1, 5] = 50232*zeta[9] + 44400*zeta[2]*zeta[7] + 85424*zeta[3]*zeta[6]
  + 73200*zeta[4]*zeta[5] + 1392*zeta[3]^3;
U[0, 5] = - 2499892/5*zeta[10] - 31168*zeta[2]*zeta[3]*zeta[5]
  - 27312*zeta[4]*zeta[3]^2 - 34112*zeta[3]*zeta[7] - 16464*zeta[5]^2;
