(* ::Package:: *)

(****************************************************************)
(*  This file contains the MRK expansion of the NMHV ratio      *)
(*  function through three loops, parceled out according to the *)
(*  functions p and q defined in the text. In this file, they   *)   
(*  are denoted with the following notation:                    *)
(*                                                              *)
(*       P[n_,m_] = p_n^{(m)} ,  Q[n_,m_] = q_n^{(m)}          *)
(*                                                              *)
(*  We use the follow notation for the SVHPLs,                  *)
(*                                                              *)
(*  lp[a__] = L_ {a}^+ = 1/2(L_{a}(-w) + L_{a}(-1/w))           *)
(*  lm[a__] = L_ {a}^- = 1/2(L_{a}(-w) - L_{a}(-1/w))           *)
(*                                                              *)
(*  See sec. 3 of arxiv:1207.0186 for more details about        *)
(*  these functions.                                            *)
(*                                                              *)
(*                                                              *)
(****************************************************************)


P[2,3]=(-(1/12))*lp[1]^3+(-(1/64))*lm[0]^3+1/4*lm[0,1,1]+1/4*lp[0,0,1]+1/4*Zeta[3]+(-(1/32))*lm[0]^2*lp[1]+1/8*lm[0,1]*lp[1]


P[1,3]=(-(3/4))*lm[0,1,1,1]+(-(1/4))*lm[0,0,0,1]+(-(5/48))*lp[1]^4+(-(1/384))*lm[0]^4+1/8*lp[0,0,1,1]+(-(1/2))*lm[0,1]*Zeta[2]+(-(9/64))*lm[0]^2*lp[1]^2+(-(1/32))*lm[0]*lp[0,0,1]+(-(5/384))*lm[0]^3*lp[1]+1/32*lm[0]*lp[1]^3+1/16*lm[0]*lm[0,1,1]+1/16*lm[0]*Zeta[3]+1/16*lm[0]^2*lm[0,1]+1/8*lm[0,1,1]*lp[1]+1/8*lp[1]*Zeta[3]+1/4*lm[0,1]*lp[1]^2+1/2*lp[1]^2*Zeta[2]+15/16*lp[1]*lp[0,0,1]+(-(1/4))*lm[0]*lp[1]*Zeta[2]+1/16*lm[0]*lm[0,1]*lp[1]


P[0,3]=(-(87/16))*lp[0,0,0,0,1]+(-(7/8))*lp[0,0,1,1,1]+(-(1/30))*lp[1]^5+3/1280*lm[0]^5+1/4*lm[0,0,0,1,1]+3/4*lm[0,1,1,1,1]+15/8*Zeta[5]+(-(11/4))*lp[1]*Zeta[4]+(-2)*lp[0,0,1]*Zeta[2]+(-1)*lm[0,1,1]*Zeta[2]+(-1)*Zeta[2]*Zeta[3]+(-(7/16))*lm[0]*lm[0,0,0,1]+(-(3/8))*lm[0,1,1,1]*lp[1]+(-(3/8))*lp[1]^2*Zeta[3]+(-(3/16))*lm[0]*lm[0,1,1,1]+(-(13/96))*lm[0]^2*lp[1]^3+(-(1/8))*lm[0,1,1]*lp[1]^2+(-(1/8))*lm[0,0,0,1]*lp[1]+(-(5/64))*lm[0]^4*lp[1]+(-(1/16))*lm[0]^2*lm[0,1,1]+1/384*lm[0]^3*lp[1]^2+1/32*lm[0]*lp[1]^4+1/32*lm[0]*lp[0,0,1,1]+5/96*lm[0]^3*Zeta[2]+1/16*lp[1]*lp[0,0,1,1]+17/256*lm[0]^3*lm[0,1]+3/32*lm[0,1]*lp[1]^3+5/32*lm[0]^2*Zeta[3]+11/16*lp[1]^2*lp[0,0,1]+45/64*lm[0]^2*lp[0,0,1]+5/6*lp[1]^3*Zeta[2]+11/8*lm[0]*Zeta[4]+(-(1/4))*lm[0]*lm[0,1]*Zeta[2]+(-(1/4))*lm[0]*lp[1]^2*Zeta[2]+(-(1/32))*lm[0]*lp[1]*lp[0,0,1]+3/128*lm[0]^2*lm[0,1]*lp[1]+5/64*lm[0]*lm[0,1]*lp[1]^2+3/16*lm[0]*lp[1]*Zeta[3]+1/4*lm[0]*lm[0,1,1]*lp[1]+5/16*lm[0]^2*lp[1]*Zeta[2]+1/2*lm[0,1]*lp[1]*Zeta[2]


Q[2,3]=0


Q[1,3]=1/6*lp[1]^3+1/4*lm[0,1,1]+1/4*lp[0,0,1]+1/4*Zeta[3]+(-(1/8))*lm[0]*lp[1]^2+(-(1/16))*lm[0]^2*lp[1]


Q[0,3]=(-(3/8))*lm[0,1,1,1]+(-(1/8))*lm[0,0,0,1]+(-(1/768))*lm[0]^4+1/16*lp[0,0,1,1]+11/96*lp[1]^4+(-(23/32))*lp[1]*lp[0,0,1]+(-(1/4))*lm[0,1]*Zeta[2]+(-(1/4))*lp[1]^2*Zeta[2]+(-(17/192))*lm[0]*lp[1]^3+(-(25/768))*lm[0]^3*lp[1]+1/32*lm[0]*lm[0,1,1]+1/32*lm[0]*Zeta[3]+1/32*lm[0]^2*lm[0,1]+1/16*lm[0,1]*lp[1]^2+11/128*lm[0]^2*lp[1]^2+3/16*lm[0,1,1]*lp[1]+3/16*lp[1]*Zeta[3]+15/64*lm[0]*lp[0,0,1]+(-(1/16))*lm[0]*lm[0,1]*lp[1]+1/8*lm[0]*lp[1]*Zeta[2]


P[1,2]=(-(1/4))*lp[1]^2+1/4*lm[0,1]+1/8*lm[0]*lp[1]


P[0,2]=(-(1/4))*lm[0,1,1]+(-(1/4))*Zeta[3]+(-(1/6))*lp[1]^3+(-(1/96))*lm[0]^3+11/8*lp[0,0,1]+(-(1/4))*lm[0]*Zeta[2]+(-(3/16))*lm[0]^2*lp[1]+1/8*lm[0]*lp[1]^2+1/8*lm[0,1]*lp[1]+3/16*lm[0]*lm[0,1]+1/2*lp[1]*Zeta[2]


Q[1,2]=0


Q[0,2]=1/8*lm[0,1]+1/8*lp[1]^2+(-(1/16))*lm[0]*lp[1]


P[0,1]=(-(1/2))*lp[1]+1/4*lm[0]


Q[0,1]=0
