print(`Welcome to the q-Bi/Trinomial Recurrence Proof assistance package.`);
print(`Version of April 9, 2003`);
print(`[annop, annopf, annop0, annopf0, applyshiftop, asoe, asoo, e0, eG0, eG1, eT0, eT02, eT02s, eT1, eTrb0, eTrb00, eTrb1, eTrb28, eTrb29, eU0, eU1, eV, expandall, gpsym, listqcoeffs, maxrepeat, mostfreqqcoeff, neg, printqmatch, printqmatchall, printsameq, printU, printT1, sameqcoeff, shiftup, shiftdown,  splitU, splitV, sym]`);
print(`Remember that the default value of the global variable 'altsign' is false.`);
print(`---------------------------------------------------------------------`);
print(`Automatically loading RRtools package...`);
read(RRtools1);
print(`Done loading RRtools package.`);
altsign:=false:

annop:= proc(a,nd,dd,m,b,c); annops(a,nd,dd,m,b,c)[1] end:
annopf:=proc(a,nd,dd,m,b,c); annops(a,nd,dd,m,b,c)[2] end:
annop0:=proc(a,nd,dd,m,b,c); annops0(a,nd,dd,m,b,c)[1] end:
annopf0:=proc(a,nd,dd,m,b,c); annops0(a,nd,dd,m,b,c)[2] end:

applyshiftop := proc(oper, summand)
 local antideg, B, C, deg, i,j, new, tmp;
 B:=0;
 deg := degree(oper,N);
 #antideg := degree(subs(N=1/N,oper),N);
 antideg := ldegree(oper,N);
 for i from antideg to deg do
   B:= B + coeff(oper,N,i) * subs(n=n+i,summand) od;
 B:= expand(B);
 B:= combine(B,power);
B
end:

asoe := proc(oper, evensummand, oddsummand )
 local antideg, B, deg, i,j, new, tmp;
 B:=0;
 deg := degree(oper,N);
 #antideg := degree(subs(N=1/N,oper),N);
 antideg:= ldegree(oper,N);
 #m:= antideg mod 2;
# build up the even parts:
 for i from 2*ceil(antideg/2) to deg by 2  do
   B:= B + subs(n=2*m, coeff(oper,N,i)) * subs(n=m+i/2,evensummand) od;
# build up the odd parts:
 for i from 1+2*floor(antideg/2) to deg by 2 do
   B := B + subs(n=2*m,coeff(oper,N,i)) * subs(n=m+ (i-1)/2,oddsummand) od;
 B:= expand(B);
 B:= combine(B,power);
B
end:

asoo := proc(oper, evensummand, oddsummand )
 local antideg, B, deg, i,j, new, tmp;
 B:=0;
 deg := degree(oper,N);
 antideg:=ldegree(oper,N);
# build up the odd parts:
 for i from 2*ceil(antideg/2) to deg by 2  do
   B:= B + subs(n=2*m + 1, coeff(oper,N,i)) * subs(n=m+i/2,oddsummand) od;
# build up the even parts:
 for i from 1+floor(antideg/2) to deg by 2 do
   B := B + subs(n=2*m + 1,coeff(oper,N,i)) * subs(n=m+ (i+1)/2,evensummand) od;
 B:= expand(B);
 B:= combine(B,power);
 B
end:

EG0 :=proc(s,c,n,m,p)
s *q^c * gp(n-1,m,p) + s* q^(c + p*(n-m))*gp(n-1,m-1,p)
end:

EG1:=  proc(s,c,n,m,p)
s*q^c * gp(n-1,m-1,p) + s*q^(c + p*m)*gp(n-1,m,p)  end:

ET1 := proc(s,c,m,A,pwr) 
  s*q^(c)*T1(m-1,A,pwr) + s*q^(c+pwr*(m+A))*T0(m-1,A+1,pwr) +  s*q^(c+pwr*(m-A))*T0(m-1,A-1,pwr) 
end:

ET0 := proc(s,c,m,A,pwr)
  s*q^(c)*T0(m-1,A-1,pwr) + s*q^(c+pwr*(m+A))*T1(m-1,A,pwr) + s*q^(c+pwr*(2*m+2*A))*T0(m-1,A+1,pwr)
 end:

ET02 := proc(s,c,m,A,pwr)
  s*q^(c)*T0(m-2,A,pwr) + s*q^(c+pwr*(m-A))*T1(m-2,A-1,pwr) + s*q^(c+pwr*(2*m-2*A))*T0(m-2,A-2,pwr) + s*q^(c+pwr*(m+A))*T1(m-1,A,pwr)
+ s*q^(c+pwr*(2*m+2*A))*T0(m-1,A+1,pwr)
 end:

ET02s := proc(s,c,m,A,pwr)
  s*q^(c)*T0(m-2,A,pwr) + s*q^(c+pwr*(m+A))*T1(m-2,A+1,pwr) + s*q^(c+pwr*(2*m+2*A))*T0(m-2,A+2,pwr) + s*q^(c+pwr*(m-A))*T1(m-1,A,pwr)
+ s*q^(c+pwr*(2*m-2*A))*T0(m-1,A-1,pwr)
 end:


E0 := proc(s,c,m,A,pwr)
   s*q^(c+pwr*(m-A))*T0(m,A,pwr) + s*q^(c)*T1(m,A+1,pwr) - s*q^(c+pwr*(m+A+1))*T0(m,A+1,pwr);
 end:

EU0 := proc(s,c,m,A,pwr)
   s*q^c * U(m-1,A,pwr) + s*q^(c + pwr)* U(m-1,A,pwr) + 
   s*q^(c+pwr*(2*m-1)) * U(m-1,A,pwr) - s*q^(c + pwr) * U(m-2,A,pwr) 
 +s* q^(c + pwr*(2*m-2*A))* T0(m-2,A-2,pwr) 
 + s*q^(c + pwr*(2*m + 2*A + 2)) * T0(m-2,A+3,1) end:

EU1 := proc(s,c,m,A,pwr)
   s*q^c * U(m-1,A,pwr) + s* q^(c+pwr*(2*m-1)) * 
    U(m-1,A,pwr)
   + s*q^(c + pwr*(m-A)) * T1(m-1,A-1,pwr) 
   + s*q^(c + pwr*(m+A+1)) * T1(m-1, A+2, pwr) 
end:

EV:= proc(s,c,m,A,pwr)
  s*q^c * V(m-1,A,pwr) + s* q^(c+pwr*(2*m-2)) * 
    V(m-1,A,pwr)
   + s*q^(c + pwr*(m-A)) * T0(m-2,A-2,pwr) 
   + s*q^(c + pwr*(m+A-1)) * T0(m-2, A+1, pwr) 
end:

ETrb1:= proc(s,c,m,A,pwr)
   s*q^(c+pwr*(m-1)) *Trb(m-1,A-1,A,pwr) + s*q^(c+pwr*A)*Trb(m-1,A+1,A+1,pwr) 
  +s*q^c *Trb(m-1,A-1,A-1,pwr)
end:

ETrb0:= proc(s,c,m,A,pwr)
   s*q^(c+pwr*(m-A)) * Trb(m-1,A-1,A-1,pwr) + s*q^(c+pwr*(m-A-1))*Trb(m-1,A-1,A,pwr)
  +s* q^c * Trb(m-1,A+1,A+1,pwr)
end:

ETrb00:= proc(s,c,m,B,A,pwr)
  s*q^c*Trb(m,A+1,A+1,pwr) -s*q^(c+pwr*m)*Trb(m,A,A+1,pwr) 
+ s*q^(c+pwr*(m-A))*Trb(m,A-1,A,pwr)
end:

ETrb28:= proc(s,c,m,B,A,pwr)
  s*q^c*Trb(m-1,B,A,pwr) + s*q^(c+pwr*(m-A-1+B))*Trb(m-1,B,A+1,pwr)
  +s*q^(c+pwr*(m-A)) * Trb(m-1,B-1,A-1,pwr)
end:

ETrb29:= proc(s,c,m,B,A,pwr)
   s*q^c*Trb(m-1,B,A,pwr) + s*q^(c+pwr*(m-A))*Trb(m-1,B-2,A-1,pwr)
  +s*q^(c+pwr*(m+B))*Trb(m-1,B+1,A+1,pwr)
end:

eG0 :=proc(t,P)
 local A,B,c,i,m,pwr,sign,switch;
   if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
   if op(0,op(-1-switch,op(t,P))) <> gp
     then ERROR(`term indicated does not contain gp.`) fi;
   B:=0;
   for i from 1 to t-1 do
     B:= B + op(i,P) od;
   c:= expand(ln(op(-2+switch,op(t,P)))/ln(q));
   m:= op(1,op(-1-switch,op(t,P)));
   A:= op(2,op(-1-switch,op(t,P)));
   pwr:=op(3,op(-1-switch,op(t,P)));
   if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
   B := B + EG0(sign,c,m,A,pwr);
   for i from t+1 to nops(P) do
     B:= B + op(i,P) od;
 B
 end:

eG1 :=proc(t,P)
 local A,B,c,i,m,pwr,sign,switch;
   if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
   if op(0,op(-1-switch,op(t,P))) <> gp
     then ERROR(`term indicated does not contain gp.`) fi;
   B:=0;
   for i from 1 to t-1 do
     B:= B + op(i,P) od;
   c:= expand(ln(op(-2+switch,op(t,P)))/ln(q));
   m:= op(1,op(-1-switch,op(t,P)));
   A:= op(2,op(-1-switch,op(t,P)));
   pwr:=op(3,op(-1-switch,op(t,P)));
   if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
   B := B + EG1(sign,c,m,A,pwr);
   for i from t+1 to nops(P) do
     B:= B + op(i,P) od;
 B
 end:

eT1 :=proc(t,P)
 local A,B,c,i,m,pwr,sign,switch;
   if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
   if op(0,op(-1-switch,op(t,P))) <> T1 
     then ERROR(`term indicated does not contain T1.`) fi;
   B:=0;
   for i from 1 to t-1 do
     B:= B + op(i,P) od;
   c:= expand(ln(op(-2+switch,op(t,P)))/ln(q));
   m:= op(1,op(-1-switch,op(t,P)));
   A:= op(2,op(-1-switch,op(t,P)));
   pwr:=op(3,op(-1-switch,op(t,P)));
   if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
   B := B + ET1(sign,c,m,A,pwr);
   for i from t+1 to nops(P) do
     B:= B + op(i,P) od;
 B
 end:

eT0 := proc(t, P)
local A, B, c, i, m, pwr, sign, switch;
    if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
    if op(0, op(-1-switch, op(t, P))) <> T0 then
        ERROR(`Term indicated does not contain T0`)
    fi;
    B := 0;
    for i to t - 1 do B := B + op(i, P) od;
    c := expand(ln(op(-2+switch, op(t, P)))/ln(q));
    m := op(1, op(-1-switch, op(t, P)));
    A := op(2, op(-1-switch, op(t, P)));
    pwr := op(3, op(-1-switch, op(t, P)));
    if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
    B := B + ET0(sign, c, m, A, pwr);
    for i from t + 1 to nops(P) do B := B + op(i, P) od;
    B
end:

eT02 := proc(t, P)
local A, B, c, i, m, pwr, sign, switch;
    if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
    if op(0, op(-1-switch, op(t, P))) <> T0 then
        ERROR(`Term indicated does not contain T0`)
    fi;
    B := 0;
    for i to t - 1 do B := B + op(i, P) od;
    c := expand(ln(op(-2+switch, op(t, P)))/ln(q));
    m := op(1, op(-1-switch, op(t, P)));
    A := op(2, op(-1-switch, op(t, P)));
    pwr := op(3, op(-1-switch, op(t, P)));
    if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
    B := B + ET02(sign, c, m, A, pwr);
    for i from t + 1 to nops(P) do B := B + op(i, P) od;
    B
end:

eT02s := proc(t, P)
local A, B, c, i, m, pwr, sign, switch;
    if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
    if op(0, op(-1-switch, op(t, P))) <> T0 then
        ERROR(`Term indicated does not contain T0`)
    fi;
    B := 0;
    for i to t - 1 do B := B + op(i, P) od;
    c := expand(ln(op(-2+switch, op(t, P)))/ln(q));
    m := op(1, op(-1-switch, op(t, P)));
    A := op(2, op(-1-switch, op(t, P)));
    pwr := op(3, op(-1-switch, op(t, P)));
    if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
    B := B + ET02s(sign, c, m, A, pwr);
    for i from t + 1 to nops(P) do B := B + op(i, P) od;
    B
end:


eU0 := proc(t, P)
local A, B, c, i, m, pwr, sign, switch;
    if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
    if op(0, op(-1-switch, op(t, P))) <> U then
        ERROR(`Term indicated does not contain U`)
    fi;
    B := 0;
    for i to t - 1 do B := B + op(i, P) od;
    c := expand(ln(op(-2+switch, op(t, P)))/ln(q));
    m := op(1, op(-1-switch, op(t, P)));
    A := op(2, op(-1-switch, op(t, P)));
    pwr := op(3, op(-1-switch, op(t, P)));
    if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
    B := B + EU0(sign, c, m, A, pwr);
    for i from t + 1 to nops(P) do B := B + op(i, P) od;
    B
end:

eU1 := proc(t, P)
local A, B, c, i, m, pwr, sign, switch;
    if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
    if op(0, op(-1-switch, op(t, P))) <> U then
        ERROR(`Term indicated does not contain U`)
    fi;
    B := 0;
    for i to t - 1 do B := B + op(i, P) od;
    c := expand(ln(op(-2+switch, op(t, P)))/ln(q));
    m := op(1, op(-1-switch, op(t, P)));
    A := op(2, op(-1-switch, op(t, P)));
    pwr := op(3, op(-1-switch, op(t, P)));
    if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
    B := B + EU1(sign, c, m, A, pwr);
    for i from t + 1 to nops(P) do B := B + op(i, P) od;
    B
end:

eV := proc(t, P)
local A, B, c, i, m, pwr, sign, switch;
    if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
    if op(0, op(-1-switch, op(t, P))) <> V then
        ERROR(`Term indicated does not contain V`)
    fi;
    B := 0;
    for i to t - 1 do B := B + op(i, P) od;
    c := expand(ln(op(-2+switch, op(t, P)))/ln(q));
    m := op(1, op(-1-switch, op(t, P)));
    A := op(2, op(-1-switch, op(t, P)));
    pwr := op(3, op(-1-switch, op(t, P)));
    if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
    B := B + EV(sign, c, m, A, pwr);
    for i from t + 1 to nops(P) do B := B + op(i, P) od;
    B
end:


e0 := proc (t, P) 
local A, B, c, i, m, pwr, sign, switch; 
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> T1 then ERROR(`Term indicated does not contain T1`) fi; 
B := 0; 
for i to t-1 do B := B+op(i,P) od; 
c := expand(ln(op(-2+switch,op(t,P)))/ln(q)); 
m := op(1,op(-1-switch,op(t,P))); 
A := op(2,op(-1-switch,op(t,P))); 
pwr := op(3,op(-1-switch,op(t,P))); 
if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi; 
B := B+E0(sign,c,m,A,pwr); 
for i from t+1 to nops(P) do B := B+op(i,P) od; 
B 
end:

eTrb1 := proc (t, P) 
local A, B, c, i, m, pwr, sign, switch; 
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> Trb then 
  ERROR(`Term indicated does not contain Trb`) fi;
if op(3,op(-1-switch,op(t,P))) - op(2,op(-1-switch,op(t,P))) <> 1 then
  ERROR(`Term indicated is not a t1`) fi; 
B := 0; 
for i to t-1 do B := B+op(i,P) od; 
c := expand(ln(op(-2+switch,op(t,P)))/ln(q)); 
m := op(1,op(-1-switch,op(t,P))); 
A := op(3,op(-1-switch,op(t,P))); 
pwr := op(4,op(-1-switch,op(t,P))); 
if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi; 
B := B+ETrb1(sign,c,m,A,pwr); 
for i from t+1 to nops(P) do B := B+op(i,P) od; 
B 
end:

eTrb0 := proc (t, P) 
local A, B, c, i, m, pwr, sign, switch; 
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> Trb then 
  ERROR(`Term indicated does not contain Trb`) fi;
if op(3,op(-1-switch,op(t,P))) <> op(2,op(-1-switch,op(t,P))) then
  ERROR(`Term indicated is not a tau0`) fi; 
B := 0; 
for i to t-1 do B := B+op(i,P) od; 
c := expand(ln(op(-2+switch,op(t,P)))/ln(q)); 
m := op(1,op(-1-switch,op(t,P))); 
A := op(3,op(-1-switch,op(t,P))); 
pwr := op(4,op(-1-switch,op(t,P))); 
if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi; 
B := B+ETrb0(sign,c,m,A,pwr); 
for i from t+1 to nops(P) do B := B+op(i,P) od; 
B 
end:

eTrb00 := proc (t, P) 
local A,A1,B, c, i, m, pwr, sign, switch; 
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> Trb then 
  ERROR(`Term indicated does not contain Trb`) fi;
if op(3,op(-1-switch,op(t,P))) <> op(3,op(-1-switch,op(t,P))) then
  ERROR(`Term indicated is not a tau0`) fi; 
B := 0; 
for i to t-1 do B := B+op(i,P) od; 
c := expand(ln(op(-2+switch,op(t,P)))/ln(q)); 
m := op(1,op(-1-switch,op(t,P))); 
A := op(2,op(-1-switch,op(t,P)));
A1:= op(3,op(-1-switch,op(t,P))); 
pwr := op(4,op(-1-switch,op(t,P))); 
if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi; 
B := B+ETrb00(sign,c,m,A,A1,pwr); 
for i from t+1 to nops(P) do B := B+op(i,P) od; 
B 
end:

eTrb28 := proc (t, P) 
local A, A2, B, c, i, m, pwr, sign, switch; 
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> Trb then 
  ERROR(`Term indicated does not contain Trb`) fi;
B := 0; 
for i to t-1 do B := B+op(i,P) od; 
c := expand(ln(op(-2+switch,op(t,P)))/ln(q)); 
m := op(1,op(-1-switch,op(t,P))); 
A := op(2,op(-1-switch,op(t,P)));
A2:= op(3,op(-1-switch,op(t,P))); 
pwr := op(4,op(-1-switch,op(t,P))); 
if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
B := B+ETrb28(sign,c,m,A,A2,pwr); 
for i from t+1 to nops(P) do B := B+op(i,P) od; 
B 
end:

eTrb29 := proc (t, P) 
local A, A2, B, c, i, m, pwr, sign, switch; 
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> Trb then 
  ERROR(`Term indicated does not contain Trb`) fi;
B := 0; 
for i to t-1 do B := B+op(i,P) od; 
c := expand(ln(op(-2+switch,op(t,P)))/ln(q)); 
m := op(1,op(-1-switch,op(t,P))); 
A := op(2,op(-1-switch,op(t,P)));
A2:= op(3,op(-1-switch,op(t,P))); 
pwr := op(4,op(-1-switch,op(t,P))); 
if type(op(1,op(t,P)),integer) then sign := op(1,op(t,P)) else sign := 1 fi;
B := B+ETrb29(sign,c,m,A,A2,pwr); 
for i from t+1 to nops(P) do B := B+op(i,P) od; 
B 
end:




splitU := proc (t, P)
local B, i, switch;
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> U 
   then ERROR(`Term indicated does not contain U.`) fi;
B := 0;
for i to t-1 do B := B+op(i,P) od;
B := B + IsplitoneU(op(t,P));
for i from t+1 to nops(P) do B := B+op(i,P) od;
B
end:

splitV := proc (t, P)
local B, i, switch;
if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
if op(0,op(-1-switch,op(t,P))) <> V
   then ERROR(`Term indicated does not contain V.`) fi;
B := 0;
for i to t-1 do B := B+op(i,P) od;
B := B + IsplitoneV(op(t,P));
for i from t+1 to nops(P) do B := B+op(i,P) od;
B
end:

sym := proc(t,P)
 local B,first,i,new,switch;
 if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
 if op(0,op(-1-switch,op(t,P))) <> T0 and op(0,op(-1-switch,op(t,P))) <> T1
   then ERROR(`Term indicated does not contain T0 or T1.`) fi;
 B:=0;
 for i from 1 to t-1 do B:= B+op(i,P) od;
 first := op(t,P)/op(-1-switch,op(t,P)); 
 #separates off the coefficient of the T0 or T1.
 new := op(0,op(-1-switch,op(t,P))) (op(1,op(-1-switch,op(t,P))),  
   -1*op(2,op(-1-switch,op(t,P))), op(3,op(-1-switch,op(t,P))));
 # negates the middle parameter of the T0 or T1.
 B := B + first * new;
 for i from t+1 to nops(P) do B:= B + op(i,P) od;
 B
 end:

gpsym := proc(t,P)
 local B,first,i,new,switch;
 if depends(op(-1,op(t,P)),q) then switch:= 1 else switch :=0 fi;
 if op(0,op(-1-switch,op(t,P))) <> gp 
   then ERROR(`Term indicated does not contain gp.`) fi;
 B:=0;
 for i from 1 to t-1 do B:= B+op(i,P) od;
 first := op(t,P)/op(-1-switch,op(t,P)); 
 #separates off the coefficient of the T0 or T1.
 new := op(0,op(-1-switch,op(t,P))) (op(1,op(-1-switch,op(t,P))),  
   op(1,op(-1-switch,op(t,P))) - op(2,op(-1-switch,op(t,P))), op(3,op(-1-switch,op(t,P))));
 # changes gp(A,B) to gp(A,A-B).
 B := B + first * new;
 for i from t+1 to nops(P) do B:= B + op(i,P) od;
 B
 end:

shiftup:= proc(t,P)
 global altsign;
 local B, i, sign;
 B:=0;
 for i from 1 to t-1 do B:= B + op(i,P) od;
 if altsign = true then sign := -1 else sign :=1 fi;
 B := B + expandexponent(sign*subs(j=j+1,op(t,P)));
 for i from t+1 to nops(P) do B:= B + op(i,P) od;
 B
 end:

shiftdown:= proc(t,P)
 global altsign;
 local B, i, sign;
 B:=0;
 for i from 1 to t-1 do B:= B + op(i,P) od;
 if altsign = true then sign := -1 else sign :=1 fi;
 B := B + expandexponent(sign*subs(j=j-1,op(t,P)));
 for i from t+1 to nops(P) do B:= B + op(i,P) od;
 B
 end:

IsplitoneU := proc(term)
 local last,qandsign,switch, Upart;
 if depends(op(-1,term),q) then switch:=1 else switch :=0 fi;
 qandsign := term/op(-1-switch,term);
 Upart := term/qandsign;
 if op(0,Upart) <> U then ERROR(`Term does not contain U.`) fi; 
   qandsign * T0( op(1,Upart), op(2,Upart)  , op(3,Upart)) 
  +qandsign * T0( op(1,Upart), op(2,Upart)+1, op(3,Upart))
end:

IsplitoneV := proc(term)
 local coeff, last,out,qandsign, qpart, switch, origexp, Upart;
 if depends(op(-1,term),q) then switch:=1 else switch :=0 fi;
 qandsign := term/op(-1-switch,term);
 Upart := term/qandsign;
 if op(0,Upart) <> V then ERROR(`Term does not contain V.`) fi; 
 if not depends(op(1,qandsign),q)  then qpart:= qandsign/op(1,qandsign)
    else qpart:=qandsign fi;
 coeff:= qandsign/qpart;
 origexp:= expand(ln(qpart)/ln(q));
 out:= coeff*q^(origexp) * T1( op(1,Upart)-1, op(2,Upart)  , op(3,Upart)) 
  +coeff*q^(expand(origexp + op(3,Upart)*(op(1,Upart)-op(2,Upart))))
     *T0( op(1,Upart)-1, op(2,Upart)-1, op(3,Upart))
end:

expandexponent := proc(term)
 local last,qpart,switch,x;
 if depends(op(-1,term),q) then switch:= 1 else switch :=0 fi;
 last := term/op(-2+switch,term);
 qpart := term/last;
 x:= expand(log[q](qpart));
 q^x * last
 end:

expandall:=proc(P)
local i,B;
B:=0;
for i from 1 to nops(P) do
  B:=B+expandexponent(op(i,P))
od;
B
end:

neg := proc(t,P)
local B,i,sign;
B:=0;
for i from 1 to t-1 do B:= B + op(i,P) od;
B := B + subs(j=-j, op(i,P));
for i from t+1 to nops(P) do B:= B + op(i,P) od;
B
end:

printT1:=proc(A)
 local i, shift;
 for i from 1 to nops(A) do
   if depends(op(-1,op(i,A)),q) then shift:=1 else shift:=0 fi;
   if op(0,op(-1-shift, op(i,A))) = T1 then 
      print(`Term number`,i,`...`, op(i,A))
   fi
 od
 end:

printU:=proc(A)
 local i, shift;
 for i from 1 to nops(A) do
   if depends(op(-1,op(i,A)),q) then shift:=1 else shift:=0 fi;
   if op(0,op(-1-shift, op(i,A))) = U then 
      print(`Term number`,i,`...`, op(i,A))
   fi
 od
 end:

listqcoeffs:= proc(A)
 local B,i,shift,tmp;
 # Input: a typical q-binomal or q-trinomial expression
 # Output: a list containing the q-coefficients in the same order
 B:=[];
 for i from 1 to nops(A) do
    if depends ( op(-1,op(i,A)),q) then shift:=0 else shift:=1 fi;
    B:= [op(B), op(-1-shift,op(i,A))]
 od;
 B
 end:

sameqcoeff:=proc(pos,B)
 local C,i;
# Input: list of q coeffs (B) and a position (pos) 
# Output: a list containing the operand number pos and all other operands which  #   have the same q coefficient as the one in operand pos.
 C:=[];
 for i from 1 to pos-1 do
   if op(i,B) = op(pos,B) then C:= [op(C),i] fi
 od;
 C:=[op(C),pos];
 for i from pos+1 to nops(B) do
   if op(i,B) = op(pos,B) then C:= [op(C),i] fi
 od;
 C
 end:

mostfreqqcoeff:= proc(B)
 local F,i, M, MFC; 
# input: list of q coefficients
# output: list containing the operand numbers of a most frequently 
# repeated coefficient.
 for i from 1 to nops(B) do
   F[i]:= sameqcoeff(i,B) od;
 # Let M be the maximum length of an F[i]:
 M:= max( seq(nops(F[i]), i=1..nops(B)));
 MFC:=[];
 i:=0;
 while nops(MFC)<M do i:=i+1; MFC:=F[i] od;
 F[i]
 end:

maxrepeat:=proc(B)
local i,F,M;
for i from 1 to nops(B) do F[i]:=samecoeff(i,B) od;
M:= max( seq(nops(F[i]),i=1..nops(B)));
end:

printqmatch:= proc(A)
 local B,H,i;
# prints a group of terms from A which share the same power of q
 B:= listqcoeffs(A);
 H:= mostfreqqcoeff(B);
 for i from 1 to nops(H) do
   print(`term number`, op(i,H), `...`, op(op(i,H),A))
 od
 end:

printqmatchall:= proc(A)
# like printqmatch, but prints all maximal groups of terms which
# share the same power of q
   local B,L,M,i;
   B:= listqcoeffs(A);
   M:=maxrepeat(B);
   for i from 1 to nops(A) do
     L:=sameqcoeff(i,B);
     if nops(L) = M then printsameq(i,A) fi
   od
 end:

printsameq:= proc(pos,A)
# prints all terms of A which share the same power of q as term pos.
 local B,i,L;
 B:= listqcoeffs(A);
 L:= sameqcoeff(pos,B);
 for i from 1 to nops(L) do
   print(`Term number`,op(i,L),`...`, op( op(i,L), A) )
 od
 end:
print(`------------------------------------------------------------------`);
print(`...done loading recpf package.`);