If[$VersionNumber>=2.,$Messages=OutputStream["",1],$Messages={}]

BeginPackage["Summatio`q`"]

Begin["`Private`"]

(*Belegen von Module durch Block f�r Versionen 1.?*)
If[$VersionNumber<2.,Module=Block]

(*!Achtung bei Erweiterungen: 
   Am Dateiende sind vielleicht Modifikationen vorzunehmen!"*)

SListe:=(Hyp`q`ph[List1_List,List2_List,q_,z_]:>
 Module[{Ph,Ausgabe={},SFrage},
    Hyp`q`Private`phRun=True;
    Ph=(Hyp`q`ph[List1,List2,q,z]/.Hyp`q`phOrdne);
    SFrage[Trans_,Perm1__,u,Perm2__,l]:=
      If[(Ph/.Hyp`q`phPerm[Perm1,Global`u]/.Hyp`q`phPerm[Perm2,Global`l]/.Regel[Trans])=!=
             (Ph/.Hyp`q`phPerm[Perm1,Global`u]/.Hyp`q`phPerm[Perm2,Global`l]),
        Ausgabe=Join[Ausgabe,{{"phPerm"[Perm1,"u"],"phPerm"[Perm2,"l"],StringJoin["S",ToString[Trans]]}}]];
    SFrage[Trans_,Perm1__,u]:=
      If[(Ph/.Hyp`q`phPerm[Perm1,Global`u]/.Regel[Trans])=!=
             (Ph/.Hyp`q`phPerm[Perm1,Global`u]),
        Ausgabe=Join[Ausgabe,{{"phPerm"[Perm1,"u"],StringJoin["S",ToString[Trans]]}}]];
    SFrage[Trans_,Perm1__,l]:=
      If[(Ph/.Hyp`q`phPerm[Perm1,Global`l]/.Regel[Trans])=!=
             (Ph/.Hyp`q`phPerm[Perm1,Global`l]),
        Ausgabe=Join[Ausgabe,{{"phPerm"[Perm1,"l"],StringJoin["S",ToString[Trans]]}}]];
    SFrage[Trans_,Perm1__,b]:=
      If[(Ph/.Hyp`q`phPerm[Perm1,Global`b]/.Regel[Trans])=!=
             (Ph/.Hyp`q`phPerm[Perm1,Global`b]),
        Ausgabe=Join[Ausgabe,{{"phPerm"[Perm1,"b"],StringJoin["S",ToString[Trans]]}}]];
    SFrage[Trans_]:=
               If[(Ph/.Regel[Trans])=!=Ph,
                Ausgabe=Join[Ausgabe,{{StringJoin["S",ToString[Trans]]}}]];
    SFrage[Global`rs01];
    SFrage[Global`rs02];
    SFrage[Global`rs03];
    SFrage[Global`rs04];
    SFrage[Global`rs05];
    SFrage[Global`rs06];
    If[MemberQ[{{1,0},{1,1},{2,1},{2,2},{3,2},{4,3},{5,4},{5,5},{6,5},{7,6},{8,7},{10,9}},
                {Length[List1],Length[List2]}],
       Switch[{Length[Ph[[1]]],Length[Ph[[2]]]},
         {1,0},Ausgabe=Join[Ausgabe,{{"S1001"}}],

         {1,1},SFrage[1101],

         {2,1},SFrage[2101];

               SFrage[2102];

               SFrage[2103];

               SFrage[2104];

               SFrage[2105];

               SFrage[2106];

               SFrage[2107];

               SFrage[2161],

         {2,2},SFrage[2201];

               SFrage[2202],

         {3,2},SFrage[3201];

               SFrage[3202];

               SFrage[3203];

               SFrage[3204];

               SFrage[3261],

         {4,3},SFrage[4301];

               SFrage[4302];

               SFrage[4303];
               SFrage[4303,1,2,4,3,u];
               SFrage[4303,1,3,4,2,u];
               SFrage[4303,2,1,3,4,u];
               SFrage[4303,2,1,4,3,u];
               SFrage[4303,2,3,4,1,u];
               SFrage[4303,3,1,2,4,u];
               SFrage[4303,3,1,4,2,u];
               SFrage[4303,3,4,2,1,u];
               SFrage[4303,4,1,2,3,u];
               SFrage[4303,4,1,3,2,u];
               SFrage[4303,4,3,2,1,u];
               SFrage[4303,2,3,1,l];
               SFrage[4303,1,2,4,3,u,2,3,1,l];
               SFrage[4303,1,3,4,2,u,2,3,1,l];
               SFrage[4303,2,1,3,4,u,2,3,1,l];
               SFrage[4303,2,1,4,3,u,2,3,1,l];
               SFrage[4303,2,3,4,1,u,2,3,1,l];
               SFrage[4303,3,1,2,4,u,2,3,1,l];
               SFrage[4303,3,1,4,2,u,2,3,1,l];
               SFrage[4303,3,4,2,1,u,2,3,1,l];
               SFrage[4303,4,1,2,3,u,2,3,1,l];
               SFrage[4303,4,1,3,2,u,2,3,1,l];
               SFrage[4303,4,3,2,1,u,2,3,1,l];
               SFrage[4303,1,3,2,l];
               SFrage[4303,1,2,4,3,u,1,3,2,l];
               SFrage[4303,1,3,4,2,u,1,3,2,l];
               SFrage[4303,2,1,3,4,u,1,3,2,l];
               SFrage[4303,2,1,4,3,u,1,3,2,l];
               SFrage[4303,2,3,4,1,u,1,3,2,l];
               SFrage[4303,3,1,2,4,u,1,3,2,l];
               SFrage[4303,3,1,4,2,u,1,3,2,l];
               SFrage[4303,3,4,2,1,u,1,3,2,l];
               SFrage[4303,4,1,2,3,u,1,3,2,l];
               SFrage[4303,4,1,3,2,u,1,3,2,l];
               SFrage[4303,4,3,2,1,u,1,3,2,l];

               SFrage[4304];
               SFrage[4304,1,2,4,3,u];
               SFrage[4304,1,3,4,2,u];
               SFrage[4304,2,1,3,4,u];
               SFrage[4304,2,1,4,3,u];
               SFrage[4304,2,3,4,1,u];
               SFrage[4304,3,1,2,4,u];
               SFrage[4304,3,1,4,2,u];
               SFrage[4304,3,4,2,1,u];
               SFrage[4304,4,1,2,3,u];
               SFrage[4304,4,1,3,2,u];
               SFrage[4304,4,3,2,1,u];
               SFrage[4304,2,3,1,l];
               SFrage[4304,1,2,4,3,u,2,3,1,l];
               SFrage[4304,1,3,4,2,u,2,3,1,l];
               SFrage[4304,2,1,3,4,u,2,3,1,l];
               SFrage[4304,2,1,4,3,u,2,3,1,l];
               SFrage[4304,2,3,4,1,u,2,3,1,l];
               SFrage[4304,3,1,2,4,u,2,3,1,l];
               SFrage[4304,3,1,4,2,u,2,3,1,l];
               SFrage[4304,3,4,2,1,u,2,3,1,l];
               SFrage[4304,4,1,2,3,u,2,3,1,l];
               SFrage[4304,4,1,3,2,u,2,3,1,l];
               SFrage[4304,4,3,2,1,u,2,3,1,l];
               SFrage[4304,1,3,2,l];
               SFrage[4304,1,2,4,3,u,1,3,2,l];
               SFrage[4304,1,3,4,2,u,1,3,2,l];
               SFrage[4304,2,1,3,4,u,1,3,2,l];
               SFrage[4304,2,1,4,3,u,1,3,2,l];
               SFrage[4304,2,3,4,1,u,1,3,2,l];
               SFrage[4304,3,1,2,4,u,1,3,2,l];
               SFrage[4304,3,1,4,2,u,1,3,2,l];
               SFrage[4304,3,4,2,1,u,1,3,2,l];
               SFrage[4304,4,1,2,3,u,1,3,2,l];
               SFrage[4304,4,1,3,2,u,1,3,2,l];
               SFrage[4304,4,3,2,1,u,1,3,2,l];

               SFrage[4305];

               SFrage[4306];

               SFrage[4307];

               SFrage[4308];

               SFrage[4361];
               SFrage[4361,1,2,4,3,u];
               SFrage[4361,1,3,4,2,u];
               SFrage[4361,2,1,3,4,u];
               SFrage[4361,2,1,4,3,u];
               SFrage[4361,2,3,4,1,u];
               SFrage[4361,3,1,2,4,u];
               SFrage[4361,3,1,4,2,u];
               SFrage[4361,3,4,2,1,u];
               SFrage[4361,4,1,2,3,u];
               SFrage[4361,4,1,3,2,u];
               SFrage[4361,4,3,2,1,u];
               SFrage[4361,2,3,1,l];
               SFrage[4361,1,2,4,3,u,2,3,1,l];
               SFrage[4361,1,3,4,2,u,2,3,1,l];
               SFrage[4361,2,1,3,4,u,2,3,1,l];
               SFrage[4361,2,1,4,3,u,2,3,1,l];
               SFrage[4361,2,3,4,1,u,2,3,1,l];
               SFrage[4361,3,1,2,4,u,2,3,1,l];
               SFrage[4361,3,1,4,2,u,2,3,1,l];
               SFrage[4361,3,4,2,1,u,2,3,1,l];
               SFrage[4361,4,1,2,3,u,2,3,1,l];
               SFrage[4361,4,1,3,2,u,2,3,1,l];
               SFrage[4361,4,3,2,1,u,2,3,1,l];
               SFrage[4361,1,3,2,l];
               SFrage[4361,1,2,4,3,u,1,3,2,l];
               SFrage[4361,1,3,4,2,u,1,3,2,l];
               SFrage[4361,2,1,3,4,u,1,3,2,l];
               SFrage[4361,2,1,4,3,u,1,3,2,l];
               SFrage[4361,2,3,4,1,u,1,3,2,l];
               SFrage[4361,3,1,2,4,u,1,3,2,l];
               SFrage[4361,3,1,4,2,u,1,3,2,l];
               SFrage[4361,3,4,2,1,u,1,3,2,l];
               SFrage[4361,4,1,2,3,u,1,3,2,l];
               SFrage[4361,4,1,3,2,u,1,3,2,l];
               SFrage[4361,4,3,2,1,u,1,3,2,l],

         {5,4},SFrage[5401];

               SFrage[5402],

         {5,5},SFrage[5501],

         {6,5},SFrage[6501];

               SFrage[6502],

         {8,7},SFrage[8701];

               SFrage[8702];
               SFrage[8702,1,2,3,4,5,7,6,b];
               SFrage[8702,1,2,3,4,6,7,5,b];
               SFrage[8702,1,2,3,5,4,6,7,b];
               SFrage[8702,1,2,3,5,4,7,6,b];
               SFrage[8702,1,2,3,5,6,7,4,b];
               SFrage[8702,1,2,3,6,4,5,7,b];
               SFrage[8702,1,2,3,6,4,7,5,b];
               SFrage[8702,1,2,3,6,5,7,4,b];
               SFrage[8702,1,2,3,7,4,5,6,b];
               SFrage[8702,1,2,3,7,4,6,5,b];
               SFrage[8702,1,2,3,7,5,6,4,b];
               SFrage[8702,1,2,4,5,3,6,7,b];
               SFrage[8702,1,2,4,5,3,7,6,b];
               SFrage[8702,1,2,4,5,6,7,3,b];
               SFrage[8702,1,2,4,6,3,5,7,b];
               SFrage[8702,1,2,4,6,3,7,5,b];
               SFrage[8702,1,2,4,6,5,7,3,b];
               SFrage[8702,1,2,4,7,3,5,6,b];
               SFrage[8702,1,2,4,7,3,6,5,b];
               SFrage[8702,1,2,4,7,5,6,3,b];
               SFrage[8702,1,2,5,6,3,4,7,b];
               SFrage[8702,1,2,5,6,3,7,4,b];
               SFrage[8702,1,2,5,6,4,7,3,b];
               SFrage[8702,1,2,5,7,3,4,6,b];
               SFrage[8702,1,2,5,7,3,6,4,b];
               SFrage[8702,1,2,5,7,4,6,3,b];
               SFrage[8702,1,2,6,7,3,4,5,b];
               SFrage[8702,1,2,6,7,3,5,4,b];
               SFrage[8702,1,2,6,7,4,5,3,b];

               SFrage[8703];
               SFrage[8703,1,2,3,4,6,5,7,b];
               SFrage[8703,1,2,3,4,7,5,6,b];
               SFrage[8703,1,2,3,5,4,6,7,b];
               SFrage[8703,1,2,3,5,6,4,7,b];
               SFrage[8703,1,2,3,5,7,4,6,b];
               SFrage[8703,1,2,3,6,4,5,7,b];
               SFrage[8703,1,2,3,6,5,4,7,b];
               SFrage[8703,1,2,3,6,7,4,5,b];
               SFrage[8703,1,2,3,7,4,5,6,b];
               SFrage[8703,1,2,3,7,5,4,6,b];
               SFrage[8703,1,2,3,7,6,4,5,b];
               SFrage[8703,1,2,4,5,3,6,7,b];
               SFrage[8703,1,2,4,6,3,5,7,b];
               SFrage[8703,1,2,4,7,3,5,6,b];
               SFrage[8703,1,2,5,6,3,4,7,b];
               (*Das stimmt so!*)

               SFrage[8704];
               SFrage[8704,1,2,3,4,6,5,7,b];
               SFrage[8704,1,2,3,4,7,5,6,b];
               SFrage[8704,1,2,3,5,4,6,7,b];
               SFrage[8704,1,2,3,5,6,4,7,b];
               SFrage[8704,1,2,3,5,7,4,6,b];
               SFrage[8704,1,2,3,6,4,5,7,b];
               SFrage[8704,1,2,3,6,5,4,7,b];
               SFrage[8704,1,2,3,6,7,4,5,b];
               SFrage[8704,1,2,3,7,4,5,6,b];
               SFrage[8704,1,2,3,7,5,4,6,b];
               SFrage[8704,1,2,3,7,6,4,5,b];
               SFrage[8704,1,2,4,5,3,6,7,b];
               SFrage[8704,1,2,4,6,3,5,7,b];
               SFrage[8704,1,2,4,7,3,5,6,b];
               SFrage[8704,1,2,5,6,3,4,7,b];
               SFrage[8704,1,2,5,6,4,3,7,b];
               SFrage[8704,1,2,5,6,7,3,4,b];
               SFrage[8704,1,2,5,7,3,4,6,b];
               SFrage[8704,1,2,5,7,4,3,6,b];
               SFrage[8704,1,2,5,7,6,3,4,b];
               SFrage[8704,1,2,6,7,3,4,5,b];
               SFrage[8704,1,2,6,7,4,3,5,b];
               SFrage[8704,1,2,6,7,5,3,4,b];

               SFrage[8761],

         {10,9},If[Factor[q-z]===
                Factor[q^3*Ph[[1,1]]^3/Ph[[1,4]]/Ph[[1,5]]/Ph[[1,6]]/Ph[[1,7]]/Ph[[1,8]]/Ph[[1,9]]/Ph[[1,10]]-z]===
                Factor[Ph[[1,2]]+Ph[[1,3]]]===0&&
                Factor[Ph[[1,1]]-(Ph[[1,2]])^2/q^2]===0&&
                Factor[Map[(q*Ph[[1,1]]/#)&,Drop[Ph[[1]],1]]-Ph[[2]]]===Table[0,{Length[Ph[[2]]]}],
                Print[""];
                Print["The series is very well-poised. \"S10901\" might be applicable."];
                Print["Please, check for yourself!"];
                Ausgabe=Ph;
                ]
        ]
      ];
    Hyp`q`Private`phRun=False;
    If[Ausgabe=!={}&&Ausgabe=!=Ph,
     Print[""];
     Print["Be sure to apply \"phOrdne\" before using the following information!"]];
     Ausgabe
]);


simplify[x_]:=(Simplify[x]/.Hyp`q`Expandq)

Srs01:=(Hyp`q`ph[List1_List,List2_List,q_,z_]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1=List1,NewList2=List2,
                ProvList1,ProvList2,mList={},Ausgabe},
   Ausgabe=Hyp`q`ph[List1,List2,q,z];
   GesList=Table[{Factor[List2[[iii]]/List1[[ii]]],ii,iii},{ii,Length[List1]},{iii,Length[List2]}];
   GesList=Apply[Join,GesList];
   If[!MemberQ[Map[#[[1]]&,GesList],q]||(List2==={})||!(Length[List1]-Length[List2]===1),
      Throw[Ausgabe],
      Var1=Position[GesList,{q,i_,j_}];
      Var1=GesList[[Hyp`q`Private`Argument[Var1[[1]]]]];
      Var1=Drop[Var1,1];
      NewList1={List1[[Var1[[1]]]]};NewList2={List2[[Var1[[2]]]]};
      ProvList1=Drop[List1,{Var1[[1]],Var1[[1]]}];ProvList2=Drop[List2,{Var1[[2]],Var1[[2]]}];
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList],ii++,
        Var2=ProvList1/GesList[[ii]];
        Var2=Map[Log[q,#]&,Var2];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[!MemberQ[Var1,True],
           Throw[Ausgabe],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`q`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      Ausgabe=
          Hyp`q`pqinf[q,q]*Hyp`q`pqinf[NewList2[[1]]/ProvList1[[1]],q]/Hyp`q`pqinf[q/ProvList1[[1]],q]/
          Hyp`q`pqinf[NewList2[[1]],q]*
          Product[Hyp`q`pq[NewList2[[ii+1]]/NewList1[[1]],mList[[ii]],q],{ii,1,Length[NewList2]-1}]/
          Product[Hyp`q`pq[NewList2[[ii+1]],mList[[ii]],q],{ii,1,Length[NewList2]-1}]*
          NewList1[[1]]^(Apply[Plus,mList]);
      If[ProvList2=!={}||(Factor[ProvList1[[1]]*q^(Apply[Plus,mList]-1)*z]=!=1)||
        Re[Log[q,ProvList1[[1]]*q^(Apply[Plus,mList]-1)]]>=0,
        Throw[Hyp`q`ph[List1,List2,q,z]],
        Throw[Ausgabe],
        Throw[Ausgabe]
        ];
   ]]]);
Srs02:=(Hyp`q`ph[List1_List,List2_List,q_,q_]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1=List1,NewList2=List2,
                ProvList1,ProvList2,mList={},Ausgabe},
   Ausgabe=Hyp`q`ph[List1,List2,q,q];
   GesList=Table[{Factor[List2[[iii]]/List1[[ii]]],ii,iii},{ii,Length[List1]},{iii,Length[List2]}];
   GesList=Apply[Join,GesList];
   If[!MemberQ[Map[#[[1]]&,GesList],q]||(List2==={})||!(Length[List1]-Length[List2]===1),
      Throw[Ausgabe],
      Var1=Position[GesList,{q,i_,j_}];
      Var1=GesList[[Hyp`q`Private`Argument[Var1[[1]]]]];
      Var1=Drop[Var1,1];
      NewList1={List1[[Var1[[1]]]]};NewList2={List2[[Var1[[2]]]]};
      ProvList1=Drop[List1,{Var1[[1]],Var1[[1]]}];ProvList2=Drop[List2,{Var1[[2]],Var1[[2]]}];
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList],ii++,
        Var2=ProvList1/GesList[[ii]];
        Var2=Map[Log[q,#]&,Var2];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[!MemberQ[Var1,True],
           Throw[Ausgabe],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`q`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      Ausgabe=
          Hyp`q`pq[q,-Log[q,ProvList1[[1]]]]/
          Hyp`q`pq[NewList2[[1]],-Log[q,ProvList1[[1]]]]*
          Product[Hyp`q`pq[NewList2[[ii+1]]/NewList1[[1]],mList[[ii]],q],{ii,1,Length[NewList2]-1}]/
          Product[Hyp`q`pq[NewList2[[ii+1]],mList[[ii]],q],{ii,1,Length[NewList2]-1}]*
          NewList1[[1]]^(-Log[q,ProvList1[[1]]]);
      If[ProvList2==={}&&Hyp`q`Private`IntegerTest[ProvList1[[1]],q]&&
         Factor[Log[q,ProvList1[[1]]]+Apply[Plus,mList]]<=0,
        Throw[Ausgabe],
        Throw[Hyp`q`ph[List1,List2,q,q]],
        Print[""];
        Print["If ",-Factor[Log[q,ProvList1[[1]]]+Apply[Plus,mList]]," is nonnegative, the expression equals"];
        Throw[Ausgabe]
        ];
   ]]]);
Srs03:=(Hyp`q`ph[List1_List,List2_List,q_,z_]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1={},NewList2={},
                ProvList1=List1,ProvList2=List2,mList={},Ausgabe1,Ausgabe2},
   Ausgabe1=Hyp`q`ph[List1,List2,q,z];
   If[(List2==={})||!(Length[List1]-Length[List2]===1),
      Throw[Ausgabe1],
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList],ii++,
        Var2=ProvList1/GesList[[ii]];
        Var2=Map[Log[q,#]&,Var2];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[!MemberQ[Var1,True],
           Throw[Ausgabe1],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`q`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      Ausgabe1=(-1)^Log[q,ProvList1[[1]]]*q^(Binomial[Log[q,ProvList1[[1]]],2])*
          Hyp`q`pq[q,-Log[q,ProvList1[[1]]]]/
          Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}];
      Ausgabe2=(-1)^Apply[Plus,mList]*q^(Sum[Binomial[mList[[ii]],2],{ii,1,Length[NewList2]}])*
          Hyp`q`pqinf[q,q]/Hyp`q`pqinf[q/ProvList1[[1]]]*
          Product[NewList2[[ii]]^mList[[ii]],{ii,1,Length[NewList2]}]/
          Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}];
      If[ProvList2==={}&&Factor[z-1]===0&&Hyp`q`Private`IntegerTest[ProvList1[[1]],q],
        Throw[Ausgabe1],
        If[ProvList2==={}&&Factor[ProvList1[[1]]*q^(Apply[Plus,mList]-1)*z]===1&&
           (Re[Log[q,ProvList1[[1]]*q^(Apply[Plus,mList]-1)]]<0),
          Throw[Ausgabe2],
        If[ProvList2=!={}||
           (Factor[ProvList1[[1]]*q^(Apply[Plus,mList])*z]=!=1)||
           (Re[Log[q,ProvList1[[1]]*q^(Apply[Plus,mList])]]>0),
          Throw[Hyp`q`ph[List1,List2,q,z]],Throw[0],Throw[0]
           ],
          Throw[Ausgabe2]
          ]
        ];
   ]]]);
Srs04:=(Hyp`q`ph[List1_List,List2_List,q_,q_]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1={},NewList2={},
                ProvList1=List1,ProvList2=List2,mList={},Ausgabe},
   Ausgabe=Hyp`q`ph[List1,List2,q,q];
   If[(List2==={})||!(Length[List1]-Length[List2]===1),
      Throw[Ausgabe],
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList],ii++,
        Var2=ProvList1/GesList[[ii]];
        Var2=Map[Log[q,#]&,Var2];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[!MemberQ[Var1,True],
           Throw[Ausgabe],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`q`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      If[ProvList2==={}&&Hyp`q`Private`IntegerTest[ProvList1[[1]],q]&&
         Factor[Log[q,ProvList1[[1]]*q^(Apply[Plus,mList])]]<0,
        Throw[0],
        Throw[Hyp`q`ph[List1,List2,q,q]],
        Print[""];
        Print["If ",-Factor[Log[q,ProvList1[[1]]]+Apply[Plus,mList]]," is positive, the expression equals"];
        Throw[0]
        ];
   ]]]);
Srs05:=(Hyp`q`ph[List1_List,List2_List,q_,z_]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1=List1,NewList2=List2,
                ProvList1,ProvList2,mList={},Ausgabe},
   Ausgabe=Hyp`q`ph[List1,List2,q,z];
   GesList=Table[{Factor[List2[[iii]]/List1[[ii]]],ii,iii},{ii,Length[List1]},{iii,Length[List2]}];
   GesList=Apply[Join,GesList];
   If[!MemberQ[Map[#[[1]]&,GesList],q]||(List2==={})||!(Length[List1]-Length[List2]===0),
      Throw[Ausgabe],
      Var1=Position[GesList,{q,i_,j_}];
      Var1=GesList[[Hyp`q`Private`Argument[Var1[[1]]]]];
      Var1=Drop[Var1,1];
      NewList1={List1[[Var1[[1]]]]};NewList2={List2[[Var1[[2]]]]};
      ProvList1=Drop[List1,{Var1[[1]],Var1[[1]]}];ProvList2=Drop[List2,{Var1[[2]],Var1[[2]]}];
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList],ii++,
        Var2=ProvList1/GesList[[ii]];
        Var2=Map[Log[q,#]&,Var2];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[!MemberQ[Var1,True],
           Throw[Ausgabe],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`q`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      Ausgabe=
          Hyp`q`pqinf[q,q]/Hyp`q`pqinf[NewList2[[1]],q]*
          Product[Hyp`q`pq[NewList2[[ii+1]]/NewList1[[1]],mList[[ii]],q],{ii,1,Length[NewList2]-1}]/
          Product[Hyp`q`pq[NewList2[[ii+1]],mList[[ii]],q],{ii,1,Length[NewList2]-1}]*
          NewList1[[1]]^(Apply[Plus,mList]);
      If[ProvList2=!={}||(Factor[q^(Apply[Plus,mList]-1)*z]=!=1),
        Throw[Hyp`q`ph[List1,List2,q,z]],
        Throw[Ausgabe],
        Throw[Ausgabe]
        ];
   ]]]);
Srs06:=(Hyp`q`ph[List1_List,List2_List,q_,z_]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1={},NewList2={},
                ProvList1=List1,ProvList2=List2,mList={},Ausgabe},
   Ausgabe=Hyp`q`ph[List1,List2,q,z];
   If[(List2==={})||!(Length[List1]-Length[List2]===0),
      Throw[Ausgabe],
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList],ii++,
        Var2=ProvList1/GesList[[ii]];
        Var2=Map[Log[q,#]&,Var2];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[!MemberQ[Var1,True],
           Throw[Ausgabe],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`q`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      Ausgabe=(-1)^Apply[Plus,mList]*q^(Sum[Binomial[mList[[ii]],2],{ii,1,Length[NewList2]}])*
          Hyp`q`pqinf[q,q]*
          Product[NewList2[[ii]]^mList[[ii]],{ii,1,Length[NewList2]}]/
          Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}];
      Switch[ProvList2==={}&&Factor[q^(Apply[Plus,mList])*z],
        1,Throw[0],
        q,Throw[Ausgabe],
        _,Throw[Hyp`q`ph[List1,List2,q,z]]
        ];
   ]]]);
S1001:=
   (Hyp`q`ph[{a_},{},q_,z_]:>Hyp`q`pqinf[{a*z},{z},q]);
S1101:=
   (Hyp`q`ph[{a_},{c_},q_,z_]:>Hyp`q`pqinf[{c/a},{c},q]/;
        Factor[z-c/a]===0);
S2101:=
  {(Hyp`q`ph[{a_,b_},{c_},q_,q_]:>Hyp`q`pq[c/a,-Log[q,simplify[b]],q]/
      Hyp`q`pq[c,-Log[q,simplify[b]],q]*a^(-Log[q,simplify[b]])/;
            Hyp`q`Private`IntegerTest[b,q]),
   (Hyp`q`ph[{a_,b_},{c_},q_,q_]:>Hyp`q`pq[c/b,-Log[q,simplify[a]],q]/
      Hyp`q`pq[c,-Log[q,simplify[a]],q]*b^(-Log[q,simplify[a]])/;
            Hyp`q`Private`IntegerTest[a,q])};
S2102:=
  {(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pq[c/a,-Log[q,simplify[b]],q]/
      Hyp`q`pq[c,-Log[q,simplify[b]],q]/;
            Factor[z-c/(a*b)]===0&&Hyp`q`Private`IntegerTest[b,q]),
   (Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pq[c/b,-Log[q,simplify[a]],q]/
      Hyp`q`pq[c,-Log[q,simplify[a]],q]/;
            Factor[z-c/(a*b)]===0&&Hyp`q`Private`IntegerTest[a,q])};
S2103:=
   (Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{c/a,c/b},
                {c,c/(a*b)},q]/;
            Factor[z-c/(a*b)]===0);
S2104:=
  {(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{-q},{-q/b,a*q/b},q]*
        Hyp`q`pqinf[{a*q,a*q^2/b^2},{},q^2]/;
           Factor[c-a*q/b]===0&&Factor[z+q/b]===0),
   (Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{-q},{-q/a,b*q/a},q]*
        Hyp`q`pqinf[{b*q,b*q^2/a^2},{},q^2]/;
           Factor[c-b*q/a]===0&&Factor[z+q/a]===0)};
S2105:=
   {(Hyp`q`ph[{a_,aa_},{b_},q_,q_]:>
        Hyp`q`pq[b/Sqrt[q],-Log[q,simplify[a^2]],q]/
        (q^(Binomial[-Log[q,simplify[a^2]],2]/2)*Hyp`q`pq[b/Sqrt[q],-Log[q,simplify[a^2]],Sqrt[q]])/;
            Factor[a^2*q-aa^2]===0&&Hyp`q`Private`IntegerTest[a^2,q]),
    (Hyp`q`ph[{aa_,a_},{b_},q_,q_]:>
        Hyp`q`pq[b/Sqrt[q],-Log[q,simplify[a^2]],q]/
        (q^(Binomial[-Log[q,simplify[a^2]],2]/2)*Hyp`q`pq[b/Sqrt[q],-Log[q,simplify[a^2]],Sqrt[q]])/;
            Factor[a^2*q-aa^2]===0&&Hyp`q`Private`IntegerTest[a^2,q])};
S2106:=
   {(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>
        ((1+c*z)*Hyp`q`pqinf[c^2*q*z,q])/Hyp`q`pqinf[z,q]/;
                Factor[a-c^2]===0&&Factor[b-c*q]===0),
    (Hyp`q`ph[{b_,a_},{c_},q_,z_]:>
        ((1+c*z)*Hyp`q`pqinf[c^2*q*z,q])/Hyp`q`pqinf[z,q]/;
                Factor[a-c^2]===0&&Factor[b-c*q]===0)};
S2107:=
   {(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>
        ((Hyp`q`pqinf[{-(c/Sqrt[a])},{-Sqrt[a]},Sqrt[q]]+Hyp`q`pqinf[{c/Sqrt[a]},{Sqrt[a]},Sqrt[q]])*
        Hyp`q`pqinf[{a,Sqrt[q]},{c,z},q])/2/;
                Factor[a-b*c]===0&&Factor[b*z-Sqrt[q]]===0),
    (Hyp`q`ph[{b_,a_},{c_},q_,z_]:>
        ((Hyp`q`pqinf[{-(c/Sqrt[a])},{-Sqrt[a]},Sqrt[q]]+Hyp`q`pqinf[{c/Sqrt[a]},{Sqrt[a]},Sqrt[q]])*
        Hyp`q`pqinf[{a,Sqrt[q]},{c,z},q])/2/;
                Factor[a-b*c]===0&&Factor[b*z-Sqrt[q]]===0)};
S3204:=
   (Hyp`q`ph[{a_,c_,b_},{d_,e_},q_,z_]:>
  ((1-d+(d*(1-d/a))/b)*
     Hyp`q`pqinf[{d^2/b^2,(d^2*q)/(a*b)},{(d^2*q)/b,d^2/(a*b^2)},q])/
   ((1-d)*(1+d/b))/;
                Factor[c-d*q]===Factor[e-(d^2*q)/b]===
                Factor[z-d^2/(a*b^2)]===0);
S2201:=
  {(Hyp`q`ph[{a_,c_},{d_,b_},q_,z_]:>Hyp`q`pqinf[{a*b,b*q/a},{},q^2]*
        Hyp`q`pqinf[{},{b},q]/;
            Factor[c-q/a]===0&&Factor[d+q]===0&&Factor[z+b]===0),
   (Hyp`q`ph[{a_,c_},{d_,b_},q_,z_]:>Hyp`q`pqinf[{c*b,b*q/c},{},q^2]*
        Hyp`q`pqinf[{},{b},q]/;
            Factor[a-q/c]===0&&Factor[d+q]===0&&Factor[z+b]===0),
   (Hyp`q`ph[{a_,c_},{d_,b_},q_,z_]:>Hyp`q`pqinf[{a*d,d*q/a},{},q^2]*
        Hyp`q`pqinf[{},{d},q]/;
            Factor[c-q/a]===0&&Factor[b+q]===0&&Factor[z+d]===0),
   (Hyp`q`ph[{a_,c_},{d_,b_},q_,z_]:>Hyp`q`pqinf[{c*d,d*q/c},{},q^2]*
        Hyp`q`pqinf[{},{d},q]/;
            Factor[a-q/c]===0&&Factor[b+q]===0&&Factor[z+d]===0)};
S2202:=
   (Hyp`q`ph[{a_,b_},{c_,d_},q_,z_]:>
             Hyp`q`pqinf[{a*q,b*q},{q,a*b*q},q^2]/;
            Factor[a*b*q+c*d]===0&&Factor[c+d]===0&&Factor[z+q]===0);
S3201:=
  {(Hyp`q`ph[{a_,b_,d_},{c_,e_},q_,q_]:>
        Hyp`q`pq[c/a,-Log[q,simplify[d]],q]*
        Hyp`q`pq[c/b,-Log[q,simplify[d]],q]/
        (Hyp`q`pq[c,-Log[q,simplify[d]],q]*
        Hyp`q`pq[c/(a*b),-Log[q,simplify[d]],q])/;
          Factor[e-a*b*d*q/c]===0&&Hyp`q`Private`IntegerTest[d,q]),
   (Hyp`q`ph[{a_,b_,d_},{c_,e_},q_,q_]:>
        Hyp`q`pq[c/a,-Log[q,simplify[b]],q]*
        Hyp`q`pq[c/d,-Log[q,simplify[b]],q]/
        (Hyp`q`pq[c,-Log[q,simplify[b]],q]*
        Hyp`q`pq[c/(a*d),-Log[q,simplify[b]],q])/;
          Factor[e-a*b*d*q/c]===0&&Hyp`q`Private`IntegerTest[b,q]),
   (Hyp`q`ph[{a_,b_,d_},{c_,e_},q_,q_]:>
        Hyp`q`pq[c/d,-Log[q,simplify[a]],q]*
        Hyp`q`pq[c/b,-Log[q,simplify[a]],q]/
        (Hyp`q`pq[c,-Log[q,simplify[a]],q]*
        Hyp`q`pq[c/(d*b),-Log[q,simplify[a]],q])/;
          Factor[e-a*b*d*q/c]===0&&Hyp`q`Private`IntegerTest[a,q])};
S3203:=
   (Hyp`q`ph[{a_,aa_,aaa_},{aaaa_,aaaaa_},q_,t_]:>
        (1-a*q*t^2)*Hyp`q`pqinf[{a*q^2*t},{t},q]/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0);
S4301:=
  {(Hyp`q`ph[{a_,aa_,b_,c_},{aaa_,d_,e_},q_,z_]:>
        Hyp`q`pqinf[{a*q,q*a^(1/2)/b,q*a^(1/2)/c,a*q/(b*c)},
               {a*q/b,a*q/c,q*a^(1/2),q*a^(1/2)/(b*c)},q]/;
            Factor[aa+q*a^(1/2)]===Factor[q*aaa+q*a^(1/2)]===0&&
              Factor[b*d-q*a]===Factor[c*e-q*a]===0&&
              Factor[z-q*a^(1/2)/(b*c)]===0)};
S4302:=
   (Hyp`q`ph[{a_,aa_,b_,c_},{aaa_,d_,e_},q_,z_]:>
        Hyp`q`pq[a*q,-Log[q,simplify[c]],q]*Hyp`q`pq[q*a^(1/2)/b,-Log[q,simplify[c]],q]/
        (Hyp`q`pq[a*q/b,-Log[q,simplify[c]],q]*Hyp`q`pq[q*a^(1/2),-Log[q,simplify[c]],q])/;
              Factor[aa+q*a^(1/2)]===Factor[q*aaa+q*a^(1/2)]===0&&
              Factor[b*d-q*a]===Factor[c*e-q*a]===0&&
              Factor[z-q*a^(1/2)/(b*c)]===0&&
              Hyp`q`Private`IntegerTest[c,q]);
S3202:=
  {(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:>
        Hyp`q`pq[b,-Log[q,simplify[a]]/2,q]*Hyp`q`pq[c,-Log[q,simplify[a]]/2,q]*
        Hyp`q`pq[q,-Log[q,simplify[a]],q]*Hyp`q`pq[b*c,-Log[q,simplify[a]],q]/
        (Hyp`q`pq[q,-Log[q,simplify[a]]/2,q]*Hyp`q`pq[b*c,-Log[q,simplify[a]]/2,q]*
         Hyp`q`pq[b,-Log[q,simplify[a]],q]*Hyp`q`pq[c,-Log[q,simplify[a]],q])/;
               Factor[b*d-q*a]===Factor[c*e-q*a]===0&&
               Factor[z-q^2*a^(1/2)/(b*c)]===0&&
              Hyp`q`Private`IntegerTest[Sqrt[a],q])};
S8702:=
    (Hyp`q`ph[{la_,laa_,laaa_,a_,b_,c_,d_,e_},
       {laaaa_,laaaaa_,aa_,bb_,cc_,dd_,ee_},q_,z_]:>
      Hyp`q`pqinf[{q*la,c^2/la},{q*la/a,q*la/b},q]*
      Hyp`q`pqinf[{a*q,b*q,c^2*q/a,c^2*q/b},
             {q,a*b*q,c^2*q,c^2*q/(a*b)},q^2]/;
               Factor[laa/q+laaaaa]===Factor[laaaa+laaaaa]===Factor[la^(1/2)+laaaaa]===
               Factor[-laaa/q+laaaaa]===0&&
               Factor[a*aa-q*la]===Factor[b*bb-q*la]===Factor[c*cc-q*la]===
                        Factor[d*dd-q*la]===Factor[e*ee-q*la]===0&&
               Factor[c+d]===0&&
               Factor[ee-c^2]===0&&
               Factor[z+q*la/(a*b)]===0);
S4303:=
   (Hyp`q`ph[{b_,c_,d_,a_},{e_,f_,g_},q_,q_]:>Module[{nn=-Log[q,simplify[a]]},
      If[IntegerQ[nn],
             If[EvenQ[nn],
                  c^nn*Hyp`q`pq[q,nn/2,q^2]*Hyp`q`pq[e^2/c^2,nn/2,q^2]/
                  (Hyp`q`pq[e^2,nn/2,q^2]*Hyp`q`pq[g*q,nn/2,q^2]),
                  0],
             Print[StringJoin["Result=0 for ",
                ToString[StringForm["``",nn]]," odd. For ",
                ToString[StringForm["``",nn]]," even one obtains:"]];
             c^nn*Hyp`q`pq[q,nn/2,q^2]*Hyp`q`pq[e^2/c^2,nn/2,q^2]/
                  (Hyp`q`pq[e^2,nn/2,q^2]*Hyp`q`pq[c^2*q,nn/2,q^2])]]/;
               Factor[a*b*q-e^2]===0&&
               Factor[c+d]===0&&
               Factor[g-c^2]===0&&
               Factor[f+e]===0&&
               Hyp`q`Private`IntegerTest[a,q]);
S8703:=
   (Hyp`q`ph[{la_,laa_,laaa_,a_,b_,c_,d_,e_},
       {laaaa_,laaaaa_,aa_,bb_,cc_,dd_,ee_},q_,z_]:>
      Hyp`q`pqinf[{-c,-c*q},{-c*d,-c*q/d,-a*c,-c*q/a},q]*
      Hyp`q`pqinf[{-a*c*d,-a*c*q/d,-c*d*q/a,-c*q^2/(a*d)},{},q^2]/;
               Factor[laa/q+laaaaa]===Factor[laaaa+laaaaa]===Factor[la^(1/2)+laaaaa]===
               Factor[-laaa/q+laaaaa]===0&&
               Factor[a*aa-q*la]===Factor[b*bb-q*la]===Factor[c*cc-q*la]===
                        Factor[d*dd-q*la]===Factor[e*ee-q*la]===0&&
               Factor[b-q/a]===0&&
               Factor[c+la]===0&&
               Factor[e-q/d]===0&&
               Factor[z+la]===0);
S8704:=
   (Hyp`q`ph[{la_,laa_,laaa_,a_,b_,c_,d_,e_},
   {laaaa_,laaaaa_,aa_,bb_,cc_,dd_,ee_},q_,z_]:>
  Hyp`q`pqinf[{-la*q,-la/c,(la*q),-la/d^2,(-la*q)/(c*d),((la*q)/(c*d))},
   {-la,(-la*q)/c,((la*q)/c),(-la*q)/d,((la*q)/d),-la/(c*d^2)},q]/;
               Factor[laa/q+laaaaa]===Factor[laaaa+laaaaa]===Factor[la^(1/2)+laaaaa]===
               Factor[-laaa/q+laaaaa]===0&&
               Factor[a*aa-q*la]===Factor[b*bb-q*la]===Factor[c*cc-q*la]===
                        Factor[d*dd-q*la]===Factor[e*ee-q*la]===0&&
               Factor[a+b]===Factor[a^2+la*q^2]===Factor[d+e]===
               Factor[z+la/(c*d^2)]===0);
S4304:=
   (Hyp`q`ph[{b_,c_,d_,a_},{e_,f_,g_},q_,q_]:>
      q^(n*(n+1)/2)*Hyp`q`pqinf[{e*a,e*b,c^2*q*a/e,c^2*q*b/e},{},q^2]*
      Hyp`q`pqinf[{},{e,f},q]/;
               Factor[b-q/a]===0&&
               Factor[c+d]===0&&
               Factor[e*f-q*c^2]===0&&
               Factor[g+q]===0&&
               Hyp`q`Private`IntegerTest[a,q]);
S4305:=
   {(Hyp`q`ph[{a_,b_,c_,d_},{bb_,cc_,dd_},q_,q_]:>Module[{nn=-Log[q,simplify[a]]},
      If[IntegerQ[nn],
             If[EvenQ[nn],
                  Hyp`q`pq[{b*c},{b,c},nn,q]*
                  Hyp`q`pq[{q,b^2,c^2},{b^2*c^2},nn/2,q^2],
                  0],
             Print[StringJoin["Result=0 for ",
                ToString[StringForm["``",nn]]," odd. For ",
                ToString[StringForm["``",nn]]," even one obtains:"]];
             Hyp`q`pq[{b*c},{b,c},nn,q]*
                 Hyp`q`pq[{q,b^2,c^2},{b^2*c^2},nn/2,q^2]]]/;
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0&&
               Factor[d+q*a/b/c]===0&&Hyp`q`Private`IntegerTest[a,q]),
    (Hyp`q`ph[{a_,b_,d_,c_},{bb_,dd_,cc_},q_,q_]:>Module[{nn=-Log[q,simplify[a]]},
      If[IntegerQ[nn],
             If[EvenQ[nn],
                  Hyp`q`pq[{b*c},{b,c},nn,q]*
                  Hyp`q`pq[{q,b^2,c^2},{b^2*c^2},nn/2,q^2],
                  0],
             Print[StringJoin["Result=0 for ",
                ToString[StringForm["``",nn]]," odd. For ",
                ToString[StringForm["``",nn]]," even one obtains:"]];
             Hyp`q`pq[{b*c},{b,c},nn,q]*
                 Hyp`q`pq[{q,b^2,c^2},{b^2*c^2},nn/2,q^2]]]/;
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0&&
               Factor[d+q*a/b/c]===0&&Hyp`q`Private`IntegerTest[a,q]),
    (Hyp`q`ph[{a_,c_,d_,b_},{cc_,dd_,bb_},q_,q_]:>Module[{nn=-Log[q,simplify[a]]},
      If[IntegerQ[nn],
             If[EvenQ[nn],
                  Hyp`q`pq[{b*c},{b,c},nn,q]*
                  Hyp`q`pq[{q,b^2,c^2},{b^2*c^2},nn/2,q^2],
                  0],
             Print[StringJoin["Result=0 for ",
                ToString[StringForm["``",nn]]," odd. For ",
                ToString[StringForm["``",nn]]," even one obtains:"]];
             Hyp`q`pq[{b*c},{b,c},nn,q]*
                 Hyp`q`pq[{q,b^2,c^2},{b^2*c^2},nn/2,q^2]]]/;
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0&&
               Factor[d+q*a/b/c]===0&&Hyp`q`Private`IntegerTest[a,q])};
S4306:=
   (Hyp`q`ph[{a_,aa_,b_,c_},{aaaa_,bb_,cc_},q_,q_]:>
  Hyp`q`pq[{a/b^2,b^(-1),-((a^(1/2)*q)/b)},{b^(-2),(a*q)/b,-(a^(1/2)/b)},-Log[q,simplify[c]],q]/;
               Factor[aa/q-aaaa]===Factor[a^(1/2)-aaaa]===
               Factor[b*bb-q*a]===Factor[cc/c-b^2*q]===0&&
               Hyp`q`Private`IntegerTest[c,q]);
S4307:=
  (Hyp`q`ph[{a_,aa_,b_,c_},{aaa_,d_,e_},q_,z_]:>
   Hyp`q`pqinf[{a*q,(a*q)/(b*c),-((a^(1/2)*q)/b),
    -((a^(1/2)*q)/c)},{(a*q)/b,(a*q)/c,-(a^(1/2)*q),
    -((a^(1/2)*q)/(b*c))},q]/;
            Factor[aa-q*a^(1/2)]===Factor[aaa-a^(1/2)]===0&&
              Factor[b*d-q*a]===Factor[c*e-q*a]===0&&
              Factor[z+q*a^(1/2)/(b*c)]===0);
S4308:=
   (Hyp`q`ph[{a_,aa_,b_,c_},{aaa_,bb_,cc_},q_,q_]:>
  Hyp`q`pq[{a/b^2,b^(-1),(a^(1/2)*q)/b},{b^(-2),(a*q)/b,a^(1/2)/b},-Log[q,simplify[c]],q]/;
    Factor[aa+q*a^(1/2)]===Factor[aaa+a^(1/2)]===
              Factor[b*bb-q*a]===Factor[cc-b^2*q*c]===0&&
    Hyp`q`Private`IntegerTest[c,q]);
S5401:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_},{aaaa_,aaaaa_,bb_,cc_},q_,z_]:>
  Hyp`q`pqinf[{a*q,(a*q)/(b*c),(a^(1/2)*q^(1/2))/b,(a^(1/2)*q^(1/2))/c},
   {(a*q)/b,(a*q)/c,a^(1/2)*q^(1/2),(a^(1/2)*q^(1/2))/(b*c)},q]/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===
               Factor[z-(a^(1/2)*q^(1/2))/(b*c)]===0);
S5402:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_},{aaaa_,aaaaa_,bb_,cc_},q_,q_]:>
  Hyp`q`pq[{(a*q)/b^2},{a/(b^2*q)},-Log[q,simplify[c]],q^2]*
   Hyp`q`pq[{a/(b^2*q),1/(b*q)},{1/(b^2*q),(a*q)/b},-Log[q,simplify[c]],q]/;
    Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
    Factor[-aaa/q+aaaaa]===Factor[b*bb-q*a]===Factor[cc-b^2*q^2*c]===0&&
    Hyp`q`Private`IntegerTest[c,q]);
S5501:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_},{aaaa_,aaaaa_,bb_,cc_,0},q_,z_]:>
  Hyp`q`pqinf[{a*q,(a*q)/(b*c)},{(a*q)/b,(a*q)/c},q]/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===
               Factor[z-(a*q)/(b*c)]===0);
S6501:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_},{aaaa_,aaaaa_,bb_,cc_,dd_},q_,z_]:>
      Hyp`q`pqinf[{a*q,a*q/(b*c),a*q/(b*d),a*q/(c*d)},
             {bb,cc,dd,a*q/(b*c*d)},q]/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0&&
               Factor[z-a*q/(b*c*d)]===0);
S6502:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_},{aaaa_,aaaaa_,bb_,cc_,dd_},q_,z_]:>
      Hyp`q`pq[a*q,-Log[q,simplify[d]],q]*
      Hyp`q`pq[a*q/(b*c),-Log[q,simplify[d]],q]/
        (Hyp`q`pq[bb,-Log[q,simplify[d]],q]*Hyp`q`pq[cc,-Log[q,simplify[d]],q])/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0&&
               Factor[z-a*q/(b*c*d)]===0&&
               Hyp`q`Private`IntegerTest[d,q]);
S8701:=
    (Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_},{aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},
                q_,q_]:>
      Hyp`q`pq[a*q,-Log[q,simplify[f]],q]*
      Hyp`q`pq[a*q/(b*c),-Log[q,simplify[f]],q]*
      Hyp`q`pq[a*q/(b*d),-Log[q,simplify[f]],q]*
      Hyp`q`pq[a*q/(c*d),-Log[q,simplify[f]],q]/
      (Hyp`q`pq[bb,-Log[q,simplify[f]],q]*Hyp`q`pq[cc,-Log[q,simplify[f]],q]*
       Hyp`q`pq[dd,-Log[q,simplify[f]],q]*
       Hyp`q`pq[a*q/(b*c*d),-Log[q,simplify[f]],q])/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===
                        Factor[e*ee-q*a]===Factor[f*ff-q*a]===0&&
               Factor[a^2*q-b*c*d*e*f]===0&&
               Hyp`q`Private`IntegerTest[f,q]);
S2161:=
    (Hyp`q`ph[{a_,b_},{c_},q_,q_]:>
     (-Hyp`q`pqinf[{q/c,a,b},{c/q,a*q/c,b*q/c},q]*Hyp`q`ph[{a*q/c,b*q/c},{q^2/c},q,q]+
      Hyp`q`pqinf[{q/c,a*b*q/c},{a*q/c,b*q/c},q]));
S3261:=
    (Hyp`q`ph[{a_,b_,c_},{e_,f_},q_,q_]:>
    (-Hyp`q`pqinf[{q/e,a,b,c,q*f/e},{e/q,a*q/e,b*q/e,c*q/e,f},q]*
      Hyp`q`ph[{a*q/e,b*q/e,c*q/e},{q^2/e,q*f/e},q,q]+
     Hyp`q`pqinf[{q/e,f/a,f/b,f/c},{a*q/e,b*q/e,c*q/e,f},q])/;
          Factor[e*f-a*b*c*q]===0);
S4361:=
   (Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]:>
   -Hyp`q`pqinf[{q/b^2,a,b,-b,d,(e*q)/(b^2),-((e*q)/(b^2))},
     {b^2/q,q/b,-(q/b),(a*q)/b^2,e,-e,(d*q)/(b^2)},
     q]*Hyp`q`ph[{q/b,-(q/b),(a*q)/b^2,(d*q)/(b^2)},
     {(e*q)/(b^2),-((e*q)/(b^2)),q^2/b^2},q,q]+
  Hyp`q`pqinf[{q/b^2,-q},{(a*q)/b^2,-(a*q)},q]*
   Hyp`q`pqinf[{a^2*q^2,(a*q^2)/b^2,(d*q),(e^2)/(b^2)},
    {q^2/b^2,e^2,a*q^2,(d*q)/(b^2)},q^2]/;
                Factor[b+c]===Factor[b^2-g]===Factor[e+f]===
                Factor[e*f+a*d*q]===0);
S8761:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_},
       {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,q_]:>
    -Hyp`q`pqinf[{a*q,c,d,e,f,b/a,b*q/c,b*q/d,b*q/e,b*q/f},
          {bb/q,cc,dd,ee,ff,b*c/a,b*d/a,b*e/a,b*f/a,b^2*q/a},q]*
      Hyp`q`ph[{b^2/a,q*b*a^(-1/2),-q*b*a^(-1/2),b,b*c/a,b*d/a,b*e/a,b*f/a},
         {b*a^(-1/2),-b*a^(-1/2),b*q/a,b*q/c,b*q/d,b*q/e,b*q/f},
                q,q]+
    Hyp`q`pqinf[{a*q,b/a,a*q/(c*d),a*q/(c*e),
        a*q/(c*f),a*q/(d*e),a*q/(d*f),a*q/(e*f)},
           {cc,dd,ee,ff,b*c/a,b*d/a,b*e/a,b*f/a},q]/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===
                        Factor[e*ee-q*a]===Factor[f*ff-q*a]===0&&
               Factor[a^2*q-b*c*d*e*f]===0);
S10901:=
   (Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_,g_,h_},
   {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},q_,q_]:>
  Hyp`q`pq[{a*q,(a^2*q)/b^4},{(a*q)/b^2,(a^2*q)/b^2},-Log[q,simplify[h]],q]/;
               Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]===
               Factor[-aaa/q+aaaaa]===0&&
               Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===
                        Factor[e*ee-q*a]===Factor[f*ff-q*a]===
                        Factor[g*gg-q*a]===Factor[h*hh-q*a]===0&&
                        Factor[b+c]===Factor[d+e]===Factor[b^2*q-d^2]===0&&
                        Factor[f*b^2-a]===Factor[g*h*b^2-a^2*q]===0&&
               Hyp`q`Private`IntegerTest[h,q]);

Regel[Global`rs01]=Summatio`q`Srs01;
Regel[Global`rs02]=Summatio`q`Srs02;
Regel[Global`rs03]=Summatio`q`Srs03;
Regel[Global`rs04]=Summatio`q`Srs04;
Regel[Global`rs05]=Summatio`q`Srs05;
Regel[Global`rs06]=Summatio`q`Srs06;
Regel[1001]=Summatio`q`S1001;
Regel[1101]=Summatio`q`S1101;
Regel[2101]=Summatio`q`S2101;
Regel[2102]=Summatio`q`S2102;
Regel[2103]=Summatio`q`S2103;
Regel[2104]=Summatio`q`S2104;
Regel[2105]=Summatio`q`S2105;
Regel[2106]=Summatio`q`S2106;
Regel[2107]=Summatio`q`S2107;
Regel[2161]=Summatio`q`S2161;
Regel[2201]=Summatio`q`S2201;
Regel[2202]=Summatio`q`S2202;
Regel[3201]=Summatio`q`S3201;
Regel[3202]=Summatio`q`S3202;
Regel[3203]=Summatio`q`S3203;
Regel[3204]=Summatio`q`S3204;
Regel[3261]=Summatio`q`S3261;
Regel[4301]=Summatio`q`S4301;
Regel[4302]=Summatio`q`S4302;
Regel[4303]=Summatio`q`S4303;
Regel[4304]=Summatio`q`S4304;
Regel[4305]=Summatio`q`S4305;
Regel[4306]=Summatio`q`S4306;
Regel[4307]=Summatio`q`S4307;
Regel[4308]=Summatio`q`S4308;
Regel[4361]=Summatio`q`S4361;
Regel[5401]=Summatio`q`S5401;
Regel[5402]=Summatio`q`S5402;
Regel[5501]=Summatio`q`S5501;
Regel[6501]=Summatio`q`S6501;
Regel[6502]=Summatio`q`S6502;
Regel[8701]=Summatio`q`S8701;
Regel[8702]=Summatio`q`S8702;
Regel[8703]=Summatio`q`S8703;
Regel[8704]=Summatio`q`S8704;
Regel[8761]=Summatio`q`S8761;
Regel[10901]=Summatio`q`S10901;


End[]

Protect[
Srs01,
Srs02,
Srs03,
Srs04,
Srs05,
Srs06,
S1001,
S1101,
S2101,
S2102,
S2103,
S2104,
S2105,
S2106,
S2107,
S3204,
S2201,
S2202,
S3201,
S3203,
S4301,
S4302,
S3202,
S8702,
S4303,
S8703,
S4304,
S4305,
S4306,
S4307,
S4308,
S5401,
S5402,
S5501,
S6501,
S6502,
S8701,
S8704,
S2161,
S3261,
S4361,
S8761,
S10901,
SListe,
SumListe
]

EndPackage[]


If[$VersionNumber>=2.,$Messages=OutputStream["stdout",1],$Messages={"stdout"}];