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

BeginPackage["Transfor`m`"]

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!"*)

TListe:=(Hyp`m`F[List1_List,List2_List,z_]:>
 Module[{HF,Ausgabe={},TFrage},
    Hyp`m`Private`FRun=True;
    HF=(Hyp`m`F[List1,List2,z]/.Hyp`m`FOrdne);
    TFrage[Trans_,Perm1__,u,Perm2__,l]:=
      If[(HF/.Hyp`m`FPerm[Perm1,Global`u]/.Hyp`m`FPerm[Perm2,Global`l]/.Regel[Trans])=!=
             (HF/.Hyp`m`FPerm[Perm1,Global`u]/.Hyp`m`FPerm[Perm2,Global`l]),
        Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"u"],"FPerm"[Perm2,"l"],StringJoin["T",ToString[Trans]]}}]];
    TFrage[Trans_,Perm1__,u]:=
      If[(HF/.Hyp`m`FPerm[Perm1,Global`u]/.Regel[Trans])=!=
             (HF/.Hyp`m`FPerm[Perm1,Global`u]),
        Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"u"],StringJoin["T",ToString[Trans]]}}]];
    TFrage[Trans_,Perm1__,l]:=
      If[(HF/.Hyp`m`FPerm[Perm1,Global`l]/.Regel[Trans])=!=
             (HF/.Hyp`m`FPerm[Perm1,Global`l]),
        Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"l"],StringJoin["T",ToString[Trans]]}}]];
    TFrage[Trans_,Perm1__,b]:=
      If[(HF/.Hyp`m`FPerm[Perm1,Global`b]/.Regel[Trans])=!=
             (HF/.Hyp`m`FPerm[Perm1,Global`b]),
        Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"b"],StringJoin["T",ToString[Trans]]}}]];
    TFrage[Trans_]:=
               If[(HF/.Regel[Trans])=!=HF,
                Ausgabe=Join[Ausgabe,{{StringJoin["T",ToString[Trans]]}}]];
    TFrage[Global`rs01];
    If[MemberQ[{{2,1},{3,2},{4,3},{5,4},{6,5},{7,6},{8,7},{9,8},{11,10}},
                {Length[List1],Length[List2]}],
       Switch[{Length[HF[[1]]],Length[HF[[2]]]},
         {2,1},TFrage[2103];

               TFrage[2104];

               TFrage[2106];

               TFrage[2107];

               TFrage[2110];

               TFrage[2112];

               TFrage[2131];

               TFrage[2132];

               TFrage[2133];

               TFrage[2134];

               TFrage[2135];

               TFrage[2136];

               TFrage[2137];

               TFrage[2138];

               TFrage[2139];

               TFrage[2140];

               TFrage[2141];

               TFrage[2163];

               TFrage[2191];

               TFrage[2192],

         {3,2},TFrage[3204];

               TFrage[3205];

               TFrage[3206];

               TFrage[3207];

               TFrage[3217];

               TFrage[3231];
               TFrage[3231,1,3,2,u];
               TFrage[3231,2,3,1,u];
               TFrage[3231,2,1,l];
               TFrage[3231,1,3,2,u,2,1,l];
               TFrage[3231,2,3,1,u,2,1,l];

               TFrage[3232];
               TFrage[3232,1,3,2,u];
               TFrage[3232,2,3,1,u];
               TFrage[3232,2,1,3,u];
               TFrage[3232,3,1,2,u];
               TFrage[3232,3,2,1,u];

               TFrage[3233];
               TFrage[3233,1,3,2,u];
               TFrage[3233,2,3,1,u];
               TFrage[3233,2,1,3,u];
               TFrage[3233,3,1,2,u];
               TFrage[3233,3,2,1,u];

               TFrage[3234];
               TFrage[3234,1,3,2,u];
               TFrage[3234,2,3,1,u];
               TFrage[3234,2,1,l];
               TFrage[3234,1,3,2,u,2,1,l];
               TFrage[3234,2,3,1,u,2,1,l];

               TFrage[3235];
               TFrage[3235,1,3,2,u];
               TFrage[3235,2,3,1,u];
               TFrage[3235,2,1,l];
               TFrage[3235,1,3,2,u,2,1,l];
               TFrage[3235,2,3,1,u,2,1,l];

               TFrage[3236];

               TFrage[3237];

               TFrage[3238];
               TFrage[3238,1,3,2,u];
               TFrage[3238,2,3,1,u];
               TFrage[3238,2,1,3,u];
               TFrage[3238,3,1,2,u];
               TFrage[3238,3,2,1,u];

               TFrage[3239];

               TFrage[3240];
               TFrage[3240,1,3,2,u];
               TFrage[3240,2,3,1,u];
               TFrage[3240,2,1,3,u];
               TFrage[3240,3,1,2,u];
               TFrage[3240,3,2,1,u];

               TFrage[3261];

               TFrage[3262];

               TFrage[3263];

               TFrage[3264];

               TFrage[3267];

               TFrage[3268],

         {4,3},TFrage[4301];

               TFrage[4302];

               TFrage[4303];

               TFrage[4304];

               TFrage[4306];
               TFrage[4306,1,3,2,4,u];
               TFrage[4306,1,4,2,3,u];
               TFrage[4306,2,3,1,4,u];
               TFrage[4306,2,4,1,3,u];
               TFrage[4306,3,4,1,2,u];
               TFrage[4306,1,3,2,l];
               TFrage[4306,1,3,2,4,u,1,3,2,l];
               TFrage[4306,1,4,2,3,u,1,3,2,l];
               TFrage[4306,2,3,1,4,u,1,3,2,l];
               TFrage[4306,2,4,1,3,u,1,3,2,l];
               TFrage[4306,3,4,1,2,u,1,3,2,l];
               TFrage[4306,2,1,3,l];
               TFrage[4306,1,3,2,4,u,2,1,3,l];
               TFrage[4306,1,4,2,3,u,2,1,3,l];
               TFrage[4306,2,3,1,4,u,2,1,3,l];
               TFrage[4306,2,4,1,3,u,2,1,3,l];
               TFrage[4306,3,4,1,2,u,2,1,3,l];
               TFrage[4306,2,3,1,l];
               TFrage[4306,1,3,2,4,u,2,3,1,l];
               TFrage[4306,1,4,2,3,u,2,3,1,l];
               TFrage[4306,2,3,1,4,u,2,3,1,l];
               TFrage[4306,2,4,1,3,u,2,3,1,l];
               TFrage[4306,3,4,1,2,u,2,3,1,l];
               TFrage[4306,3,1,2,l];
               TFrage[4306,1,3,2,4,u,3,1,2,l];
               TFrage[4306,1,4,2,3,u,3,1,2,l];
               TFrage[4306,2,3,1,4,u,3,1,2,l];
               TFrage[4306,2,4,1,3,u,3,1,2,l];
               TFrage[4306,3,4,1,2,u,3,1,2,l];
               TFrage[4306,3,2,1,l];
               TFrage[4306,1,3,2,4,u,3,2,1,l];
               TFrage[4306,1,4,2,3,u,3,2,1,l];
               TFrage[4306,2,3,1,4,u,3,2,1,l];
               TFrage[4306,2,4,1,3,u,3,2,1,l];
               TFrage[4306,3,4,1,2,u,3,2,1,l];

               TFrage[4309];

               TFrage[4310];

               If[Factor[z-1]===0&&
                  ((Factor[HF[[1,1]]+1/2-HF[[1,2]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,1]]])||
                   (Factor[HF[[1,1]]+1/2-HF[[1,3]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,1]]])||
                   (Factor[HF[[1,1]]+1/2-HF[[1,4]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,1]]])||
                   (Factor[HF[[1,2]]+1/2-HF[[1,1]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,2]]])||
                   (Factor[HF[[1,2]]+1/2-HF[[1,3]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,2]]])||
                   (Factor[HF[[1,2]]+1/2-HF[[1,4]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,2]]])||
                   (Factor[HF[[1,3]]+1/2-HF[[1,1]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,3]]])||
                   (Factor[HF[[1,3]]+1/2-HF[[1,2]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,3]]])||
                   (Factor[HF[[1,3]]+1/2-HF[[1,4]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,3]]])||
                   (Factor[HF[[1,4]]+1/2-HF[[1,1]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,4]]])||
                   (Factor[HF[[1,4]]+1/2-HF[[1,2]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,4]]])||
                   (Factor[HF[[1,4]]+1/2-HF[[1,3]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,4]]])),
                Print[""];
                Print["\"T4312\" might be applicable."];
                Print["Please, check for yourself!"];
                ];

               TFrage[4331];

               If[Factor[z-1]===0,
                Print["If the series is nearly-poised of the first kind"];
                Print["the transformation \"T4332\" might be applicable."];
                TFrage[4332];
                TFrage[4332,1,3,2,b];
                TFrage[4332,2,3,1,b]
               ];

               TFrage[4362];

               TFrage[4391];
               TFrage[4391,2,1,3,4,u];
               TFrage[4391,3,1,2,4,u];
               TFrage[4391,4,1,2,3,u];
               TFrage[4391,2,1,3,l];
               TFrage[4391,2,1,3,4,u,2,1,3,l];
               TFrage[4391,3,1,2,4,u,2,1,3,l];
               TFrage[4391,4,1,2,3,u,2,1,3,l];
               TFrage[4391,1,3,2,l];
               TFrage[4391,2,1,3,4,u,1,3,2,l];
               TFrage[4391,3,1,2,4,u,1,3,2,l];
               TFrage[4391,4,1,2,3,u,1,3,2,l];
               TFrage[4391,2,3,1,l];
               TFrage[4391,2,1,3,4,u,2,3,1,l];
               TFrage[4391,3,1,2,4,u,2,3,1,l];
               TFrage[4391,4,1,2,3,u,2,3,1,l];
               TFrage[4391,3,2,1,l];
               TFrage[4391,2,1,3,4,u,3,2,1,l];
               TFrage[4391,3,1,2,4,u,3,2,1,l];
               TFrage[4391,4,1,2,3,u,3,2,1,l];
               TFrage[4391,3,1,2,l];
               TFrage[4391,2,1,3,4,u,3,1,2,l];
               TFrage[4391,3,1,2,4,u,3,1,2,l];
               TFrage[4391,4,1,2,3,u,3,1,2,l],

         {5,4},TFrage[5401];
               TFrage[5401,2,3,4,1,b];
               TFrage[5401,1,3,4,2,b];
               TFrage[5401,1,2,4,3,b];

               TFrage[5402];
               TFrage[5402,2,3,4,1,b];
               TFrage[5402,1,3,4,2,b];
               TFrage[5402,1,2,4,3,b];

               If[Factor[z-1]===0&&
                  (Hyp`m`Private`IntegerTest[HF[[1,1]]]||
                   Hyp`m`Private`IntegerTest[HF[[1,2]]]||
                   Hyp`m`Private`IntegerTest[HF[[1,3]]]||
                   Hyp`m`Private`IntegerTest[HF[[1,4]]]||
                   Hyp`m`Private`IntegerTest[HF[[1,5]]]),
                Print[""];
                Print["\"T5403\" might be applicable."];
                Print["Please, check for yourself!"];
                ];

               TFrage[5468],

          {6,5},TFrage[6501];
               TFrage[6501,1,3,4,5,2,b];
               TFrage[6501,1,2,4,5,3,b];
               TFrage[6501,1,2,3,5,4,b];

               TFrage[6531];
               TFrage[6531,1,3,4,5,2,b];
               TFrage[6531,1,2,4,5,3,b];
               TFrage[6531,1,2,3,5,4,b];

               TFrage[6532];
               TFrage[6532,1,3,2,4,5,b];
               TFrage[6532,1,4,2,3,5,b];
               TFrage[6532,1,5,2,3,4,b];

               TFrage[6533];
               TFrage[6533,1,3,4,5,2,b];
               TFrage[6533,1,2,4,5,3,b];
               TFrage[6533,1,2,3,5,4,b];

               TFrage[6534],

          {7,6},TFrage[7631];

               TFrage[7632];

               TFrage[7633];
               TFrage[7633,1,2,3,5,4,6,b];
               TFrage[7633,1,2,3,6,4,5,b];
               TFrage[7633,1,2,4,5,3,6,b];
               TFrage[7633,1,2,4,6,3,5,b];
               TFrage[7633,1,2,5,6,3,4,b];
               TFrage[7633,1,3,4,5,2,6,b];
               TFrage[7633,1,3,4,6,2,5,b];
               TFrage[7633,1,3,5,6,2,4,b];
               TFrage[7633,1,4,5,6,2,3,b];

               TFrage[7634];

               TFrage[7635];

               TFrage[7691];

               TFrage[7692];

               TFrage[7693];

               TFrage[7694];

               If[Factor[z-1]===0&&
                  Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&&
                  Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}],
                Print[""];
                Print["The series is very well-poised. In addition to the transformations"];
                Print["in the following list the transformations \"T7636\" and \"T7637\""];
                Print["might be applicable."];
                Print["Please, check for yourself!"];
                ],

         {8,7},If[Factor[z+1]===0&&
                  Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&&
                  Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}],
                Print[""];
                Print["The series is very well-poised. In addition to the transformations"];
                Print["in the following list the transformations \"T8731\" or \"T8732\""];
                Print["might be applicable. Please, check for yourself!"];
                ],

         {9,8},TFrage[9831];

               TFrage[9835];
               TFrage[9835,1,2,3,4,5,6,8,7,b];
               TFrage[9835,1,2,3,4,5,7,8,6,b];
               TFrage[9835,1,2,3,4,6,7,8,5,b];
               TFrage[9835,1,2,3,5,6,7,8,4,b];
               TFrage[9835,1,2,4,5,6,7,8,3,b];
               TFrage[9835,1,3,4,5,6,7,8,2,b];

               TFrage[9891];

               TFrage[9893];

               If[Factor[z-1]===0&&
                  Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&&
                  Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}],
                Print[""];
                Print["The series is very well-poised. In addition to the transformations"];
                Print["in the following list the transformations \"T9832\", \"T9833\","];
                Print["\"T9834\", \"T9837\", \"T9892\", or \"T9894\""];
                Print["might be applicable. Please, check for yourself!"];
                ];

                Print[""];
                Print["In addition to the transformations in the following"];
                Print["list the \"split-poised\" transformation \"T9836\""];
                Print["might be applicable. Please, check for yourself!"],

         {11,10},If[Factor[z-1]===0&&
                  Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&&
                  Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}],
                Print[""];
                Print["The series is very well-poised. The transformations \"T111031\""];
                Print["or \"T111032\" might be applicable. Please, check for yourself!"];
                ];
        ]
      ];
    Hyp`m`Private`FRun=False;
    If[Ausgabe=!={}&&Ausgabe=!=HF,
     Print[""];
     Print["Be sure to apply \"FOrdne\" before using the following information!"]];
     Ausgabe
]);

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


Trs01:=(Hyp`m`F[List1_List,List2_List,1]:>
  Catch[
   Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1={},NewList2={},
                ProvList1=List1,ProvList2=List2,mList={},Ausgabe},
   Ausgabe=Hyp`m`F[List1,List2,1];
   If[(List2==={})||!(Length[List1]-Length[List2]===1),
      Throw[Ausgabe],
      GesList=ProvList2;
      For[ii=1,ii<=Length[GesList]&&Length[ProvList2]>1,ii++,
        Var2=ProvList1-GesList[[ii]];
        Var1=Map[(IntegerQ[#]&&#>=0)&,Var2];
        If[MemberQ[Var1,True],
           Var1=Var1/.True->1/.False->Indeterminate;
           Var2=Var2*Var1;
           Var2=Var2/.Indeterminate->Infinity;
           MinEl=Min[Var2];
           mList=Join[mList,{MinEl}];
           POSX=Hyp`m`Private`POS[Var2,MinEl];
           {ProvList1,ProvList2,NewList1,NewList2}=
              Hyp`m`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2,
                           ProvList1[[POSX]],GesList[[ii]]];
          ]
        ];
      Clear[ii];
      If[Length[ProvList2]===1,
        Throw[1/Hyp`m`GAMMA[1-ProvList1[[1]]+ProvList1[[2]]]/
          Hyp`m`GAMMA[ProvList2[[1]]-ProvList1[[2]]]*
          Hyp`m`GAMMA[1-ProvList1[[1]]]*
          Hyp`m`GAMMA[ProvList2[[1]]]*
          Product[Hyp`m`p[NewList2[[ii]]-ProvList1[[2]],mList[[ii]]],{ii,1,Length[NewList2]}]/
          Product[Hyp`m`p[NewList2[[ii]],mList[[ii]]],{ii,1,Length[NewList2]}]*
          Hyp`m`F[Join[{1+ProvList1[[2]]-ProvList2[[1]],ProvList1[[2]]},
                   1+ProvList1[[2]]-NewList2],
                Join[{1-ProvList1[[1]]+ProvList1[[2]]},
                   1+ProvList1[[2]]-NewList1],1]],
        Throw[Hyp`m`F[List1,List2,1]]
        ];
   ]]]);
T2103:=(Hyp`m`F[{a_,b_},{c_},z_]:>(1-z)^(c-a-b)*Hyp`m`F[{c-a,c-b},{c},z]);
T2104:=(Hyp`m`F[{a_,b_},{c_},z_]:>(1-z)^(-a)*Hyp`m`F[{a,c-b},{c},-z/(1-z)]);
T2106:={Hyp`m`F[{a_,b_},{c_},z_]:>Hyp`m`p[c-b,-a]/
           Hyp`m`p[c,-a]*(z)^(-a)*
           Hyp`m`F[{a,1+a-c},{b-c+1+a},-(1-z)/z]/;
           Hyp`m`Private`IntegerTest[a],
          Hyp`m`F[{b_,a_},{c_},z_]:>Hyp`m`p[c-b,-a]/
           Hyp`m`p[c,-a]*(z)^(-a)*
           Hyp`m`F[{a,1+a-c},{b-c+1+a},-(1-z)/z]/;
           Hyp`m`Private`IntegerTest[a]};
T2107:={Hyp`m`F[{a_,b_},{c_},z_]:>Hyp`m`p[c-b,-a]/
                Hyp`m`p[c,-a]*
           Hyp`m`F[{a,b},{b-c+1+a},1-z]/;
           Hyp`m`Private`IntegerTest[a],
          Hyp`m`F[{b_,a_},{c_},z_]:>Hyp`m`p[c-b,-a]/
                Hyp`m`p[c,-a]*
           Hyp`m`F[{a,b},{b-c+1+a},1-z]/;
           Hyp`m`Private`IntegerTest[a]};
T2131:={Hyp`m`F[{c_,a_},{d_},z_]:>Hyp`m`F[{a,d-c},{1+a-c},1/(1-z)]/
           (Hyp`m`p[d,-a])*(1-z)^(-a)*
             Hyp`m`p[c,-a]/;
          Hyp`m`Private`IntegerTest[a],
         Hyp`m`F[{a_,c_},{d_},z_]:>Hyp`m`F[{a,d-c},{1+a-c},1/(1-z)]/
           (Hyp`m`p[d,-a])*(1-z)^(-a)*
             Hyp`m`p[c,-a]/;
          Hyp`m`Private`IntegerTest[a]};
T3204:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>
         Hyp`m`GAMMA[{e,d+e-(a+b+c)},{e-a,d+e-(b+c)}]*
         Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]);
T3205:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>
         Hyp`m`GAMMA[{d,e,d+e-(a+b+c)},{b,d+e-(a+b),d+e-(b+c)}]*
         Hyp`m`F[{d-b,e-b,d+e-(a+b+c)},{d+e-(a+b),d+e-(b+c)},1]);
T3206:={Hyp`m`F[{b_,c_,a_},{d_,e_},1]:>
         Hyp`m`p[d+e-(b+c),-a]/Hyp`m`p[e,-a]*
         Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]/;
         Hyp`m`Private`IntegerTest[a],
      Hyp`m`F[{b_,a_,c_},{d_,e_},1]:>
         Hyp`m`p[d+e-(b+c),-a]/Hyp`m`p[e,-a]*
         Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]/;
         Hyp`m`Private`IntegerTest[a],
      Hyp`m`F[{a_,c_,b_},{d_,e_},1]:>
         Hyp`m`p[d+e-(b+c),-a]/Hyp`m`p[e,-a]*
         Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]/;
         Hyp`m`Private`IntegerTest[a]};
T3207:={Hyp`m`F[{b_,c_,a_},{d_,e_},1]:>
         Hyp`m`p[e-c,-a]/Hyp`m`p[e,-a]*
         Hyp`m`F[{a,c,d-b},{d,c+1+a-e},1]/;
         Hyp`m`Private`IntegerTest[a],
      Hyp`m`F[{b_,a_,c_},{d_,e_},1]:>
         Hyp`m`p[e-c,-a]/Hyp`m`p[e,-a]*
         Hyp`m`F[{a,c,d-b},{d,c+1+a-e},1]/;
         Hyp`m`Private`IntegerTest[a],
      Hyp`m`F[{a_,c_,b_},{d_,e_},1]:>
         Hyp`m`p[e-c,-a]/Hyp`m`p[e,-a]*
         Hyp`m`F[{a,c,d-b},{d,c+1+a-e},1]/;
         Hyp`m`Private`IntegerTest[a]};
T3239:=(Hyp`m`F[{a_,b_,c_},{d_,e_},z_]:>
         (1-z)^(-a)*
         Hyp`m`F[{(a/2),(a+1)/2,a+1-(b+c)},
                {a+1-b,a+1-c},-4*z/(1-z)^2]/;
         Factor[a+1-b-d]===Factor[a+1-c-e]===0);
T4301:={Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:>
         Hyp`m`p[{e-a,f-a},{e,f},-d]*
         Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)},
         {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
      Hyp`m`F[{a_,b_,d_,c_},{e_,f_,g_},1]:>
         Hyp`m`p[{e-a,f-a},{e,f},-d]*
         Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)},
         {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
      Hyp`m`F[{a_,d_,c_,b_},{e_,f_,g_},1]:>
         Hyp`m`p[{e-a,f-a},{e,f},-d]*
         Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)},
         {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
      Hyp`m`F[{d_,b_,c_,a_},{e_,f_,g_},1]:>
         Hyp`m`p[{e-a,f-a},{e,f},-d]*
         Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)},
         {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d]};
T4302:={Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:>
         Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]*
         Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
      Hyp`m`F[{a_,b_,d_,c_},{e_,f_,g_},1]:>
         Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]*
         Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
      Hyp`m`F[{a_,d_,c_,b_},{e_,f_,g_},1]:>
         Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]*
         Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
      Hyp`m`F[{d_,b_,c_,a_},{e_,f_,g_},1]:>
         Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]*
         Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d]};
T7631:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},z_]:>
         Hyp`m`GAMMA[{a+1-d,a+1-e,a+1-f,a+1-(d+e+f)},
                {a+1,a+1-(d+e),a+1-(d+f),a+1-(e+f)}]*
         Hyp`m`F[{a+1-(b+c),d,e,f},{a+1-b,a+1-c,d+e+f-a},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0&&
         (Hyp`m`Private`IntegerTest[a+1-b-c]||Hyp`m`Private`IntegerTest[d]||Hyp`m`Private`IntegerTest[e]||Hyp`m`Private`IntegerTest[f]));
T7632:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},z_]:>
         Hyp`m`p[{a+1,a+1-(d+e)},{a+1-d,a+1-e},-f]*
         Hyp`m`F[{a+1-(b+c),d,e,f},{a+1-b,a+1-c,d+e+f-a},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0&&
         Hyp`m`Private`IntegerTest[f]);
T4303:={Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:>
   Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d},
    {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b),
     (e+f)-(a+c),(e+f)-(a+d)},1]*
   Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)},
                -d]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
   Hyp`m`F[{a_,b_,d_,c_},{e_,f_,g_},1]:>
   Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d},
    {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b),
     (e+f)-(a+c),(e+f)-(a+d)},1]*
   Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)},
                -d]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
   Hyp`m`F[{a_,d_,c_,b_},{e_,f_,g_},1]:>
   Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d},
    {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b),
     (e+f)-(a+c),(e+f)-(a+d)},1]*
   Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)},
                -d]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d],
   Hyp`m`F[{d_,b_,c_,a_},{e_,f_,g_},1]:>
   Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d},
    {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b),
     (e+f)-(a+c),(e+f)-(a+d)},1]*
   Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)},
                -d]/;
         Factor[g-(a+b+c+d+1)+(e+f)]===0&&
         Hyp`m`Private`IntegerTest[d]};
T4304:={Hyp`m`F[{a_,b_,c_,g_},{d_,e_,f_},1] :> 
         Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g},
           {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]*
         Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g},
            {(d/2)+(e/2)-(1/2)-(g/2),
            (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/;
         Factor[f-(a+b+c+g+1)+(d+e)]===0&&
         Hyp`m`Private`IntegerTest[g],
      Hyp`m`F[{a_,b_,g_,c_},{d_,e_,f_},1] :> 
         Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g},
           {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]*
         Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g},
            {(d/2)+(e/2)-(1/2)-(g/2),
            (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/;
         Factor[f-(a+b+c+g+1)+(d+e)]===0&&
         Hyp`m`Private`IntegerTest[g],
      Hyp`m`F[{a_,g_,c_,b_},{d_,e_,f_},1] :> 
         Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g},
           {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]*
         Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g},
            {(d/2)+(e/2)-(1/2)-(g/2),
            (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/;
         Factor[f-(a+b+c+g+1)+(d+e)]===0&&
         Hyp`m`Private`IntegerTest[g],
      Hyp`m`F[{g_,b_,c_,a_},{d_,e_,f_},1] :> 
         Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g},
           {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]*
         Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g},
            {(d/2)+(e/2)-(1/2)-(g/2),
            (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/;
         Factor[f-(a+b+c+g+1)+(d+e)]===0&&
         Hyp`m`Private`IntegerTest[g]};
T7633:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:>
        Hyp`m`GAMMA[{(a+1)-d,(a+1)-c,(a+1)-b,(a+1)-(b+c+d)},
             {(a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),a+1}]*
        Hyp`m`F[{b,c,d,a+1-(e+f)},{(a+1)-e,(b+c+d)-a,a+1-f},1]/;
        Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
        Factor[b+bb-1-a]===Factor[c+cc-1-a]===Factor[d+dd-1-a]===
                 Factor[e+ee-1-a]===Factor[f+ff-1-a]===0&&
        Hyp`m`Private`IntegerTest[a+1-(e+f)]);
T3231:=(Hyp`m`F[{a_,b_,c_},{e_,g_},1]:>
        Hyp`m`F[{a/2,b/2,c,g-c},{e,g/2,(g+1)/2},1]/;
        Factor[e-((a/2)+(b/2)+(1/2))]===0&&
        (Hyp`m`Private`IntegerTest[a/2]||Hyp`m`Private`IntegerTest[b/2]||Hyp`m`Private`IntegerTest[c]||
         (Hyp`m`Private`IntegerTest[g-c]&&(Hyp`m`Private`IntegerTest[a]||Hyp`m`Private`IntegerTest[b]))));
T3232:=(Hyp`m`F[{a_,d_,e_},{b_,c_},z_]:>
  (1-Factor[((Factor[1-z])^(1/2)+1)/((Factor[1-z])^(1/2)-1)])^(2*a)*
   Hyp`m`F[{2*a,1+2*a-b,1+2*a-c},{b,c},Factor[((Factor[1-z])^(1/2)+1)/((Factor[1-z])^(1/2)-1)]]/;
   Factor[d-(1/2+a)]===Factor[e-(-1-2*a+b+c)]===0);
T3233:=(Hyp`m`F[{a_,d_,e_},{b_,c_},z_]:>
  (1-Factor[((Factor[1-z])^(1/2)-1)/((Factor[1-z])^(1/2)+1)])^(2*a)*
   Hyp`m`F[{2*a,1+2*a-b,1+2*a-c},{b,c},Factor[((Factor[1-z])^(1/2)-1)/((Factor[1-z])^(1/2)+1)]]/;
   Factor[d-(1/2+a)]===Factor[e-(-1-2*a+b+c)]===0);
T3234:=(Hyp`m`F[{a_,b_,c_},{d_,e_},z_]:>
  Hyp`m`F[{a/2,b/2},{1/2+a/2+b/2},z]^2/;
   Factor[c-(a/2+b/2)]===Factor[d-(a+b)]===Factor[e-(1/2+a/2+b/2)]===0);
T4306:=(Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:>
        Hyp`m`F[{2*a,2*b,c},{e,c+d},1]/;
        Factor[e-(a+b+(1/2))]===Factor[f-(c+d)/2]===Factor[g-(c+d+1)/2]===0&&
        (Hyp`m`Private`IntegerTest[a]||Hyp`m`Private`IntegerTest[b]||Hyp`m`Private`IntegerTest[c]||
         (Hyp`m`Private`IntegerTest[d]&&(Hyp`m`Private`IntegerTest[2*a]||Hyp`m`Private`IntegerTest[2*b]))));
T2132:=(Hyp`m`F[{a_,b_},{e_},z_]^exp_:1:>
        Hyp`m`F[{2*a,2*b,a+b},
                {2*a+2*b,a+b+(1/2)},z]^(exp/2)/;
        Factor[e-(a+b+(1/2))]===0);
T7634:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:>
        Hyp`m`GAMMA[{(a+1)-e,(a+1)-f,(2*a+2)-(b+c+d),(2*a+2)-(b+c+d+e+f)},
          {a+1,(a+1)-(e+f),(2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f)}]*
        Hyp`m`F[{(2*a+1)-(b+c+d),a+3/2-((b/2)+(c/2)+(d/2)),
           (a+1)-(c+d),(a+1)-(b+d),
           (a+1)-(b+c),e,f},{(a+(1/2))-((b/2)+(c/2)+(d/2)),
           (a+1)-b,(a+1)-c,(a+1)-d,
           (2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f)},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0);
T7635:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:>
        Hyp`m`GAMMA[{(a+1)-c,(a+1)-d,(a+1)-e,(a+1)-f,(3*a+3)-(2*b+c+d+e+f),
           (2*a+2)-(b+c+d+e+f)},
          {a+1,b,(2*a+2)-(b+d+e+f),(2*a+2)-(b+c+e+f),
           (2*a+2)-(b+c+d+f),(2*a+2)-(b+c+d+e)}]*
        Hyp`m`F[{(3*a+2)-(2*b+c+d+e+f),(a*(3/2)+2)-
            (b+(c/2)+(d/2)+(e/2)+(f/2)),(a+1)-(b+c),
           (a+1)-(b+d),(a+1)-(b+e),(a+1)-(b+f),(2*a+2)-(b+c+d+e+f)},
          {(a*(3/2)+1)-(b+(c/2)+(d/2)+(e/2)+(f/2)),(2*a+2)-(b+d+e+f),
           (2*a+2)-(b+c+e+f),(2*a+2)-(b+c+d+f),(2*a+2)-(b+c+d+e),(a+1)-b},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0);
T5401:=(Hyp`m`F[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},1]:>
  Hyp`m`p[{(a+2)-(b+c+d),(a*3+3)-(2*b+2*c+2*d)},
    {(2*a+2)-(b+c+d),(2*a+3)-(2*b+2*c+2*d)},-e]*
   Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)),
     (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),(a/2),(a/2)+(1/2),
     (a*3+(3))-(2*b+2*c+2*d+e),e},
    {(a+(1/2))-((b/2)+(c/2)+(d/2)),(a+1)-b,(a+1)-c,(a+1)-d,
     (a*(3/2)+2)-(b+c+d),(a*(3/2)+(3/2))-(b+c+d),
     (b+c+d+(-1)+e)-a,(2*a+(2))-(b+c+d+e)},1]/;
    Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0&&
    Factor[ee-(2*b+2*c+2*d+e+(-2)-2*a)]===0&&
    Hyp`m`Private`IntegerTest[e]);
T9832:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,g_,i_,j_},
                {aaaa_,bb_,cc_,dd_,ee_,gg_,ii_,jj_},1]:>
  Hyp`m`p[{a+1,(2*b+2*c+2*d)-(2*a+1)},{(b+c+d)-a,b+c+d},-j]*
  Hyp`m`F[{(2*a+1)-(b+c+d),(a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),j},
   {(a+1)-b,(a+1)-c,(a+1)-d,(2*a+(2)+j)-(2*b+2*c+2*d)},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]===0&&
         Factor[e-(a+(1/2)-(b/2)-(c/2)-(d/2))]===
           Factor[g-(1/2)-(a+(1/2)-(b/2)-(c/2)-(d/2))]===
         Factor[i-(b+c+d-j)]===0&&
         Hyp`m`Private`IntegerTest[j]);
T5402:=(Hyp`m`F[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},1]:>
  Hyp`m`F[{1+2*a-(b+c+d),(3/2)+a-((b/2)+(c/2)+(d/2)),1+a-(c+d),
     1+a-(b+d),1+a-(b+c),(a)/2,(1/2)+(a)/2,e,(3)+a*3-(2*b+2*c+2*d+e)},
    {(1/2)+a-((b/2)+(c/2)+(d/2)),1+a-b,1+a-c,
     1+a-d,(2)+a*(3/2)-(b+c+d),
     (3/2)+a*(3/2)-(b+c+d),
     (2)+2*a-(b+c+d+e),b+c+d+e+(-1)-a},1]*
   Hyp`m`p[{(2)+2*a-(b+c+d+e),(3)+a*3-(2*b+2*c+2*d)},
    {(2)+2*a-(b+c+d),(3)+a*3-(2*b+2*c+2*d+e)},-a]/;
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
   Factor[ee-2*(b+c+d-1-a)-e]===0&&
   Hyp`m`Private`IntegerTest[a]);
T9833:=(Hyp`m`F[{a_,aa_,b_,c_,d_,f_,h_,e_,j_},
    {aaaa_,bb_,cc_,dd_,ff_,hh_,ee_,jj_},1]:>
  Hyp`m`F[{2*f,((b/2)+(1/2)+f)-((c/2)+(d/2)),
    ((c/2)+(1/2)+f)-((b/2)+(d/2)),
    ((d/2)+(1/2)+f)-((b/2)+(c/2)),e},
   {((c/2)+(d/2)+(1/2)+f)-(b/2),
    ((b/2)+(d/2)+(1/2)+f)-(c/2),
    ((b/2)+(c/2)+(1/2)+f)-(d/2),(e+1+2*f)-(b+c+d)},1]*
   Hyp`m`p[{(b/2)+(c/2)+(d/2)+(1/2)+f,(b+c+d)-e},
    {((b/2)+(c/2)+(d/2)+(1/2)+f)-e,b+c+d},-2*f]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===
           Factor[h+hh-(1+a)]===Factor[j+jj-(1+a)]===0&&
   Factor[a-((b/2)+(c/2)+(d/2)+h-1)]===0&&
   Factor[j-(b+c+d-e)]===Factor[f+1/2-h]===0&&
   Hyp`m`Private`IntegerTest[2*f]);
T6531:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_},
   {aaaa_,bb_,cc_,dd_,ee_},1]:>
   (((a*3+1-2*e)-(2*b+2*c+2*d))*
     Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)),
       (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),(a/2)+(1/2),(a/2)+1,
       (a*3+1)-(2*b+2*c+2*d+e),e},
      {(a+(1/2))-((b/2)+(c/2)+(d/2)),(a+1)-b,(a+1)-c,(a+1)-d,
       (a*(3/2)+(3/2))-(b+c+d),(a*(3/2)+1)-(b+c+d),(b+c+d+1+e)-a,
       (2*a+(2))-(b+c+d+e)},1]*
     Hyp`m`p[{a-(b+c+d),(a*3+1)-(2*b+2*c+2*d)},
      {(2*a+2)-(b+c+d),(2*a+1)-(2*b+2*c+2*d)},-e])/
   ((a*3+1)-(2*b+2*c+2*d))/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0&&
   Factor[ee-(2*b+2*c+2*d+e-(2*a))]===0&&
   Hyp`m`Private`IntegerTest[e]);
T9834:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,g_,i_,j_},
      {aaaa_,bb_,cc_,dd_,ee_,gg_,ii_,jj_},1]:>
  Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)),
    (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),j},{(a+(1/2))-((b/2)+(c/2)+(d/2)),
    (a+1)-b,(a+1)-c,(a+1)-d,(2*a+(4)+j)-(2*b+2*c+2*d)},1]*
   ((b+c+d)-2)/(b+c+d+(-2)-2*j)*
  Hyp`m`p[{a+1,(2*b+2*c+2*d)-(2*a+3)},
      {(b+c+d)-(a+2),(b+c+d)-2},-j]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]===0&&
   Factor[e-g+(1/2)]===Factor[(a+1)-((b/2)+(c/2)+(d/2))-e]===
   Factor[i-(b+c+d+(-2)-j)]===0&&
   Hyp`m`Private`IntegerTest[j]);
T9831:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,h_},
            {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},1] :> 
  Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)),
     (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),e,f,(a*3+(2))-(b+c+d+e+f+h),h},
    {(a+(1/2))-((b/2)+(c/2)+(d/2)),(a+1)-b,(a+1)-c,(a+1)-d,
     (2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f),(e+f+h)-(a),
     (2*a+(2))-(b+c+d+h)},1]*
   Hyp`m`p[{a+1,(a+1)-(e+f),(2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f)},
    {(a+1)-e,(a+1)-f,(2*a+2)-(b+c+d+e+f),(2*a+2)-(b+c+d)},-h]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===0&&
   Factor[g-(a*3+(2))+(b+c+d+e+f+h)]===0&&
   Hyp`m`Private`IntegerTest[h]);
T2191:=(Hyp`m`F[{a_,b_},{c_},z_]:>
  (1-z)^(-a-b+c)*Hyp`m`F[{-b+c,-a+c},{1-a-b+c},1-z]*
    Hyp`m`GAMMA[{c,a+b-c},{a,b}]+
  Hyp`m`F[{a,b},{1+a+b-c},1-z]*Hyp`m`GAMMA[{c,-a-b+c},{-b+c,-a+c}]);
T3261:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>
  Hyp`m`GAMMA[{c,c+1-d,1-a,e-(b+c)},{e-b,e-c,c+1-a,1-d}]*
    Hyp`m`F[{c,d-a,c+1-e},{c+1-a,b+c+1-e},1]-
  Hyp`m`GAMMA[{d-1,e,b+1-d,c+1-d,1-a,e-(b+c),b+c+1-e},
         {1-d,e+1-d,b,c,d-a,d+e-(b+c+1),b+c+2-(d+e)}]*
    Hyp`m`F[{a+1-d,b+1-d,c+1-d},{2-d,e+1-d},1]);
T3262:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>
  Hyp`m`GAMMA[{e,e-(b+c)},{e-b,e-c}]*Hyp`m`F[{d-a,b,c},{d,b+c+1-e},1]+
  Hyp`m`GAMMA[{d,c,b+c-e,d+e-(a+b+c)},{d-a,b,c,d+e-(b+c)}]*
    Hyp`m`F[{e-b,e-c,d+e-(a+b+c)},{d+e-(b+c),e+1-(b+c)},1]);
T7691:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:>
  Hyp`m`GAMMA[{a+1-d,a+1-e,a+1-f,a+1-(d+e+f)},{a+1,a+1-(d+e),a+1-(d+f),a+1-(e+f)}]*
    Hyp`m`F[{a+1-(b+c),d,e,f},{a+1-b,a+1-c,d+e+f-a},1]+
  Hyp`m`GAMMA[{a+1-b,a+1-c,a+1-d,a+1-e,a+1-f,2*a+2-(b+c+d+e+f),d+e+f-(a+1)},
        {a+1,a+1-(b+c),d,e,f,2*a+2-(b+d+e+f),2*a+2-(c+d+e+f)}]*
    Hyp`m`F[{a+1-(d+e),a+1-(d+f),a+1-(e+f),2*a+2-(b+c+d+e+f)},
        {2*a+2-(b+d+e+f),2*a+2-(c+d+e+f),a+2-(d+e+f)},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0);
T7692:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:>
  Hyp`m`GAMMA[{a+1-d,a+1-e,a+1-f,a+1-(d+e+f),1-c,e+f+1-c,b+e-a,b+f-a},
        {a+1,a+1-(d+e),a+1-(d+f),a+1-(e+f),e+1-c,f+1-c,b+e+f-a}]*
    Hyp`m`F[{e+f-c,1+(e+f-c)/2,a+1-(b+c),a+1-(c+d),e+f-a,e,f},
        {(e+f-c)/2,b+e+f-a,d+e+f-a,a+1-c,f+1-c,e+1-c},1]-
  Hyp`m`GAMMA[{a-b,a+1-c,a+1-d,a+1-e,a+1-f,b+d-a,b+e-a,b+f-a,d+e+f-a,a+1-(d+e+f),
        1-c,2*b+1-a},
        {a+1,b-a,b+1-c,b+1-d,b+1-e,b+1-f,d,e,f,a+1-(b+c),
        b+d+e+f-2*a,2*a+1-(b+d+e+f)}]*
    Hyp`m`F[{2*b-a,1+(2*b-a)/2,b,b+c-a,b+d-a,b+e-a,b+f-a},
        {(2*b-a)/2,b+1-a,b+1-c,b+1-d,b+1-e,b+1-f},1]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0);
T9891:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,h_},
         {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},1]:>
   -Hyp`m`GAMMA[{(2*b+1)-a,a-b,(a+1)-c,(a+1)-d,(a+1)-e,(a+1)-f,(a+1)-g,
      (b+c+d+e+f+g)-(2*a+1),(b+c)-a,(b+d)-a,(b+e)-a,(b+f)-a,(b+g)-a,
      (2*a+2)-(c+d+e+f+g)},
     {a+1,b-a,c,d,e,f,g,(a*3+2)-(b+c+d+e+f+g),(b+1)-c,
      (b+1)-d,(b+1)-e,(b+1)-f,(b+1)-g,(2*b+c+d+e+f+g)-(a*3+1)}]*
    Hyp`m`F[{2*b-a,(b+1)-(a/2),b,(b+c)-a,(b+d)-a,
      (b+e)-a,(b+f)-a,(b+g)-a,(2*a+2)-(c+d+e+f+g)},
     {b-(a/2),(b+1)-a,(b+1)-c,(b+1)-d,(b+1)-e,(b+1)-f,
      (b+1)-g,(2*b+c+d+e+f+g)-(a*3+1)},1]+
  Hyp`m`GAMMA[{(2*b+c+d+e)-2*a,(2*a+1)-(b+c+d+e),(a+1)-c,(a+1)-d,(a+1)-e,
      (a+1)-f,(a+1)-g,(b+c+d+e+f+g)-(2*a+1),(b+c)-a,(b+d)-a,(b+e)-a,
      (b+f)-a,(b+g)-a,(2*a+2)-(c+d+e+f+g)},
     {a+1,b-a,f,g,(a*3+2)-(b+c+d+e+f+g),(b+1)-f,(b+1)-g,
      (2*b+c+d+e+f+g)-(a*3+1),(a+1)-(d+e),(a+1)-(c+e),(a+1)-(c+d),
      (b+d+e)-a,(b+c+e)-a,(b+c+d)-a}]*
    Hyp`m`F[{(2*b+c+d+e)-(2*a+1),(b+(c/2)+(d/2)+(e/2)+(1/2))-a,
      b,(b+c)-a,(b+d)-a,
      (b+e)-a,(b+c+d+e+f)-(2*a+1),(b+c+d+e+g)-(2*a+1),(a+1)-(f+g)},
     {(b+(c/2)+(d/2)+(e/2))-(a+(1/2)),(b+c+d+e)-2*a,(b+d+e)-a,
      (b+c+e)-a,(b+c+d)-a,(b+1)-f,(b+1)-g,(2*b+c+d+e+f+g)-(a*3+1)},1]\
    +Hyp`m`GAMMA[{(2*a+2)-(c+d+e),(b+c+d+e)-(2*a+1),(a+1)-f,(a+1)-g,
      (b+c+d+e+f+g)-(2*a+1),(b+f)-a,(b+g)-a,(2*a+2)-(c+d+e+f+g)},
     {a+1,b-a,(2*a+2)-(c+d+e+f),(2*a+2)-(c+d+e+g),
      (b+f+g)-a,(b+c+d+e+f)-(2*a+1),(b+c+d+e+g)-(2*a+1),(a+1)-(f+g)}]*
    Hyp`m`F[{(2*a+1)-(c+d+e),(a+(3/2))-((c/2)+(d/2)+(e/2)),
      b,(a+1)-(d+e),(a+1)-(c+e),(a+1)-(c+d),f,g,(a*3+2)-(b+c+d+e+f+g)},
     {(a+(1/2))-((c/2)+(d/2)+(e/2)),(2*a+2)-(b+c+d+e),
      (a+1)-c,(a+1)-d,(a+1)-e,(2*a+2)-(c+d+e+f),(2*a+2)-(c+d+e+g),
      (b+f+g)-a},1]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===0&&
   Factor[h-a*3-2+(b+c+d+e+f+g)]===0);


T2110:=
   (Hyp`m`F[{a_,b_},{c_},z_]:>
     Hyp`m`F[{a/2,1/2+a/2},{1+a-b},(4*z)/(1+z)^2]/(1+z)^a/;
    Factor[c-1-a+b]===0);

T2112:=
   {(Hyp`m`F[{a_,c_},{b_},z_]:>
  Hyp`m`F[{2*a,b-1/2},{2*b-1},(2*Sqrt[z])/(-1+Sqrt[z])]/(1-Sqrt[z])^(2*a)/;
    Factor[c-a-1/2]===0),
    (Hyp`m`F[{c_,a_},{b_},z_]:>
  Hyp`m`F[{2*a,b-1/2},{2*b-1},(2*Sqrt[z])/(-1+Sqrt[z])]/(1-Sqrt[z])^(2*a)/;
    Factor[c-a-1/2]===0)};

T2163:=
   (Hyp`m`F[{a_,b_},{c_},z_]:>(Hyp`m`F[{b,-a+c},{1-a+b},-(-1+z)^(-1)]*
      Hyp`m`GAMMA[{a-b,c},{a,-b+c}])/(1-z)^b+
   (Hyp`m`F[{a,-b+c},{1+a-b},-(-1+z)^(-1)]*
      Hyp`m`GAMMA[{-a+b,c},{b,-a+c}])/(1-z)^a);

T2133:=
   (Hyp`m`F[{a_,b_},{c_},z_] :> (1-2*z-2*(z^2-z)^(1/2))^a*
     Hyp`m`F[{2*a,a+b},{2*a+2*b},2*(z+(z^2-z)^(1/2))]/;
    Factor[c-(1/2+a+b)]===0);

T2134:=
   (Hyp`m`F[{a_,b_},{c_},z_] :> 
  Hyp`m`F[{a/2,b/2},{1/2+a/2+b/2},4*(1-z)*z]/;
    Factor[c-(1/2+a/2+b/2)]===0);

T2135:=
   (Hyp`m`F[{a_,b_},{c_},z_] :> Hyp`m`F[{2*a,2*b},{1/2+a+b},
   (1-(1-z)^(1/2))/2]/;
    Factor[c-(1/2+a+b)]===0);

T2136:=
   {(Hyp`m`F[{a_,b_},{c_},z_] :> (2^a*Hyp`m`F[{a/2,1/2+a/2},{1/2+b},z^2/(-2+z)^2])/
   (2-z)^a/;
    Factor[c-2*b]===0),
    (Hyp`m`F[{b_,a_},{c_},z_] :> (2^a*Hyp`m`F[{a/2,1/2+a/2},{1/2+b},z^2/(-2+z)^2])/
   (2-z)^a/;
    Factor[c-2*b]===0)};

T2137:=
   {(Hyp`m`F[{a_,b_},{c_},z_] :> 
     Hyp`m`F[{a/2,(-a+2*b)/2},{(1+2*b)/2},z^2/(4*(-1+z))]/(1-z)^(a/2)/;
    Factor[c-2*b]===0),
    (Hyp`m`F[{b_,a_},{c_},z_] :> 
     Hyp`m`F[{a/2,(-a+2*b)/2},{(1+2*b)/2},z^2/(4*(-1+z))]/(1-z)^(a/2)/;
    Factor[c-2*b]===0)};

T3267:=
   (Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>Hyp`m`F[{a,1+a-e,1+a+b+c-d-e},
     {1+a+b-e,1+a+c-e},1]*
    Hyp`m`GAMMA[{d,1+a-e,1+b-e,1+c-e},
     {-a+d,1-e,1+a+b-e,1+a+c-e}]-
   Hyp`m`F[{1+a-e,1+b-e,1+c-e},{2-e,1+d-e},1]*
    Hyp`m`GAMMA[{d,1+a-e,1+b-e,1+c-e,-1+e},
     {a,b,c,1-e,1+d-e}]);

T3268:=
   (Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>Hyp`m`F[{b,-a+d,-a+e},
     {1-a+b,-a-c+d+e},1]*
    Hyp`m`GAMMA[{a-b,d,e,-a-b-c+d+e},
     {a,-b+d,-b+e,-a-c+d+e}]+
   Hyp`m`F[{a,-b+d,-b+e},{-b-c+d+e,1+a-b},1]*
    Hyp`m`GAMMA[{-a+b,d,e,-a-b-c+d+e},
     {b,-a+d,-a+e,-b-c+d+e}]);

T2192:=
   (Hyp`m`F[{a_,b_},{c_},z_] :> (Hyp`m`F[{a,1+a-c},{1+a+b-c},(z-1)/z]*
      Hyp`m`GAMMA[{1+a-c,1+b-c},{1-c,1+a+b-c}])/z^a-
   z^(1-c)*Hyp`m`F[{1+a-c,1+b-c},{2-c},z]*
    Hyp`m`GAMMA[{1+a-c,1+b-c,-1+c},{a,b,1-c}]);

T3235:=
   (Hyp`m`F[{a_,b_,n_},{d_,e_},2] :> (Hyp`m`F[{a/2,1/2+a/2,1/2+n/2,n/2},
      {1/2+a/2-d/2+n/2,1+a/2-d/2+n/2,1/2+b},1]*Hyp`m`p[-a+d,-n])/
   Hyp`m`p[d,-n]/;
    Factor[e-2*b]===0&&
    Hyp`m`Private`IntegerTest[n]);

T4309:=
   (Hyp`m`F[{a_,b_,c_,d_},{bb_,cc_,dd_},1]:>
  Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,a/2,1/2+a/2,
     1+a-c-d,1+a-b-d,1+a-b-c},
    {1/2+a-b/2-c/2-d/2,2+(3*a)/2-b-c-d,
     3/2+(3*a)/2-b-c-d,1+a-b,1+a-c,1+a-d},1]*
   Hyp`m`GAMMA[{3+2*a-2*b-2*c-2*d,2+2*a-b-c-d},
    {3+3*a-2*b-2*c-2*d,2+a-b-c-d}]/;
    Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0);

T4310:=
   (Hyp`m`F[{a_,b_,c_,d_},{bb_,cc_,dd_},-1]:>
  Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,a/2,1+a-c-d,
     1+a-b-d,1+a-b-c},
    {1/2+a-b/2-c/2-d/2,2+(3*a)/2-b-c-d,1+a-b,
     1+a-c,1+a-d},-1]*
   Hyp`m`GAMMA[{2+2*a-b-c-d,1+a/2},{1+a,2+(3*a)/2-b-c-d}]/;
    Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0);

T3236:=
   (Hyp`m`F[{a_,aa_,b_},{aaaa_,bb_},z_]:>
  (1-z)*(1+z)^(-1-a)*Hyp`m`F[{1/2+a/2,1+a/2},{1+a-b},
    (4*z)/(1+z)^2]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===0);

T4312:=
   (Hyp`m`F[{a_,aa_,nn_,n_},{d_,dd_,b_},1]:>
  Hyp`m`F[{2*a,b-1/2,2*n},{1+2*a-2*d+2*n,2*b-1},2]*Hyp`m`p[{-2*a+2*d},{2*d},-2*n]/;
    Factor[aa-1/2-a]===Factor[nn-1/2-n]===Factor[dd-1/2-d]===0&&
    Hyp`m`Private`IntegerTest[2*n]);

T4391:=
   (Hyp`m`F[{a_,c_,d_,e_},{b_,aa_,f_},1] :> 
  Hyp`m`F[{-1/2+b,3/4+b/2,-a+b,c/2,1/2+c/2,d/2,1/2+d/2,e/2,
      1/2+e/2},{-1/4+b/2,1/2+a,1/2+b-c/2,b-c/2,
      1/2+b-d/2,b-d/2,1/2+b-e/2,b-e/2},1]*
    Hyp`m`GAMMA[{b,1/2+b,b-c/2-d/2,1/2+b-c/2-d/2,b-c/2-e/2,
      1/2+b-c/2-e/2,b-d/2-e/2,1/2+b-d/2-e/2},
     {b-c/2,1/2+b-c/2,b-d/2,1/2+b-d/2,b-e/2,
      1/2+b-e/2,b-c/2-d/2-e/2,1/2+b-c/2-d/2-e/2}]-
   Hyp`m`F[{a+2*b-c-d-e,2*b-c-d,2*b-c-e,2*b-d-e},
     {3*b-c-d-e,2*a+2*b-c-d-e,1+2*b-c-d-e},1]*
    Hyp`m`GAMMA[{1/2+a,b,b-c/2-d/2,1/2+b-c/2-d/2,
      a+2*b-c-d-e,b-c/2-e/2,1/2+b-c/2-e/2,
      b-d/2-e/2,1/2+b-d/2-e/2,-b+c/2+d/2+e/2,
      1/2-b+c/2+d/2+e/2},
     {c/2,1/2+c/2,d/2,1/2+d/2,3*b-c-d-e,b-c/2-d/2-e/2,
      1/2+b-c/2-d/2-e/2,a+b-c/2-d/2-e/2,
      1/2+a+b-c/2-d/2-e/2,e/2,1/2+e/2}]/;
    Factor[aa-2*a]===Factor[f-(1-2*b+c+d+e)]===0);

T5468:=
   (Hyp`m`F[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},1] :> 
   -Hyp`m`F[{3+2*a-2*b-2*c-2*d,3+3*a-2*b-2*c-2*d-e,
        3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e,
        3+2*a-2*b-2*c-d-e},
       {4+2*a-2*b-2*c-2*d-e,4+3*a-3*b-2*c-2*d-e,
        4+3*a-2*b-3*c-2*d-e,4+3*a-2*b-2*c-3*d-e},1]*
      Hyp`m`GAMMA[{1+a-b,1+a-c,3+2*a-2*b-2*c-2*d,
      1+a-d,3+3*a-2*b-2*c-2*d-e,3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e,
      3+2*a-2*b-2*c-d-e,-3-2*a+2*b+2*c+2*d+e},
    {a,b,c,d,4+3*a-2*b-2*c-3*d-e,4+3*a-2*b-3*c-2*d-e,4+3*a-3*b-2*c-2*d-e,
      3+2*a-2*b-2*c-2*d-e,e}] +
  Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,a/2,1/2+a/2,
      1+a-c-d,1+a-b-d,1+a-b-c,e,
      3+3*a-2*b-2*c-2*d-e},
     {1/2+a-b/2-c/2-d/2,2+(3*a)/2-b-c-d,
      3/2+(3*a)/2-b-c-d,1+a-b,1+a-c,1+a-d,
      2+2*a-b-c-d-e,-1-a+b+c+d+e},1]*
    Hyp`m`GAMMA[{3+2*a-2*b-2*c-2*d,2+2*a-b-c-d,
      3+3*a-2*b-2*c-2*d-e,2+a-b-c-d-e},
     {3+3*a-2*b-2*c-2*d,2+a-b-c-d,
      3+2*a-2*b-2*c-2*d-e,2+2*a-b-c-d-e}]+
   Hyp`m`F[{5+4*a-3*b-3*c-3*d-2*e,
      7/2+2*a-(3*b)/2-(3*c)/2-(3*d)/2-e,
      2+(3*a)/2-b-c-d-e,5/2+(3*a)/2-b-c-d-e,
      2+a-b-c-d,3+3*a-2*b-2*c-2*d-e,
      3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e,
      3+2*a-2*b-2*c-d-e},
     {5/2+2*a-(3*b)/2-(3*c)/2-(3*d)/2-e,
      4+(5*a)/2-2*b-2*c-2*d-e,
      7/2+(5*a)/2-2*b-2*c-2*d-e,4+3*a-2*b-2*c-2*d-2*e,
      3+a-b-c-d-e,3+2*a-2*b-c-d-e,
      3+2*a-b-2*c-d-e,3+2*a-b-c-2*d-e},1]*
    Hyp`m`GAMMA[{1+a-b,1+a-c,3+2*a-2*b-2*c-2*d,1+a-d,
      6+4*a-3*b-3*c-3*d-2*e,3+3*a-2*b-2*c-2*d-e,
      3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e,
      3+2*a-2*b-2*c-d-e,-2-a+b+c+d+e},
     {a,1+a-b-c,1+a-b-d,1+a-c-d,
      7+5*a-4*b-4*c-4*d-2*e,3+2*a-2*b-2*c-2*d-e,
      3+2*a-b-c-2*d-e,3+2*a-b-2*c-d-e,
      3+2*a-2*b-c-d-e,e}]/;
    Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
    Factor[ee-(-2-2*a+2*b+2*c+2*d+e)]===0);

T6501:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,n_},{aaaa_,bb_,cc_,dd_,nn_},1]:>
  Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,1+a-c-d,
     1+a-b-d,1+a-b-c,1+a/2,1/2+a/2,
     2+3*a-2*b-2*c-2*d-n,n},
    {1/2+a-b/2-c/2-d/2,1+a-b,1+a-c,1+a-d,
     1+(3*a)/2-b-c-d,3/2+(3*a)/2-b-c-d,
     -a+b+c+d+n,2+2*a-b-c-d-n},1]*
   Hyp`m`p[{2+3*a-2*b-2*c-2*d,1+a-b-c-d},
    {2+2*a-2*b-2*c-2*d,2+2*a-b-c-d},-n]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
         Factor[nn-(-1-2*a+2*b+2*c+2*d+n)]===0&&
         Hyp`m`Private`IntegerTest[n]);

T6532:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,e_},
   {aaaa_,bb_,cc_,dd_,ee_},-1]:>
  Hyp`m`F[{2*b,-a+2*b+c,-a+2*b+d,1+a-c-d},
    {1+a-c,1+a-d,-a+2*b+c+d},-1]*
   Hyp`m`GAMMA[{1+2*b,1+a-b},{1+b,1+a}]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[e-(1+2*a-2*b-c-d)]===0);

T7636:=
   (Hyp`m`F[{a_,aa_,b_,c_,e_,d_,f_},
   {aaaa_,bb_,cc_,ee_,dd_,ff_},1]:>
  Hyp`m`F[{2*c,b,1/2+a-2*d},{1+2*a-b-2*d,1/2+a},1]*
   Hyp`m`GAMMA[{1+2*a-2*b,1+2*a-2*c,1+2*a-2*d,
     1+2*a-b-2*c-2*d},{1+2*a,1+2*a-2*b-2*c,
     1+2*a-b-2*d,1+2*a-2*c-2*d}]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===
         Factor[e-1/2-c]===Factor[f-1/2-d]===0);

T7693:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},
   {aaaa_,bb_,cc_,dd_,ee_,ff_},1] :> 
  -(Hyp`m`F[{-a+2*b,1-a/2+b,b,-a+b+c,-a+b+d,-a+b+e,
        -a+b+f},{-a/2+b,1-a+b,1+b-c,1+b-d,
        1+b-e,1+b-f},1]*
      Hyp`m`GAMMA[{a-b,1-a+2*b,-b+c,-a+b+c,1-d,1+a-d,
        1-e,1+a-e,1-f,1+a-f},
       {1+a,-a+b,-a+c,c,1+a-b-d,1+b-d,1+a-b-e,
        1+b-e,1+a-b-f,1+b-f}])-
   Hyp`m`F[{-a+2*c,1-a/2+c,c,-a+b+c,-a+c+d,-a+c+e,
      -a+c+f},{-a/2+c,1-a+c,1-b+c,1+c-d,1+c-e,
      1+c-f},1]*Hyp`m`GAMMA[{a-c,b-c,-a+b+c,1-a+2*c,1-d,
      1+a-d,1-e,1+a-e,1-f,1+a-f},
     {1+a,-a+b,b,-a+c,1+a-c-d,1+c-d,1+a-c-e,
      1+c-e,1+a-c-f,1+c-f}]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0);

T7637:=
   (Hyp`m`F[{a_,aa_,b_,e_,c_,d_,f_},
   {aaaa_,bb_,ee_,cc_,dd_,ff_},1] :>
    Hyp`m`F[{2*b,-a+2*b+c,-a+2*b+d,1+a-c-d},
    {1+a-c,1+a-d,-a+2*b+c+d},1]*
   Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b},{1+a,1+2*a-4*b}]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===
         Factor[e-1/2-b]===Factor[f-(1+2*a-2*b-c-d)]===0);

T9835:=
  (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,n_},
   {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,nn_},1] :> 
  Hyp`m`F[{-b+e+n,1-b/2+e/2+n/2,e,1+a-b-c,
     1+a-b-d,1+a-b-f,-1-2*a+c+d+e+f+n,
     -a+e+n,n},{-b/2+e/2+n/2,1-b+n,-a+c+e+n,
     -a+d+e+n,-a+e+f+n,2+2*a-b-c-d-f,1+a-b,
     1-b+e},1]*Hyp`m`p[{1+a,b,1+a-c-e,1+a-d-e,
     1+a-e-f,-1-2*a+b+c+d+f+n},
    {1+a-c,1+a-d,1+a-e,b-e,1+a-f,
     -1-2*a+b+c+d+e+f+n},-n]/;
       Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===
           Factor[g+gg-(1+a)]===Factor[n+nn-(1+a)]===
        Factor[g-(2+3*a-b-c-d-e-f-n)]===0&&
           Hyp`m`Private`IntegerTest[n]);

T9836:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,A_,B_,C_,n_},
   {aaaa_,bb_,cc_,dd_,AA_,BB_,CC_,nn_},1]:>
  Hyp`m`F[{-A/2-B/2-C/2+(3*n)/2,1-A/4-B/4-C/4+(3*n)/4,
     -A/2-B/2+C/2+n/2,A/2-B/2-C/2+n/2,
     -A/2+B/2-C/2+n/2,-a+c+n,-b-c+n,-a+b+n,n},
    {-A/4-B/4-C/4+(3*n)/4,1-C+n,1-A+n,1-B+n,
     -c+n,-a+b+c+n,-b+n,-a+n},1]*
   Hyp`m`p[{1+c,1-C+n,1-A+n,1-B+n,1+a,1+b,
     1+a-b-c},{1+b+c,1-A/2-B/2-C/2+(3*n)/2,
     1-A/2-B/2+C/2+n/2,1-A/2+B/2-C/2+n/2,
     1+A/2-B/2-C/2+n/2,1+a-b,1+a-c},-n]/;
     Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
     Factor[d-(a-b-c)]===
     Factor[B+BB-(A+B+C+n)/2]===Factor[C+CC-(A+B+C+n)/2]===Factor[n+nn-(A+B+C+n)/2]===0&&
     Hyp`m`Private`IntegerTest[n]);

T8731:=
   (Hyp`m`F[{a_,aa_,c_,d_,e_,b_,f_,n_},
   {aaaa_,cc_,dd_,ee_,bb_,ff_,nn_},-1]:>
  Hyp`m`F[{a/2+n/2,1+a/4+n/4,n,c/2,1/2+c/2,d/2,1/2+d/2,e/2,
     1/2+e/2,1/2+a-c/2-d/2-e/2+n/2,
     1+a-c/2-d/2-e/2+n/2},
    {a/4+n/4,1+a/2-n/2,1+a/2-c/2+n/2,1/2+a/2-c/2+n/2,
     1+a/2-d/2+n/2,1/2+a/2-d/2+n/2,1+a/2-e/2+n/2,
     1/2+a/2-e/2+n/2,1/2-a/2+c/2+d/2+e/2,
     -a/2+c/2+d/2+e/2},1]*
   Hyp`m`p[{1+a-c+n,1+a-d+n,1+a-e+n,1+a-c-d-e+n},
    {1+a+n,1+a-c-d+n,1+a-c-e+n,1+a-d-e+n},-n]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===
           Factor[n+nn-(1+a)]===
   Factor[b-(1/2+a/2-n/2)]===Factor[f-(1+2*a-c-d-e+n)]===0&&
   Hyp`m`Private`IntegerTest[n]);

T8732:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,n_},
   {aaaa_,bb_,cc_,dd_,ee_,ff_,nn_},-1]:>
  Hyp`m`F[{a/2+e/2,1+a/4+e/4,e,c/2,1/2+c/2,d/2,1/2+d/2,
     1/2+a-c/2-d/2+e/2-n/2,1+a-c/2-d/2+e/2-n/2,
     1/2+n/2,n/2},{a/4+e/4,1+a/2-e/2,1+a/2-c/2+e/2,
     1/2+a/2-c/2+e/2,1+a/2-d/2+e/2,1/2+a/2-d/2+e/2,
     1/2-a/2+c/2+d/2+n/2,-a/2+c/2+d/2+n/2,
     1/2+a/2+e/2-n/2,1+a/2+e/2-n/2},1]*
   Hyp`m`p[{1+a-c+e,1+a-d+e,1+a,1+a-c-d},
    {1+a+e,1+a-c-d+e,1+a-c,1+a-d},-n]/;
    Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===
           Factor[n+nn-(1+a)]===
    Factor[b-(1/2+a/2-e/2)]===Factor[f-(1+2*a-c-d+e-n)]===0&&
    Hyp`m`Private`IntegerTest[n]);

T9892:=
   (Hyp`m`F[{a_,aa_,b_,c_,f_,d_,g_,e_,h_},
   {aaaa_,bb_,cc_,ff_,dd_,gg_,ee_,hh_},1]:>
  Hyp`m`F[{1/2+a-b,2*c,2*d,2*e},
     {1/2+a,1+2*a-2*b,-2*a+2*c+2*d+2*e},1]*
    Hyp`m`GAMMA[{1/2+a-c,1+a-c,1/2+a-d,1+a-d,1/2+a-e,
      1+a-e,1/2+a-c-d-e,1+a-c-d-e},
     {1/2+a,1+a,1/2+a-c-d,1+a-c-d,1/2+a-c-e,
      1+a-c-e,1/2+a-d-e,1+a-d-e}]+
   Hyp`m`F[{3/2+3*a-b-2*c-2*d-2*e,1+2*a-2*c-2*d,
      1+2*a-2*c-2*e,1+2*a-2*d-2*e},
     {3/2+3*a-2*c-2*d-2*e,2+4*a-2*b-2*c-2*d-2*e,
      2+2*a-2*c-2*d-2*e},1]*
    Hyp`m`GAMMA[{1+a-b,1/2+a-c,1+a-c,1/2+a-d,1+a-d,
      3/2+3*a-b-2*c-2*d-2*e,1/2+a-e,1+a-e,
      -1/2-a+c+d+e,-a+c+d+e},
     {1+a,c,1/2+c,d,1/2+d,3/2+3*a-2*c-2*d-2*e,
      1+2*a-b-c-d-e,3/2+2*a-b-c-d-e,e,1/2+e}]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===
   Factor[f-1/2-c]===Factor[g-1/2-d]===Factor[h-1/2-e]===0);

T9893:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,h_},
    {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},1] :>
   -Hyp`m`F[{-a+2*b,1-a/2+b,b,-a+b+c,-a+b+d,-a+b+e,
        -a+b+f,-a+b+g,2+2*a-c-d-e-f-g},
       {-a/2+b,1-a+b,1+b-c,1+b-d,1+b-e,1+b-f,
        1+b-g,-1-3*a+2*b+c+d+e+f+g},1]*
      Hyp`m`GAMMA[{a-b,1-a+2*b,1+a-c,-a+b+c,1+a-d,-a+b+d,1+a-e,-a+b+e,
      1+a-f,-a+b+f,1+a-g,2+2*a-c-d-e-f-g,-a+b+g,-1-2*a+b+c+d+e+f+g},
    {1+a,-a+b,1+b-c,c,1+b-d,d,1+b-e,e,1+b-f,f,1+b-g,2+3*a-b-c-d-e-f-g,g,
      -1-3*a+2*b+c+d+e+f+g}] +
  Hyp`m`F[{2+3*a-c-d-e-f-2*g,
      2+(3*a)/2-c/2-d/2-e/2-f/2-g,b,1+a-c-g,
      1+a-d-g,1+a-e-g,1+a-f-g,
      2+2*a-c-d-e-f-g,2+3*a-b-c-d-e-f-g},
     {1+(3*a)/2-c/2-d/2-e/2-f/2-g,
      3+3*a-b-c-d-e-f-2*g,2+2*a-d-e-f-g,
      2+2*a-c-e-f-g,2+2*a-c-d-f-g,
      2+2*a-c-d-e-g,1+a-g,1+b-g},1]*
    Hyp`m`GAMMA[{1+a-c,-a+b+c,1+a-d,-a+b+d,1+a-e,
      -a+b+e,1+a-f,-a+b+f,3+3*a-c-d-e-f-2*g,
      2+2*a-c-d-e-f-g,-1-2*a+b+c+d+e+f+g,
      -2-3*a+b+c+d+e+f+2*g},
     {1+a,-a+b,1+b-g,2+2*a-c-d-e-g,
      2+2*a-c-d-f-g,2+2*a-c-e-f-g,
      2+2*a-d-e-f-g,g,-1-2*a+b+c+d+e+g,
      -1-2*a+b+c+d+f+g,-1-2*a+b+c+e+f+g,
      -1-2*a+b+d+e+f+g}]+
   Hyp`m`F[{-2-3*a+2*b+c+d+e+f+2*g,
      (-3*a)/2+b+c/2+d/2+e/2+f/2+g,b,
      -1-2*a+b+d+e+f+g,-1-2*a+b+c+e+f+g,
      -1-2*a+b+c+d+f+g,-1-2*a+b+c+d+e+g,
      -a+b+g,g},{-1-(3*a)/2+b+c/2+d/2+e/2+f/2+g,
      -1-3*a+b+c+d+e+f+2*g,-a+b+c+g,-a+b+d+g,
      -a+b+e+g,-a+b+f+g,-1-2*a+b+c+d+e+f+g,
      -1-3*a+2*b+c+d+e+f+g},1]*
    Hyp`m`GAMMA[{1+a-c,-a+b+c,1+a-d,-a+b+d,1+a-e,
      -a+b+e,1+a-f,-a+b+f,2+3*a-b-c-d-e-f-2*g,
      1+a-g,-a+b+g,-1-3*a+2*b+c+d+e+f+2*g},
     {1+a,-a+b,1+a-c-g,1+a-d-g,1+a-e-g,
      1+a-f-g,2+3*a-b-c-d-e-f-g,-a+b+c+g,
      -a+b+d+g,-a+b+e+g,-a+b+f+g,
      -1-3*a+2*b+c+d+e+f+g}]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===Factor[h-(2+3*a-b-c-d-e-f-g)]===0);

T9837:=
   (Hyp`m`F[{a_,aa_,c_,d_,e_,b_,f_,g_,n_},
   {aaaa_,cc_,dd_,ee_,bb_,ff_,gg_,nn_},1]:>
  Hyp`m`F[{-2+2*b,b,-2-a+2*b+c,-2-a+2*b+d,1+a-c-d,n},
    {-1+b,1+a-c,1+a-d,-2-a+2*b+c+d,
     -3-2*a+4*b+n},1]*Hyp`m`p[{1+a,4+2*a-4*b},
    {2+a-2*b,2+2*a-2*b},-n]/;
  Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[n+nn-(1+a)]===
   Factor[e-(3+2*a-2*b-c-d)]===Factor[f+1/2-b]===Factor[g-(2+2*a-2*b-n)]===0&&
   Hyp`m`Private`IntegerTest[n]);

T111031:=
   (Hyp`m`F[{a_,aa_,c_,f_,d_,g_,e_,h_,i_,j_,n_},
   {aaaa_,cc_,ff_,dd_,gg_,ee_,hh_,ii_,jj_,nn_},1]:>
   Hyp`m`F[{2*a-n,1+a-n/2,2*c,2*d,2*e,1/2+a-n,
     1+4*a-2*c-2*d-2*e-n,n},
    {a-n/2,1+2*a-2*c-n,1+2*a-2*d-n,1+2*a-2*e-n,
     1/2+a,-2*a+2*c+2*d+2*e,1+2*a-2*n},-1]*
   Hyp`m`p[{1+2*a,1+2*a-2*c-2*d,1+2*a-2*c-2*e,
     1+2*a-2*d-2*e},{1+2*a-2*c,1+2*a-2*d,1+2*a-2*e,
     1+2*a-2*c-2*d-2*e},-n]/;
  Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[n+nn-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]===
   Factor[f-1/2-c]===Factor[g-1/2-d]===Factor[h-1/2-e]===
   Factor[i-(1/2+2*a-c-d-e-n/2)]===Factor[j-(1+2*a-c-d-e-n/2)]===0&&
   Hyp`m`Private`IntegerTest[n]);

T111032:=
   (Hyp`m`F[{a_,aa_,e_,c_,f_,d_,g_,h_,i_,j_,n_},
   {aaaa_,ee_,cc_,ff_,dd_,gg_,hh_,ii_,jj_,nn_},1]:>
   Hyp`m`F[{2*a-e,1+a-e/2,1/2+a-e,2*c,2*d,e,
     1+4*a-2*c-2*d-e-2*n,2*n},
    {a-e/2,1/2+a,1+2*a-2*c-e,1+2*a-2*d-e,1+2*a-2*e,
     -2*a+2*c+2*d+2*n,1+2*a-e-2*n},-1]*
   Hyp`m`p[{1+2*a,1+2*a-2*c-2*d,1+2*a-2*c-e,1+2*a-2*d-e},
    {1+2*a-2*c,1+2*a-2*d,1+2*a-e,1+2*a-2*c-2*d-e},-2*n]/;
  Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[n+nn-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]===
   Factor[f-1/2-c]===Factor[g-1/2-d]===Factor[h-(1/2+2*a-c-d-e/2-n)]===
   Factor[i-(1+2*a-c-d-e/2-n)]===Factor[j-1/2-n]===0&&
   Hyp`m`Private`IntegerTest[2*n]);

T9894:=
   (Hyp`m`F[{a_,aa_,b_,f_,c_,d_,g_,e_,h_},
   {aaaa_,bb_,ff_,cc_,dd_,gg_,ee_,hh_},1] :>
   (-Hyp`m`F[{2+3*a-4*b-2*e,2+(3*a)/2-2*b-e,1+a-b-e,
        3/2+a-b-e,1+a-2*b,1+2*a-2*b-e,
        1+a-2*b+c-e,1+a-2*b+d-e,
        2+3*a-4*b-c-d-e},
       {1+(3*a)/2-2*b-e,2+2*a-3*b-e,3/2+2*a-3*b-e,
        2+2*a-2*b-2*e,2+a-2*b-e,2+2*a-2*b-c-e,
        2+2*a-2*b-d-e,1+c+d-e},1]*
      Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b,1+a-c,1+a-d,-a+2*b+c+d,3+3*a-4*b-2*e,
      1+a-e,1+a-2*b+c-e,2+3*a-4*b-c-d-e,1+a-2*b+d-e,-1-a+2*b+e},
    {1+a,2*b,c,1+2*a-2*b-c-d,d,3+4*a-6*b-2*e,1+a-2*b-e,2+2*a-2*b-c-e,
    2+2*a-2*b-d-e,1+c+d-e,e}]) +
  Hyp`m`F[{2*b,-a+2*b+c,-a+2*b+d,1+a-c-d,e},
     {1+a-c,1+a-d,-a+2*b+c+d,-2*a+4*b+e},1]*
    Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b,1+a-e,1+2*a-4*b-e},
     {1+a,1+2*a-4*b,1+a-2*b-e,1+2*a-2*b-e}]+
   Hyp`m`F[{1+2*a-4*b,1+2*a-2*b-e,1+a-2*b+c-e,
      1+a-2*b+d-e,2+3*a-4*b-c-d-e},
     {2+2*a-4*b-e,2+3*a-4*b-c-e,2+3*a-4*b-d-e,
      1+a-2*b+c+d-e},1]*
    Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b,1+a-c,1+a-d,
      -a+2*b+c+d,1+a-e,1+a-2*b+c-e,
      2+3*a-4*b-c-d-e,1+a-2*b+d-e,-1-2*a+4*b+e},
     {1+a,2*b,-a+2*b+c,1+a-c-d,-a+2*b+d,1+a-2*b-e,
      2+3*a-4*b-c-e,2+3*a-4*b-d-e,1+a-2*b+c+d-e,
      e}]/;
   Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]===
           Factor[h+hh-(1+a)]===
   Factor[f-1/2-b]===Factor[g-(1+2*a-2*b-c-d)]===Factor[h-(1+2*a-2*b-e)]===0);

T5403:=
   (Hyp`m`F[{x_,y_,a_,c_,n_},{d_,b_,e_,f_},1] :> 
  Hyp`m`F[{-2*a+2*b,x,y,n},{2*b-x,2*b-y,2*b-n},1]*
   Hyp`m`p[{2*b-x,2*b-y},{2*b,2*b-x-y},-n]/;
    Factor[c-1/2-a]===Factor[d-2*a]===Factor[e-1/2-b]===
    Factor[f-(1-2*b+n+x+y)]===0&&
    Hyp`m`Private`IntegerTest[n]);

T6533:=
   (Hyp`m`F[{a_,aa_,b_,x_,y_,n_},{aaaa_,bb_,xx_,yy_,nn_},-1]:>
   Hyp`m`F[{n,x,y},{-a+n+x+y,1+a-b},1]*
   Hyp`m`p[{1+a,1+a-x-y},{1+a-x,1+a-y},-n]/;
       Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[x+xx-(1+a)]===Factor[y+yy-(1+a)]===
           Factor[n+nn-(1+a)]===0&&
          Hyp`m`Private`IntegerTest[n]);

T6534:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_},{aaaa_,bb_,cc_,dd_,ee_},-1]:>
  Hyp`m`F[{1+a-b-c,d,e},{1+a-b,1+a-c},1]*
   Hyp`m`GAMMA[{1+a-d,1+a-e},{1+a,1+a-d-e}]/;
         Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
         Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
                  Factor[e+ee-(1+a)]===0);

T3217:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>
    Hyp`m`F[{-1-a+d+e,1/2-a/2+d/2+e/2,-a+e,-a+d,b,c},
    {-1/2-a/2+d/2+e/2,d,e,-a-b+d+e,-a-c+d+e},-1]*
   Hyp`m`GAMMA[{-a+d+e,-a-b-c+d+e},{-a-b+d+e,-a-c+d+e}]);

T3263:=
   (Hyp`m`F[{a_,b_,c_},{d_,e_},1] :> Hyp`m`F[{1+a-d,-c+e,a},
     {1+a+b-d,1+a-c},1]*
    Hyp`m`GAMMA[{1-c,d,-a-b+d,1+a-e},
     {1+a-c,-a+d,-b+d,1-e}]+
   Hyp`m`F[{1-b,-a-b-c+d+e,-b+d},{1-a-b+d,1-b-c+d},1]*
    Hyp`m`GAMMA[{1-c,a+b-d,d,1+a-e,e,-a-b-c+d+e},
     {a,b,1-b-c+d,1+a+b-d-e,-c+e,-a-b+d+e}]);

T3264:=
   (Hyp`m`F[{a_,b_,c_},{d_,e_},1] :> Hyp`m`F[{-a+d,b,c},{d,1+b+c-e},1]*
    Hyp`m`GAMMA[{1+b-e,1+c-e},{1-e,1+b+c-e}]-
   Hyp`m`F[{1+c-e,1+b-e,1+a-e},{1+d-e,2-e},1]*
    Hyp`m`GAMMA[{d,1+a-e,1+b-e,1+c-e,-1+e},
     {a,b,c,1-e,1+d-e}]);

T4362:=
   (Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1] :> 
  Hyp`m`F[{-1-a+e+f,1/2-a/2+e/2+f/2,-a+f,-a+e,b,c,d},
     {-1/2-a/2+e/2+f/2,e,f,-a-b+e+f,-a-c+e+f,
      -a-d+e+f},1]*Hyp`m`GAMMA[{-a+e+f,-a-b-c+e+f,
      -a-b-d+e+f,-a-c-d+e+f},
     {-a-b+e+f,-a-c+e+f,-a-d+e+f,-a-b-c-d+e+f}]
    -Hyp`m`F[{-a-b-c+e+f,-a-b-d+e+f,-a-c-d+e+f,
      -b-c-d+e+f},{-a-b-c-d+2*e+f,
      -a-b-c-d+e+2*f,1-a-b-c-d+e+f},1]*
    Hyp`m`GAMMA[{e,a+b+c+d-e-f,f,-a-b-c+e+f,
      -a-b-d+e+f,-a-c-d+e+f,-b-c-d+e+f},
     {a,b,c,d,-a-b-c-d+e+f,-a-b-c-d+2*e+f,
      -a-b-c-d+e+2*f}]/;
    Factor[g-(1+a+b+c+d-e-f)]===0);

T7694:=
   (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},{aaaa_,bb_,cc_,dd_,ee_,ff_},1] :> 
  Hyp`m`F[{-d+e+f,1-d/2+e/2+f/2,1+a-b-d,-a+e+f,
      1+a-c-d,e,f},{-d/2+e/2+f/2,-a+b+e+f,1+a-d,
      -a+c+e+f,1-d+f,1-d+e},1]*
    Hyp`m`GAMMA[{1+a-b,1-d,1+a-e,-a+c+e,1+a-f,
      1+a-b-e-f,-a+c+f,1-d+e+f},
     {1+a,-a+c,1+a-b-e,1-d+e,1+a-b-f,1+a-e-f,
      1-d+f,-a+c+e+f}]+
   Hyp`m`F[{2+2*a-2*b-d-e-f,2+a-b-d/2-e/2-f/2,1+a-b-d,
      1-b,2+2*a-b-c-d-e-f,1+a-b-f,1+a-b-e},
     {1+a-b-d/2-e/2-f/2,2+a-b-e-f,
      2+2*a-b-d-e-f,1-b+c,2+a-b-d-e,
      2+a-b-d-f},1]*Hyp`m`GAMMA[{1+a-b,1+a-c,1-d,1+a-d,
      1+a-e,-a+c+e,1+a-f,3+2*a-2*b-d-e-f,
      2+2*a-b-c-d-e-f,-a+c+f,-1-a+b+e+f},
     {1+a,b,1-b+c,1+a-c-d,2+a-b-d-e,e,
      2+a-b-d-f,2+2*a-b-c-e-f,2+2*a-b-d-e-f,f,
      -1-2*a+b+c+e+f}]/;
       Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===
           Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0);

T2138:=
   (Hyp`m`F[{a_,b_},{c_},z_] :> (1-z)^(-1+c)*
   Hyp`m`F[{(-a+c)/2,(-1+a+c)/2},{c},4*(1-z)*z]/;
    Factor[b-1+a]===0);

T2139:=
   (Hyp`m`F[{c_,b_},{a_},z_] :> 
  (1/2)^(1-a)*(1+(1-z)^(1/2))^(1-a)*
   Hyp`m`F[{a-2*c,1-a+2*c},{a},(1-(1-z)^(1/2))/2]/;
    Factor[b+1/2-a+c]===0);


T4331:=
   (Hyp`m`F[{a_,aa_,b_,c_},{aaaa_,bb_,cc_},z_] :> 
  (1-z)^(-1-a)*(1+z)*Hyp`m`F[{1/2+a/2,1+a/2,1+a-b-c},
    {1+a-b,1+a-c},(-4*z)/(-1+z)^2]/;
       Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]===
   Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===0);

T3238:=
   (Hyp`m`F[{a_,d_,e_},{b_,c_},z_] :> 
  -((2^(2*a-1)*(1+(1-z)^(1/2))^(2*a-1)*
       Hyp`m`F[{2*a-1,1/2+a,1/2+a-b,2*a-c},{a-1/2,b,c},
        (-2-2*(1-z)^(1/2)+z)/z])/((1-z)^(1/2)*z^(2*a-1)))/;
    Factor[d-1/2-a]===Factor[e-(-2*a+b+c)]===0);

T2140:=
   {(Hyp`m`F[{a_,aa_},{b_},z_] :> (2^(2*a)*(1+(1-z)^(1/2))^(2*a)*
     Hyp`m`F[{2*a,1+2*a-b},{b},(1+(1-z)^(1/2))^2/z])/z^(2*a)/;
    Factor[aa-a-1/2]===0),
    (Hyp`m`F[{aa_,a_},{b_},z_] :> (2^(2*a)*(1+(1-z)^(1/2))^(2*a)*
     Hyp`m`F[{2*a,1+2*a-b},{b},(1+(1-z)^(1/2))^2/z])/z^(2*a)/;
    Factor[aa-a-1/2]===0)};

T2141:=
   {(Hyp`m`F[{a_,aa_},{b_},z_] :> -(2^(2*a)*(1+(1-z)^(1/2))^(2*a)*z^(1-2*a)*
      Hyp`m`F[{-1+2*a,1/2+a,2*a-b},{-1/2+a,b},(1+(1-z)^(1/2))^2/z])
    /(2*(1+(1-z)^(1/2)-z))/;
    Factor[aa-a-1/2]===0),
    (Hyp`m`F[{aa_,a_},{b_},z] :> -(2^(2*a)*(1+(1-z)^(1/2))^(2*a)*z^(1-2*a)*
      Hyp`m`F[{-1+2*a,1/2+a,2*a-b},{-1/2+a,b},(1+(1-z)^(1/2))^2/z])
    /(2*(1+(1-z)^(1/2)-z))/;
    Factor[aa-a-1/2]===0)};

T4332:=
   (Hyp`m`F[{b_,x_,y_,n_},{xx_,yy_,nn_},1] :> 
  Hyp`m`F[{x,y,(x+xx)/2-b/2,1/2+(x+xx)/2-b/2,n},
    {(x+xx)-b,(x+xx)/2,1/2+(x+xx)/2,1-(xx)+n+y},1]*
   Hyp`m`p[{(x+xx),(xx)-y},{(xx),(x+xx)-y},-n]/;
   Factor[yy+y-xx-x]===Factor[n+nn-xx-x]===0&&Hyp`m`Private`IntegerTest[n]);

T3237:=
   {(Hyp`m`F[{x_,y_,n_},{b_,a_},1] :> Hyp`m`F[{-a+n+x+y,1-a/2+n/2+x/2+y/2,
     1-a-b+n+x+y,x,y,n},
    {-a/2+n/2+x/2+y/2,b,1-a+n+y,1-a+n+x,1-a+x+y},
    -1]*Hyp`m`p[{a-x,a-y},{a,a-x-y},-n]/;
    Hyp`m`Private`IntegerTest[n]),
    (Hyp`m`F[{x_,n_,y_},{b_,a_},1] :> Hyp`m`F[{-a+n+x+y,1-a/2+n/2+x/2+y/2,
     1-a-b+n+x+y,x,y,n},
    {-a/2+n/2+x/2+y/2,b,1-a+n+y,1-a+n+x,1-a+x+y},
    -1]*Hyp`m`p[{a-x,a-y},{a,a-x-y},-n]/;
    Hyp`m`Private`IntegerTest[n]),
    (Hyp`m`F[{n_,y_,x_},{b_,a_},1] :> Hyp`m`F[{-a+n+x+y,1-a/2+n/2+x/2+y/2,
     1-a-b+n+x+y,x,y,n},
    {-a/2+n/2+x/2+y/2,b,1-a+n+y,1-a+n+x,1-a+x+y},
    -1]*Hyp`m`p[{a-x,a-y},{a,a-x-y},-n]/;
    Hyp`m`Private`IntegerTest[n])};

T3240:=
   (Hyp`m`F[{c_,b_,d_},{a_,e_},1] :> 
  Hyp`m`F[{-1/2+a,3/4+a/2,b,c/2,1/2+c/2,a/2-d/2,1/2+a/2-d/2},
    {-1/4+a/2,1/2+a-b,1/2+a-c/2,a-c/2,1/2+a/2+d/2,
     a/2+d/2},1]*Hyp`m`GAMMA[{2*a,2*a-2*b-c,a-b+d,a-c+d},
    {2*a-2*b,2*a-c,a+d,a-b-c+d}]/;
    Factor[e-(a-b+d)]===0);



    


Regel[Global`rs01]:=Transfor`m`Trs01;
Regel[2103]:=Transfor`m`T2103;
Regel[2104]:=Transfor`m`T2104;
Regel[2106]:=Transfor`m`T2106;
Regel[2107]:=Transfor`m`T2107;
Regel[2131]:=Transfor`m`T2131;
Regel[2132]:=Transfor`m`T2132;
Regel[3204]:=Transfor`m`T3204;
Regel[3205]:=Transfor`m`T3205;
Regel[3206]:=Transfor`m`T3206;
Regel[3207]:=Transfor`m`T3207;
Regel[3217]:=Transfor`m`T3217;
Regel[3239]:=Transfor`m`T3239;
Regel[4301]:=Transfor`m`T4301;
Regel[4302]:=Transfor`m`T4302;
Regel[7631]:=Transfor`m`T7631;
Regel[7632]:=Transfor`m`T7632;
Regel[4303]:=Transfor`m`T4303;
Regel[4304]:=Transfor`m`T4304;
Regel[7633]:=Transfor`m`T7633;
Regel[3231]:=Transfor`m`T3231;
Regel[3232]:=Transfor`m`T3232;
Regel[3233]:=Transfor`m`T3233;
Regel[3234]:=Transfor`m`T3234;
Regel[4306]:=Transfor`m`T4306;
Regel[7634]:=Transfor`m`T7634;
Regel[7635]:=Transfor`m`T7635;
Regel[5401]:=Transfor`m`T5401;
Regel[9832]:=Transfor`m`T9832;
Regel[5402]:=Transfor`m`T5402;
Regel[9833]:=Transfor`m`T9833;
Regel[6531]:=Transfor`m`T6531;
Regel[9834]:=Transfor`m`T9834;
Regel[9831]:=Transfor`m`T9831;
Regel[2191]:=Transfor`m`T2191;
Regel[3261]:=Transfor`m`T3261;
Regel[3262]:=Transfor`m`T3262;
Regel[7691]:=Transfor`m`T7691;
Regel[7692]:=Transfor`m`T7692;
Regel[9891]:=Transfor`m`T9891;
Regel[2110]:=Transfor`m`T2110;
Regel[2112]:=Transfor`m`T2112;
Regel[2133]:=Transfor`m`T2133;
Regel[2134]:=Transfor`m`T2134;
Regel[2135]:=Transfor`m`T2135;
Regel[2136]:=Transfor`m`T2136;
Regel[2137]:=Transfor`m`T2137;
Regel[2138]:=Transfor`m`T2138;
Regel[2139]:=Transfor`m`T2139;
Regel[2140]:=Transfor`m`T2140;
Regel[2141]:=Transfor`m`T2141;
Regel[2163]:=Transfor`m`T2163;
Regel[3235]:=Transfor`m`T3235;
Regel[3236]:=Transfor`m`T3236;
Regel[3237]:=Transfor`m`T3237;
Regel[3240]:=Transfor`m`T3240;
Regel[3263]:=Transfor`m`T3263;
Regel[3264]:=Transfor`m`T3264;
Regel[3267]:=Transfor`m`T3267;
Regel[3268]:=Transfor`m`T3268;
Regel[2192]:=Transfor`m`T2192;
Regel[3238]:=Transfor`m`T3238;
Regel[4309]:=Transfor`m`T4309;
Regel[4310]:=Transfor`m`T4310;
Regel[4312]:=Transfor`m`T4312;
Regel[4362]:=Transfor`m`T4362;
Regel[4391]:=Transfor`m`T4391;
Regel[4331]:=Transfor`m`T4331;
Regel[4332]:=Transfor`m`T4332;
Regel[5403]:=Transfor`m`T5403;
Regel[5468]:=Transfor`m`T5468;
Regel[6501]:=Transfor`m`T6501;
Regel[6532]:=Transfor`m`T6532;
Regel[6533]:=Transfor`m`T6533;
Regel[6534]:=Transfor`m`T6534;
Regel[7636]:=Transfor`m`T7636;
Regel[7637]:=Transfor`m`T7637;
Regel[7693]:=Transfor`m`T7693;
Regel[7694]:=Transfor`m`T7694;
Regel[8731]:=Transfor`m`T8731;
Regel[8732]:=Transfor`m`T8732;
Regel[9835]:=Transfor`m`T9835;
Regel[9836]:=Transfor`m`T9836;
Regel[9837]:=Transfor`m`T9837;
Regel[9892]:=Transfor`m`T9892;
Regel[9893]:=Transfor`m`T9893;
Regel[9894]:=Transfor`m`T9894;
Regel[111031]:=Transfor`m`T111031;
Regel[111032]:=Transfor`m`T111032;


End[]
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