(*If[$VersionNumber>=2.,$Messages=OutputStream["",1],$Messages={}]*) BeginPackage["Transfor`q`"] Begin["`Private`"] (*Belegen von Module durch Block fr Versionen 1.?*) If[$VersionNumber<2.,Module=Block] (*!Achtung bei Erweiterungen: Am Dateiende sind vielleicht Modifikationen vorzunehmen!"*) TListe:={(Hyp`q`ph[List1_List,List2_List,q_,z_]:> Module[{Ph,Ausgabe={},TFrage}, Hyp`q`Private`phRun=True; Hyp`q`Private`IntegerTestIf=False; Ph=(Hyp`q`ph[List1,List2,q,z]/.Hyp`q`phOrdne); TFrage[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["T",ToString[Trans]]}}]]; TFrage[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["T",ToString[Trans]]}}]]; TFrage[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["T",ToString[Trans]]}}]]; TFrage[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["T",ToString[Trans]]}}]]; TFrage[Trans_]:= If[(Ph/.Regel[Trans])=!=Ph, Ausgabe=Join[Ausgabe,{{StringJoin["T",ToString[Trans]]}}]]; TFrage[Global`rs01]; If[MemberQ[{{2,1},{2,2},{3,1},{3,2},{4,2},{4,3},{5,4},{6,5},{7,6},{7,7},{8,7}, {10,9},{12,11}},{Length[List1],Length[List2]}], Switch[{Length[Ph[[1]]],Length[Ph[[2]]]}, {2,1},TFrage[2101]; TFrage[2102]; TFrage[2103]; TFrage[2104]; TFrage[2105]; TFrage[2106]; TFrage[2107]; TFrage[2108]; TFrage[2109]; TFrage[2110]; TFrage[2111]; TFrage[2112]; TFrage[2161]; TFrage[2162]; TFrage[2163], {2,2},TFrage[2201]; TFrage[2202], {3,1},TFrage[3101], {3,2},TFrage[3201]; TFrage[3202]; TFrage[3203]; TFrage[3204]; TFrage[3205]; TFrage[3206]; TFrage[3207]; TFrage[3208]; TFrage[3209]; TFrage[3210]; TFrage[3211]; TFrage[3211,1,3,2,u]; TFrage[3211,2,3,1,u]; TFrage[3212]; TFrage[3212,1,3,2,u]; TFrage[3212,2,3,1,u]; TFrage[3213]; TFrage[3213,2,1,3,u]; TFrage[3213,3,1,2,u]; TFrage[3213,2,1,l]; TFrage[3213,2,1,3,u,2,1,l]; TFrage[3213,3,1,2,u,2,1,l]; TFrage[3214]; TFrage[3214,2,1,3,u]; TFrage[3214,3,1,2,u]; TFrage[3214,2,1,l]; TFrage[3214,2,1,3,u,2,1,l]; TFrage[3214,3,1,2,u,2,1,l]; TFrage[3215]; TFrage[3215,1,3,2,u]; TFrage[3215,2,3,1,u]; TFrage[3216]; TFrage[3216,1,3,2,u]; TFrage[3216,2,3,1,u]; TFrage[3217]; TFrage[3261]; TFrage[3262]; TFrage[3263]; TFrage[3264]; TFrage[3265]; TFrage[3266]; TFrage[3266,2,1,3,u]; TFrage[3266,3,1,2,u]; TFrage[3266,2,1,l]; TFrage[3266,2,1,3,u,2,1,l]; TFrage[3266,3,1,2,u,2,1,l]; TFrage[3267]; TFrage[3268]; TFrage[3269], {4,2},TFrage[4201]; TFrage[4201,1,2,4,3,u]; TFrage[4201,1,3,4,2,u]; TFrage[4201,2,1,3,4,u]; TFrage[4201,2,1,4,3,u]; TFrage[4201,2,3,4,1,u]; TFrage[4201,3,1,2,4,u]; TFrage[4201,3,1,4,2,u]; TFrage[4201,3,2,4,1,u]; TFrage[4201,4,1,2,3,u]; TFrage[4201,4,1,3,2,u]; TFrage[4201,4,2,3,1,u]; TFrage[4201,2,1,l]; TFrage[4201,1,2,4,3,u,2,1,l]; TFrage[4201,1,3,4,2,u,2,1,l]; TFrage[4201,2,1,3,4,u,2,1,l]; TFrage[4201,2,1,4,3,u,2,1,l]; TFrage[4201,2,3,4,1,u,2,1,l]; TFrage[4201,3,1,2,4,u,2,1,l]; TFrage[4201,3,1,4,2,u,2,1,l]; TFrage[4201,3,2,4,1,u,2,1,l]; TFrage[4201,4,1,2,3,u,2,1,l]; TFrage[4201,4,1,3,2,u,2,1,l]; TFrage[4201,4,2,3,1,u,2,1,l], {4,3},TFrage[4301]; TFrage[4302]; TFrage[4303]; TFrage[4304]; TFrage[4305]; TFrage[4305,1,3,2,4,u]; TFrage[4305,1,4,2,3,u]; TFrage[4305,2,3,1,4,u]; TFrage[4305,2,4,1,3,u]; TFrage[4305,3,4,1,2,u]; TFrage[4305,1,3,2,l]; TFrage[4305,1,3,2,4,u,1,3,2,l]; TFrage[4305,1,4,2,3,u,1,3,2,l]; TFrage[4305,2,3,1,4,u,1,3,2,l]; TFrage[4305,2,4,1,3,u,1,3,2,l]; TFrage[4305,3,4,1,2,u,1,3,2,l]; TFrage[4305,2,1,3,l]; TFrage[4305,1,3,2,4,u,2,1,3,l]; TFrage[4305,1,4,2,3,u,2,1,3,l]; TFrage[4305,2,3,1,4,u,2,1,3,l]; TFrage[4305,2,4,1,3,u,2,1,3,l]; TFrage[4305,3,4,1,2,u,2,1,3,l]; TFrage[4305,2,3,1,l]; TFrage[4305,1,3,2,4,u,2,3,1,l]; TFrage[4305,1,4,2,3,u,2,3,1,l]; TFrage[4305,2,3,1,4,u,2,3,1,l]; TFrage[4305,2,4,1,3,u,2,3,1,l]; TFrage[4305,3,4,1,2,u,2,3,1,l]; TFrage[4305,3,1,2,l]; TFrage[4305,1,3,2,4,u,3,1,2,l]; TFrage[4305,1,4,2,3,u,3,1,2,l]; TFrage[4305,2,3,1,4,u,3,1,2,l]; TFrage[4305,2,4,1,3,u,3,1,2,l]; TFrage[4305,3,4,1,2,u,3,1,2,l]; TFrage[4305,3,2,1,l]; TFrage[4305,1,3,2,4,u,3,2,1,l]; TFrage[4305,1,4,2,3,u,3,2,1,l]; TFrage[4305,2,3,1,4,u,3,2,1,l]; TFrage[4305,2,4,1,3,u,3,2,1,l]; TFrage[4305,3,4,1,2,u,3,2,1,l]; 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[4307]; TFrage[4307,1,3,2,4,u]; TFrage[4307,1,4,2,3,u]; TFrage[4307,2,3,1,4,u]; TFrage[4307,2,4,1,3,u]; TFrage[4307,3,4,1,2,u]; TFrage[4307,1,3,2,l]; TFrage[4307,1,3,2,4,u,1,3,2,l]; TFrage[4307,1,4,2,3,u,1,3,2,l]; TFrage[4307,2,3,1,4,u,1,3,2,l]; TFrage[4307,2,4,1,3,u,1,3,2,l]; TFrage[4307,3,4,1,2,u,1,3,2,l]; TFrage[4307,2,1,3,l]; TFrage[4307,1,3,2,4,u,2,1,3,l]; TFrage[4307,1,4,2,3,u,2,1,3,l]; TFrage[4307,2,3,1,4,u,2,1,3,l]; TFrage[4307,2,4,1,3,u,2,1,3,l]; TFrage[4307,3,4,1,2,u,2,1,3,l]; TFrage[4307,2,3,1,l]; TFrage[4307,1,3,2,4,u,2,3,1,l]; TFrage[4307,1,4,2,3,u,2,3,1,l]; TFrage[4307,2,3,1,4,u,2,3,1,l]; TFrage[4307,2,4,1,3,u,2,3,1,l]; TFrage[4307,3,4,1,2,u,2,3,1,l]; TFrage[4307,3,1,2,l]; TFrage[4307,1,3,2,4,u,3,1,2,l]; TFrage[4307,1,4,2,3,u,3,1,2,l]; TFrage[4307,2,3,1,4,u,3,1,2,l]; TFrage[4307,2,4,1,3,u,3,1,2,l]; TFrage[4307,3,4,1,2,u,3,1,2,l]; TFrage[4307,3,2,1,l]; TFrage[4307,1,3,2,4,u,3,2,1,l]; TFrage[4307,1,4,2,3,u,3,2,1,l]; TFrage[4307,2,3,1,4,u,3,2,1,l]; TFrage[4307,2,4,1,3,u,3,2,1,l]; TFrage[4307,3,4,1,2,u,3,2,1,l]; TFrage[4308]; TFrage[4309]; TFrage[4310]; TFrage[4311]; If[Factor[z-q]===0&& ((Factor[Ph[[1,1]]*q-Ph[[1,2]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,1]],q])|| (Factor[Ph[[1,1]]*q-Ph[[1,3]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,1]],q])|| (Factor[Ph[[1,1]]*q-Ph[[1,4]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,1]],q])|| (Factor[Ph[[1,2]]*q-Ph[[1,1]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,2]],q])|| (Factor[Ph[[1,2]]*q-Ph[[1,3]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,2]],q])|| (Factor[Ph[[1,2]]*q-Ph[[1,4]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,2]],q])|| (Factor[Ph[[1,3]]*q-Ph[[1,1]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,3]],q])|| (Factor[Ph[[1,3]]*q-Ph[[1,2]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,3]],q])|| (Factor[Ph[[1,3]]*q-Ph[[1,4]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,3]],q])|| (Factor[Ph[[1,4]]*q-Ph[[1,1]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,4]],q])|| (Factor[Ph[[1,4]]*q-Ph[[1,2]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,4]],q])|| (Factor[Ph[[1,4]]*q-Ph[[1,3]]]===0&&Hyp`q`Private`IntegerTest[Ph[[1,4]],q])), Print[""]; Print["\"T4312\" might be applicable."]; Print["Please, check for yourself!"]; ]; TFrage[4313]; TFrage[4313,2,1,3,4,u]; TFrage[4313,3,1,2,4,u]; TFrage[4313,4,1,2,3,u]; TFrage[4361]; TFrage[4362], {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-q]===0&& (Hyp`q`Private`IntegerTest[Ph[[1,1]],q]|| Hyp`q`Private`IntegerTest[Ph[[1,2]],q]|| Hyp`q`Private`IntegerTest[Ph[[1,3]],q]|| Hyp`q`Private`IntegerTest[Ph[[1,4]],q]|| Hyp`q`Private`IntegerTest[Ph[[1,5]],q]), Print[""]; Print["\"T5403\" might be applicable."]; Print["Please, check for yourself!"]; ]; If[Factor[z-q]===0&& (Hyp`q`Private`IntegerTest[Ph[[1,1]],q^(1/2)]|| Hyp`q`Private`IntegerTest[Ph[[1,2]],q^(1/2)]|| Hyp`q`Private`IntegerTest[Ph[[1,3]],q^(1/2)]|| Hyp`q`Private`IntegerTest[Ph[[1,4]],q^(1/2)]|| Hyp`q`Private`IntegerTest[Ph[[1,5]],q^(1/2)]), Print[""]; Print["\"T5404\" might be applicable."]; Print["Please, check for yourself!"]; ]; Print[""]; Print["\"T5405\" might be applicable."]; Print["Please, check for yourself!"]; TFrage[5461]; Print[""]; Print["\"T5462\" might be applicable."]; Print["Please, check for yourself!"]; Print[""]; Print["\"T5463\" might be applicable."]; Print["Please, check for yourself!"]; Print[""]; Print["\"T5464\" might be applicable."]; Print["Please, check for yourself!"]; Print[""]; Print["\"T5465\" might be applicable."]; Print["Please, check for yourself!"]; Print[""]; Print["\"T5466\" might be applicable."]; Print["Please, check for yourself!"]; Print[""]; Print["\"T5467\" might be applicable."]; Print["Please, check for yourself!"]; TFrage[5468]; Print[""]; Print["\"T5469\" might be applicable."]; Print["Please, check for yourself!"], {6,5},TFrage[6501], {7,6},TFrage[7601]; TFrage[7601,1,2,4,5,6,3,b]; TFrage[7601,1,2,3,5,6,4,b]; TFrage[7601,1,2,3,4,6,5,b], {7,7},TFrage[7701], {8,7},TFrage[8701]; TFrage[8701,1,2,3,5,4,6,7,b]; TFrage[8701,1,2,3,6,5,4,7,b]; TFrage[8701,1,2,3,7,5,6,4,b]; TFrage[8701,1,2,4,5,3,6,7,b]; TFrage[8701,1,2,4,6,3,5,7,b]; TFrage[8701,1,2,4,7,3,6,5,b]; TFrage[8701,1,2,5,6,3,4,7,b]; TFrage[8701,1,2,5,7,3,4,6,b]; TFrage[8701,1,2,6,7,3,4,5,b]; TFrage[8702]; TFrage[8702,1,2,3,4,5,7,6,b]; TFrage[8702,1,2,3,4,7,6,5,b]; TFrage[8702,1,2,3,7,5,6,4,b]; TFrage[8702,1,2,7,4,5,6,3,b]; TFrage[8702,1,7,3,4,5,6,2,b]; TFrage[8702,7,2,3,4,5,6,1,b]; TFrage[8703]; TFrage[8703,1,2,3,4,6,5,7,b]; TFrage[8703,1,2,3,4,7,5,6,b]; TFrage[8703,1,2,3,5,6,4,7,b]; TFrage[8703,1,2,3,5,7,4,6,b]; TFrage[8703,1,2,3,6,7,4,5,b]; TFrage[8703,1,2,4,5,6,3,7,b]; TFrage[8703,1,2,4,5,7,3,6,b]; TFrage[8703,1,2,4,6,7,3,5,b]; TFrage[8703,1,2,5,6,7,3,4,b]; TFrage[8704]; TFrage[8705]; TFrage[8706]; TFrage[8706,1,2,3,5,4,6,7,b]; TFrage[8706,1,2,3,6,4,5,7,b]; TFrage[8706,1,2,3,7,4,5,6,b]; TFrage[8706,1,2,4,5,3,6,7,b]; TFrage[8706,1,2,4,6,3,5,7,b]; TFrage[8706,1,2,4,7,3,5,6,b]; TFrage[8706,1,2,5,6,3,4,7,b]; TFrage[8706,1,2,5,7,3,4,6,b]; TFrage[8706,1,2,6,7,3,4,5,b]; TFrage[8707]; TFrage[8707,1,2,3,4,5,7,6,b]; TFrage[8707,1,2,3,4,6,7,5,b]; TFrage[8707,1,2,3,5,4,6,7,b]; TFrage[8707,1,2,3,5,4,7,6,b]; TFrage[8707,1,2,3,5,6,7,4,b]; TFrage[8707,1,2,3,6,4,5,7,b]; TFrage[8707,1,2,3,6,4,7,5,b]; TFrage[8707,1,2,3,6,5,7,4,b]; TFrage[8707,1,2,3,7,4,5,6,b]; TFrage[8707,1,2,3,7,4,6,5,b]; TFrage[8707,1,2,3,7,5,6,4,b]; TFrage[8707,1,2,4,5,3,6,7,b]; TFrage[8707,1,2,4,5,3,7,6,b]; TFrage[8707,1,2,4,5,6,7,3,b]; TFrage[8707,1,2,4,6,3,5,7,b]; TFrage[8707,1,2,4,6,3,7,5,b]; TFrage[8707,1,2,4,6,5,7,3,b]; TFrage[8707,1,2,4,7,3,5,6,b]; TFrage[8707,1,2,4,7,3,6,5,b]; TFrage[8707,1,2,4,7,5,6,3,b]; TFrage[8707,1,2,5,6,3,4,7,b]; TFrage[8707,1,2,5,6,3,7,4,b]; TFrage[8707,1,2,5,6,4,7,3,b]; TFrage[8707,1,2,5,7,3,4,6,b]; TFrage[8707,1,2,5,7,3,6,4,b]; TFrage[8707,1,2,5,7,4,6,3,b]; TFrage[8707,1,2,6,7,3,4,5,b]; TFrage[8707,1,2,6,7,3,5,4,b]; TFrage[8707,1,2,6,7,4,5,3,b]; TFrage[8708]; TFrage[8708,1,2,3,4,5,7,6,b]; TFrage[8708,1,2,3,4,6,7,5,b]; TFrage[8708,1,2,3,5,4,6,7,b]; TFrage[8708,1,2,3,5,4,7,6,b]; TFrage[8708,1,2,3,5,6,7,4,b]; TFrage[8708,1,2,3,6,4,5,7,b]; TFrage[8708,1,2,3,6,4,7,5,b]; TFrage[8708,1,2,3,6,5,7,4,b]; TFrage[8708,1,2,3,7,4,5,6,b]; TFrage[8708,1,2,3,7,4,6,5,b]; TFrage[8708,1,2,3,7,5,6,4,b]; TFrage[8708,1,2,4,5,3,6,7,b]; TFrage[8708,1,2,4,5,3,7,6,b]; TFrage[8708,1,2,4,5,6,7,3,b]; TFrage[8708,1,2,4,6,3,5,7,b]; TFrage[8708,1,2,4,6,3,7,5,b]; TFrage[8708,1,2,4,6,5,7,3,b]; TFrage[8708,1,2,4,7,3,5,6,b]; TFrage[8708,1,2,4,7,3,6,5,b]; TFrage[8708,1,2,4,7,5,6,3,b]; TFrage[8708,1,2,5,6,3,4,7,b]; TFrage[8708,1,2,5,6,3,7,4,b]; TFrage[8708,1,2,5,6,4,7,3,b]; TFrage[8708,1,2,5,7,3,4,6,b]; TFrage[8708,1,2,5,7,3,6,4,b]; TFrage[8708,1,2,5,7,4,6,3,b]; TFrage[8708,1,2,6,7,3,4,5,b]; TFrage[8708,1,2,6,7,3,5,4,b]; TFrage[8708,1,2,6,7,4,5,3,b]; TFrage[8709]; TFrage[8709,1,2,3,4,5,7,6,b]; TFrage[8709,1,2,3,4,6,7,5,b]; TFrage[8709,1,2,3,5,4,6,7,b]; TFrage[8709,1,2,3,5,4,7,6,b]; TFrage[8709,1,2,3,5,6,7,4,b]; TFrage[8709,1,2,3,6,4,5,7,b]; TFrage[8709,1,2,3,6,4,7,5,b]; TFrage[8709,1,2,3,6,5,7,4,b]; TFrage[8709,1,2,3,7,4,5,6,b]; TFrage[8709,1,2,3,7,4,6,5,b]; TFrage[8709,1,2,3,7,5,6,4,b]; TFrage[8709,1,2,4,5,3,6,7,b]; TFrage[8709,1,2,4,5,3,7,6,b]; TFrage[8709,1,2,4,5,6,7,3,b]; TFrage[8709,1,2,4,6,3,5,7,b]; TFrage[8709,1,2,4,6,3,7,5,b]; TFrage[8709,1,2,4,6,5,7,3,b]; TFrage[8709,1,2,4,7,3,5,6,b]; TFrage[8709,1,2,4,7,3,6,5,b]; TFrage[8709,1,2,4,7,5,6,3,b]; TFrage[8709,1,2,5,6,3,4,7,b]; TFrage[8709,1,2,5,6,3,7,4,b]; TFrage[8709,1,2,5,6,4,7,3,b]; TFrage[8709,1,2,5,7,3,4,6,b]; TFrage[8709,1,2,5,7,3,6,4,b]; TFrage[8709,1,2,5,7,4,6,3,b]; TFrage[8709,1,2,6,7,3,4,5,b]; TFrage[8709,1,2,6,7,3,5,4,b]; TFrage[8709,1,2,6,7,4,5,3,b]; If[Factor[q^2*Ph[[1,1]]^2/Ph[[1,4]]/Ph[[1,5]]/Ph[[1,6]]/Ph[[1,7]]/Ph[[1,8]]-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. \"T8710\" might be applicable."]; Print["Please, check for yourself!"]; ]; TFrage[8711]; TFrage[8711,1,2,3,4,5,7,6,b]; TFrage[8711,1,2,3,4,6,7,5,b]; TFrage[8711,1,2,3,5,4,6,7,b]; TFrage[8711,1,2,3,5,4,7,6,b]; TFrage[8711,1,2,3,5,6,7,4,b]; TFrage[8711,1,2,3,6,4,5,7,b]; TFrage[8711,1,2,3,6,4,7,5,b]; TFrage[8711,1,2,3,6,5,7,4,b]; TFrage[8711,1,2,3,7,4,5,6,b]; TFrage[8711,1,2,3,7,4,6,5,b]; TFrage[8711,1,2,3,7,5,6,4,b]; TFrage[8711,1,2,4,5,6,7,3,b]; TFrage[8711,1,2,4,6,5,7,3,b]; TFrage[8711,1,2,4,7,5,6,3,b]; (*Das stimmt so!*) TFrage[8761]; TFrage[8762]; TFrage[8763]; TFrage[8764], {10,9},TFrage[10901]; If[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. \"T10902\", \"T10904\", \"T10906\","]; Print["\"T10907\" or \"T10962\" might be applicable."]; Print["Please, check for yourself!"]; ]; TFrage[10903]; TFrage[10903,1,2,3,4,5,6,7,9,8,b]; TFrage[10903,1,2,3,4,5,6,8,9,7,b]; TFrage[10903,1,2,3,4,5,7,8,9,6,b]; TFrage[10903,1,2,3,4,6,7,8,9,5,b]; TFrage[10903,1,2,3,5,6,7,8,9,4,b]; TFrage[10903,1,2,4,5,6,7,8,9,3,b]; Print[""]; Print["\"T10905\" might be applicable if the series is \"split-poised\"."]; Print["Please, check for yourself!"]; TFrage[10961]; TFrage[10963], {12,11},If[Factor[q-z]=== Factor[Ph[[1,1]]^4*q^3-Ph[[1,4]]*Ph[[1,5]]*Ph[[1,6]]*Ph[[1,7]]*Ph[[1,8]]*Ph[[1,9]]*Ph[[1,10]]*Ph[[1,11]]*Ph[[1,12]]]=== 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. \"T121101\", \"T121102\", \"T121103\","]; Print["\"T121104\", \"T121105\", \"T121106\" or \"T121161\""]; Print["might be applicable."]; Print["Please, check for yourself! Here is your series:"]; Ausgabe=Ph; ]; If[Hyp`q`Private`intersection[z*Ph[[1]],{q}]=!={}&& Factor[Ph[[1,1]]^4*q^4-(z*Ph[[1,4]]*Ph[[1,5]]*Ph[[1,6]]*Ph[[1,7]]*Ph[[1,8]]*Ph[[1,9]]*Ph[[1,10]]*Ph[[1,11]]*Ph[[1,12]])]=== 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."]; Print["\"T121107\"might be applicable."]; Print["Please, check for yourself! Here is your series:"]; Ausgabe=Ph; ] ] ]; Hyp`q`Private`phRun=False; If[Ausgabe=!={}&&Ausgabe=!=Ph, Print[""]; Print["Be sure to apply \"phOrdne\" before using the following information!"]]; Hyp`q`Private`IntegerTestClear; Ausgabe ]), (Hyp`q`ps[List1_List,List2_List,q_,z_]:> Module[{Ph,Ausgabe={},TFrage}, Hyp`q`Private`psRun=True; Hyp`q`Private`IntegerTestIf=False; Ph=(Hyp`q`ps[List1,List2,q,z]/.Hyp`q`psOrdne); TFrage[Trans_,Perm1__,u,Perm2__,l]:= If[(Ph/.Hyp`q`psPerm[Perm1,Global`u]/.Hyp`q`psPerm[Perm2,Global`l]/.Regel[Trans])=!= (Ph/.Hyp`q`psPerm[Perm1,Global`u]/.Hyp`q`psPerm[Perm2,Global`l]), Ausgabe=Join[Ausgabe,{{"psPerm"[Perm1,"u"],"psPerm"[Perm2,"l"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_,Perm1__,u]:= If[(Ph/.Hyp`q`psPerm[Perm1,Global`u]/.Regel[Trans])=!= (Ph/.Hyp`q`psPerm[Perm1,Global`u]), Ausgabe=Join[Ausgabe,{{"psPerm"[Perm1,"u"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_,Perm1__,l]:= If[(Ph/.Hyp`q`psPerm[Perm1,Global`l]/.Regel[Trans])=!= (Ph/.Hyp`q`psPerm[Perm1,Global`l]), Ausgabe=Join[Ausgabe,{{"psPerm"[Perm1,"l"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_,Perm1__,b]:= If[(Ph/.Hyp`q`psPerm[Perm1,Global`b]/.Regel[Trans])=!= (Ph/.Hyp`q`psPerm[Perm1,Global`b]), Ausgabe=Join[Ausgabe,{{"psPerm"[Perm1,"b"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_]:= If[(Ph/.Regel[Trans])=!=Ph, Ausgabe=Join[Ausgabe,{{StringJoin["T",ToString[Trans]]}}]]; TFrage[Global`rs01]; If[MemberQ[{{8,8},{10,10}},{Length[List1],Length[List2]}], Switch[{Length[Ph[[1]]],Length[Ph[[2]]]}, {8,8},TFrage[8810], {10,10},TFrage[101010] ] ]; Hyp`q`Private`psRun=False; If[Ausgabe=!={}&&Ausgabe=!=Ph, Print[""]; Print["Be sure to apply \"psOrdne\" before using the following information!"]]; Hyp`q`Private`IntegerTestClear; Ausgabe ])}; simplify[x_]:=(Simplify[x]/.Hyp`q`Expandq); Trs01:=(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]===1), Throw[Ausgabe], GesList=ProvList2; For[ii=1,ii<=Length[GesList]&&Length[ProvList2]>1,ii++, Var2=ProvList1/GesList[[ii]]; Var2=Map[Log[q,#]&,Var2]; 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`q`Private`POS[Var2,MinEl]; {ProvList1,ProvList2,NewList1,NewList2}= Hyp`q`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2, ProvList1[[POSX]],GesList[[ii]]]; ] ]; Clear[ii]; If[Length[ProvList2]===1&& MemberQ[Map[(Factor[#*q^(Apply[Plus,mList]-1)*z])&,ProvList1],1], POSX=Hyp`q`Private`POS[Map[(Factor[#*q^(Apply[Plus,mList]-1)*z])&,ProvList1],1]; Throw[Hyp`q`pqinf[q/ProvList1[[POSX]]*ProvList1[[3-POSX]],q]* Hyp`q`pqinf[ProvList2[[1]]/ProvList1[[3-POSX]],q]/ Hyp`q`pqinf[q/ProvList1[[POSX]],q]/ Hyp`q`pqinf[ProvList2[[1]],q]* Product[Hyp`q`pq[NewList2[[ii]]/ProvList1[[3-POSX]],mList[[ii]],q],{ii,1,Length[NewList2]}]/ Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}]* ProvList1[[3-POSX]]^(Apply[Plus,mList])* Hyp`q`ph[Join[{q*ProvList1[[3-POSX]]/ProvList2[[1]],ProvList1[[3-POSX]]}, q*ProvList1[[3-POSX]]/NewList2], Join[{q/ProvList1[[POSX]]*ProvList1[[3-POSX]]}, q*ProvList1[[3-POSX]]/NewList1],q,ProvList2[[1]]/ProvList1[[3-POSX]]]], If[Length[ProvList2]===1&& Factor[ProvList1[[1]]*ProvList1[[2]]/ProvList2[[1]]*q^(Apply[Plus,mList])*z]===1&& (Var1=Map[Hyp`q`Private`IntegerTest[#,q]&,ProvList1*q/ProvList2[[1]]];Var1[[1]]||Var1[[2]]), POSX=Hyp`q`Private`POS[Var1,True]; Throw[Hyp`q`pqinf[q/ProvList1[[3-POSX]]*ProvList1[[POSX]],q]* Hyp`q`pqinf[ProvList2[[1]]/ProvList1[[POSX]],q]/ Hyp`q`pqinf[q/ProvList1[[3-POSX]],q]/ Hyp`q`pqinf[ProvList2[[1]],q]* Product[Hyp`q`pq[NewList2[[ii]]/ProvList1[[POSX]],mList[[ii]],q],{ii,1,Length[NewList2]}]/ Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}]* ProvList1[[POSX]]^(Apply[Plus,mList]-Log[q,ProvList2[[1]]/ProvList1[[POSX]]/q])* Hyp`q`ph[Join[{q*ProvList1[[POSX]]/ProvList2[[1]],ProvList1[[POSX]]}, q*ProvList1[[POSX]]/NewList2], Join[{q/ProvList1[[3-POSX]]*ProvList1[[POSX]]}, q*ProvList1[[POSX]]/NewList1],q,q]], If[Length[ProvList2]===1&&MemberQ[Map[(Factor[#*z])&,ProvList1],q], POSX=Hyp`q`Private`POS[Map[(Factor[#*z])&,ProvList1],q]; Throw[Hyp`q`pqinf[q/ProvList1[[POSX]]*ProvList1[[3-POSX]],q]* Hyp`q`pqinf[ProvList2[[1]]/ProvList1[[3-POSX]],q]/ Hyp`q`pqinf[q/ProvList1[[POSX]],q]/ Hyp`q`pqinf[ProvList2[[1]],q]* Product[Hyp`q`pq[NewList2[[ii]]/ProvList1[[3-POSX]],mList[[ii]],q],{ii,1,Length[NewList2]}]/ Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}]* Hyp`q`ph[Join[{q*ProvList1[[3-POSX]]/ProvList2[[1]],ProvList1[[3-POSX]]}, q*ProvList1[[3-POSX]]/NewList2], Join[{q/ProvList1[[POSX]]*ProvList1[[3-POSX]]}, q*ProvList1[[3-POSX]]/NewList1],q, q^(-Apply[Plus,mList])*ProvList2[[1]]/ProvList1[[3-POSX]]]], If[Length[ProvList2]===1&&Factor[z-q]===0&& (Var1=Map[Hyp`q`Private`IntegerTest[#,q]&,ProvList1];Var1[[1]]||Var1[[2]]), POSX=Hyp`q`Private`POS[Var1,True]; Throw[Hyp`q`pqinf[q/ProvList1[[POSX]]*ProvList1[[3-POSX]],q]* Hyp`q`pqinf[ProvList2[[1]]/ProvList1[[3-POSX]],q]/ Hyp`q`pqinf[q/ProvList1[[POSX]],q]/ Hyp`q`pqinf[ProvList2[[1]],q]* Product[Hyp`q`pq[NewList2[[ii]]/ProvList1[[3-POSX]],mList[[ii]],q],{ii,1,Length[NewList2]}]/ Product[Hyp`q`pq[NewList2[[ii]],mList[[ii]],q],{ii,1,Length[NewList2]}]* ProvList1[[3-POSX]]^(-Log[q,ProvList1[[POSX]]])* Hyp`q`ph[Join[{q*ProvList1[[3-POSX]]/ProvList2[[1]],ProvList1[[3-POSX]]}, q*ProvList1[[3-POSX]]/NewList2], Join[{q/ProvList1[[POSX]]*ProvList1[[3-POSX]]}, q*ProvList1[[3-POSX]]/NewList1],q, q^(-Apply[Plus,mList])*ProvList2[[1]]/ProvList1[[1]]/ProvList1[[2]]]], Throw[Hyp`q`ph[List1,List2,q,z]] ] ] ] ]; ]]]); T2101:=(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{b,a*z},{c,z},q]*Hyp`q`ph[{c/b,z},{a*z},q,b]); T2102:=(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{c/b,b*z},{c,z},q]*Hyp`q`ph[{a*b*z/c,b},{b*z},q,c/b]); T2103:=(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{a*b*z/c},{z},q]*Hyp`q`ph[{c/a,c/b},{c},q,a*b*z/c]); T2104:=(Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{a*z},{z},q]*Hyp`q`ph[{a,c/b},{c,a*z},q,b*z]); T2105:={Hyp`q`ph[{a_,b_},{c_},q_,z_]:>Hyp`q`pqinf[{a*b*z/c},{b*z/c},q]* Hyp`q`ph[{a,c/b,0},{c,c*q/(b*z)},q,q]/; Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[c/b,q], Hyp`q`ph[{b_,a_},{c_},q_,z_]:>Hyp`q`pqinf[{a*b*z/c},{b*z/c},q]* Hyp`q`ph[{a,c/b,0},{c,c*q/(b*z)},q,q]/; Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[c/b,q]}; T2201:=(Hyp`q`ph[{a_,b_},{c_,d_},q_,z_]:> Hyp`q`ph[{a,c/b},{c},q,d/a]*Hyp`q`pqinf[{d/a},{d},q]/; Factor[z-(c*d)/(a*b)]===0); T3201:={Hyp`q`ph[{a_,b_,0},{c_,d_},q_,q_]:>Hyp`q`ph[{a,c/b},{c},q,(b*q)/d]* Hyp`q`pqinf[{q/d},{a*q/d},q]/; Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q], Hyp`q`ph[{a_,0,b_},{c_,d_},q_,q_]:>Hyp`q`ph[{a,c/b},{c},q,(b*q)/d]* Hyp`q`pqinf[{q/d},{a*q/d},q]/; Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q], Hyp`q`ph[{0,a_,b_},{c_,d_},q_,q_]:>Hyp`q`ph[{a,c/b},{c},q,(b*q)/d]* Hyp`q`pqinf[{q/d},{a*q/d},q]/; Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]}; T2106:={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]*(b*z/q)^(-Log[q,simplify[a]])* Hyp`q`ph[{a,q/z,c^(-1)*q*a},{b*c^(-1)*q*a,0},q,q]/; Hyp`q`Private`IntegerTest[a,q], Hyp`q`ph[{b_,a_},{c_},q_,z_]:>Hyp`q`pq[c/b,-Log[q,simplify[a]],q]/ Hyp`q`pq[c,-Log[q,simplify[a]],q]*(b*z/q)^(-Log[q,simplify[a]])* Hyp`q`ph[{a,q/z,c^(-1)*q*a},{b*c^(-1)*q*a,0},q,q]/; Hyp`q`Private`IntegerTest[a,q]}; T2107:={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]* Hyp`q`ph[{a,b,b*z*a/c},{b*c^(-1)*q*a,0},q,q]/; Hyp`q`Private`IntegerTest[a,q], Hyp`q`ph[{b_,a_},{c_},q_,z_]:>Hyp`q`pq[c/b,-Log[q,simplify[a]],q]/ Hyp`q`pq[c,-Log[q,simplify[a]],q]* Hyp`q`ph[{a,b,b*z*a/c},{b*c^(-1)*q*a,0},q,q]/; Hyp`q`Private`IntegerTest[a,q]}; T2108:={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]*b^(-Log[q,simplify[a]])* Hyp`q`ph[{a,b,q/z},{b*c^(-1)*q*a},q,z/c]/; Hyp`q`Private`IntegerTest[a,q], Hyp`q`ph[{b_,a_},{c_},q_,z_]:>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`ph[{a,b,q/z},{b*c^(-1)*q*a},q,z/c]/; Hyp`q`Private`IntegerTest[a,q]}; T3202:={Hyp`q`ph[{b_,c_,a_},{d_,0},q_,q_]:>Hyp`q`ph[{a,d/c},{q*a/c},q,q/b]/ (d^(-Log[q,simplify[a]])*Hyp`q`pq[q*a/d,-Log[q,simplify[a]],q])* (b^(-Log[q,simplify[a]])*c^(-Log[q,simplify[a]])* Hyp`q`pq[q*a/c,-Log[q,simplify[a]],q])/; Hyp`q`Private`IntegerTest[a,q], Hyp`q`ph[{b_,c_,a_},{0,d_},q_,q_]:>Hyp`q`ph[{a,d/c},{q*a/c},q,q/b]/ (d^(-Log[q,simplify[a]])*Hyp`q`pq[q*a/d,-Log[q,simplify[a]],q])* (b^(-Log[q,simplify[a]])*c^(-Log[q,simplify[a]])* Hyp`q`pq[q*a/c,-Log[q,simplify[a]],q])/; Hyp`q`Private`IntegerTest[a,q]}; T3203:={Hyp`q`ph[{b_,c_,a_},{d_,0},q_,q_]:> Hyp`q`ph[{a,b},{(b*q*a)/d},q,(c*q)/d]/ (Hyp`q`pq[q*a/d,-Log[q,simplify[a]],q])* Hyp`q`pq[(b*q*a)/d,-Log[q,simplify[a]],q]/; Hyp`q`Private`IntegerTest[a,q], Hyp`q`ph[{b_,c_,a_},{0,d_},q_,q_]:>Hyp`q`ph[{a,b},{(b*q*a)/d},q,(c*q)/d]/ (Hyp`q`pq[q*a/d,-Log[q,simplify[a]],q])* Hyp`q`pq[(b*q*a)/d,-Log[q,simplify[a]],q]/; Hyp`q`Private`IntegerTest[a,q]}; T3101:=(Hyp`q`ph[{b_,c_,a_},{d_},q_,z_]:>Hyp`q`ph[{a,b},{q/c/z},q,(q)/c]/ (b^(-Log[q,simplify[a]])* Hyp`q`pq[q/(b*c*z),-Log[q,simplify[a]],q])*Hyp`q`pq[q/c/z,-Log[q,simplify[a]],q]/; Factor[d-b*c*a*z]===0&&Hyp`q`Private`IntegerTest[a,q]); T3204:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`pqinf[{e/a,d*e/(b*c)},{e,d*e/(a*b*c)},q]* Hyp`q`ph[{a,d/b,d/c},{d,d*e/(b*c)},q,e/a]/; Factor[z-d*e/(a*b*c)]===0); T3205:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`pqinf[{b,d*e/(a*b),d*e/(b*c)},{d,e,d*e/(a*b*c)},q]* Hyp`q`ph[{d/b,e/b,d*e/(a*b*c)},{d*e/(a*b),d*e/(b*c)},q,b]/; Factor[z-d*e/(a*b*c)]===0); T3206:=(Hyp`q`ph[{b_,c_,a_},{d_,e_},q_,q_]:> Hyp`q`pq[d*e/(b*c),-Log[q,simplify[a]],q]/Hyp`q`pq[e,-Log[q,simplify[a]],q]* (b*c/d)^(-Log[q,simplify[a]])* Hyp`q`ph[{a,d/b,d/c},{d,d*e/(b*c)},q,q]/; Hyp`q`Private`IntegerTest[a,q]); T3207:=(Hyp`q`ph[{b_,c_,a_},{d_,e_},q_,q_]:> Hyp`q`pq[e/c,-Log[q,simplify[a]],q]/Hyp`q`pq[e,-Log[q,simplify[a]],q]* (c)^(-Log[q,simplify[a]])* Hyp`q`ph[{a,c,d/b},{d,c*q*a/e},q,b*q/e]/; Hyp`q`Private`IntegerTest[a,q]); T3208:=(Hyp`q`ph[{b_,c_,a_},{d_,e_},q_,z_]:> Hyp`q`pq[e/c,-Log[q,simplify[a]],q]/Hyp`q`pq[e,-Log[q,simplify[a]],q]* Hyp`q`ph[{a,c,d/b},{d,c*q*a/e},q,q]/; Factor[z-d*e/(a*b*c)]===0&&Hyp`q`Private`IntegerTest[a,q]); T3209:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`pqinf[{a*z},{z},q]* Hyp`q`ph[{a^(1/2),-a^(1/2),(a*q)^(1/2),-(a*q)^(1/2),a*q/(b*c)}, {a*q/b,a*q/c,a*z,q/z},q,q]/; Factor[d-a*q/b]===0&&Factor[e-a*q/c]===0&& Hyp`q`Private`IntegerTest[a,q]); T4301:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]:> Hyp`q`pq[{e/a,f/a},{e,f},-Log[q,simplify[d]],q]*a^(-Log[q,simplify[d]])* Hyp`q`ph[{d,a,(a*c*d*q)/(e*f),(a*b*d*q)/(e*f)}, {(a*b*c*d*q)/(e*f),(a*q*d)/e,(a*q*d)/f},q,q]/; Factor[g-(a*b*c*d*q)/(e*f)]===0&& Hyp`q`Private`IntegerTest[d,q]); T4302:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]:> Hyp`q`pq[{a,e*f/(a*b),e*f/(a*c)},{e,f,e*f/(a*b*c)},-Log[q,simplify[d]],q]* Hyp`q`ph[{d,e/a,f/a,e*f/(a*b*c)},{e*f/(a*b),e*f/(a*c),q*d/a},q,q]/; Factor[g-(a*b*c*d*q)/(e*f)]===0&& Hyp`q`Private`IntegerTest[d,q]); T8701:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pqinf[{a*q,a*q/(d*e),a*q/(d*f),a*q/(e*f)}, {a*q/d,a*q/e,a*q/f,a*q/(d*e*f)},q]* Hyp`q`ph[{a*q/(b*c),d,e,f},{a*q/b,a*q/c,d*e*f/a},q,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[z-(a^2*q^2)/(b*c*d*e*f)]===0&& (Hyp`q`Private`IntegerTest[a*q/(b*c),q]||Hyp`q`Private`IntegerTest[d,q]||Hyp`q`Private`IntegerTest[e,q]||Hyp`q`Private`IntegerTest[f,q])); T8702:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pq[{a*q,a*q/(d*e)},{a*q/d,a*q/e},-Log[q,simplify[f]],q]* Hyp`q`ph[{a*q/(b*c),d,e,f},{a*q/b,a*q/c,d*e*f/a},q,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[z-(a^2*q^2)/(b*c*d*e*f)]===0&& Hyp`q`Private`IntegerTest[f,q]); T4303:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]:> Hyp`q`ph[{(e*f)/(a*q),(e^(1/2)*f^(1/2)*q^(1/2))/a^(1/2), -((e^(1/2)*f^(1/2)*q^(1/2))/a^(1/2)),f/a,e/a,b,c,d}, {(e^(1/2)*f^(1/2))/(a^(1/2)*q^(1/2)), -((e^(1/2)*f^(1/2))/(a^(1/2)*q^(1/2))),e,f,(e*f)/(a*b), (e*f)/(a*c),(e*f)/(a*d)},q,(e*f/d)/(b*c)]* Hyp`q`pq[{(e*f)/(a*b),(e*f)/(a*c)},{(e*f)/a,(e*f)/(a*b*c)}, -Log[q,simplify[d]],q]/; Factor[g-(a*b*c*d*q)/(e*f)]===0&& Hyp`q`Private`IntegerTest[d,q]); T4304:=(Hyp`q`ph[{a_,b_,c_,g_},{d_,e_,f_},q_,q_] :> Hyp`q`pqinf[{(d*e)/(c*g),(d*e)/(b*g),(d*e)/(a*g),(d*e)/(a*b*c*g)}, {(d*e)/(b*c*g),(d*e)/(a*c*g),(d*e)/(a*b*g),d*e/g},q]* Hyp`q`ph[{d*e/(q*g),d^(1/2)*e^(1/2)*q^(1/2)/g^(1/2), -(d^(1/2)*e^(1/2)*q^(1/2))/g^(1/2),a,b,c,d/g,e/g}, {d^(1/2)*e^(1/2)*q^(-1/2)/g^(1/2),-(d^(1/2)*e^(1/2)*q^(-1/2))/g^(1/2), (d*e)/(a*g),(d*e)/(b*g),(d*e)/(c*g),e,d},q,(d*e)/(a*b*c)]/; Factor[f-(a*b*c*g*q)/(d*e)]===0&& Hyp`q`Private`IntegerTest[g,q]); T8703:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pqinf[{(a*q)/(c*d),(a*q)/(b*d),(a*q)/(b*c),a*q}, {(a*q)/d,(a*q)/c,(a*q)/b,(a*q)/(b*c*d)},q]* Hyp`q`ph[{b,c,d,a*q/(e*f)},{(a*q)/e,(b*c*d)/a,a*q/f},q,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[z-(a^2*q^2)/(b*c*d*e*f)]===0&& Hyp`q`Private`IntegerTest[a*q/(e*f),q]); T4305:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]:> Hyp`q`ph[{(a^(1/2))^2,(b^(1/2))^2,c^2,d^2}, {(a^(1/2))^2*(b^(1/2))^2*q,-(c*d),-(c*d*q)},q^2,q^2]/; Factor[e-a^(1/2)*b^(1/2)*q^(1/2)]===0&& Factor[f+a^(1/2)*b^(1/2)*q^(1/2)]===0&&Factor[g+c*d]===0&& (Hyp`q`Private`IntegerTest[Sqrt[a],q]||Hyp`q`Private`IntegerTest[Sqrt[b],q]||Hyp`q`Private`IntegerTest[c,q]||Hyp`q`Private`IntegerTest[d,q])); T4306:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]:> Hyp`q`ph[{a,b,c^(1/2),d^(1/2)},{e^(1/2),-e^(1/2),f},q^(1/2),q^(1/2)]/; Factor[e-a*b*q^(1/2)]===0&& Factor[f+c^(1/2)*d^(1/2)]===0&& Factor[g+c^(1/2)*d^(1/2)*q^(1/2)]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[c,q]||Hyp`q`Private`IntegerTest[d,q])); T4307:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_]^exp_:1:> Hyp`q`ph[{a^2,b^2,a*b,c,d}, {a*b*q^(1/2),-a*b*q^(1/2),-a*b,a^2*b^2},q,q]^(exp/2)/; Factor[c*d-a^2*b^2]===Factor[e-a*b*q^(1/2)]===Factor[e+f]=== Factor[g+a*b]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[c,q]||Hyp`q`Private`IntegerTest[d,q])); T8704:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pqinf[{a*q,(a*q)/(e*f),(a^2*q^2)/(b*c*d*e),(a^2*q^2)/(b*c*d*f)}, {(a*q)/e,(a*q)/f,(a^2*q^2)/(b*c*d),(a^2*q^2)/(b*c*d*e*f)},q]* Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),e,f},{(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/b,(a*q)/c,(a*q)/d, (a^2*q^2)/(b*c*d*e),(a^2*q^2)/(b*c*d*f)},q,(a*q)/(e*f)]/; 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[z-(a^2*q^2)/(b*c*d*e*f)]===0); T8705:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pqinf[{a*q,b,(a^2*q^2)/(b*d*e*f),(a^2*q^2)/(b*c*e*f), (a^2*q^2)/(b*c*d*f),(a^2*q^2)/(b*c*d*e)}, {(a*q)/c,(a*q)/d,(a*q)/e,(a*q)/f,(a^3*q^3)/(b^2*c*d*e*f), (a^2*q^2)/(b*c*d*e*f)},q]* Hyp`q`ph[{(a^3*q^2)/(b^2*c*d*e*f),(a^(3/2)*q^2)/ (b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)), -((a^(3/2)*q^2)/(b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2))),(a*q)/(b*c), (a*q)/(b*d),(a*q)/(b*e),(a*q)/(b*f),(a^2*q^2)/(b*c*d*e*f)}, {(a^(3/2)*q)/(b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)), -((a^(3/2)*q)/(b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2))),(a^2*q^2)/(b*d*e*f), (a^2*q^2)/(b*c*e*f),(a^2*q^2)/(b*c*d*f),(a^2*q^2)/(b*c*d*e),(a*q)/b}, q,b]/; 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[z-(a^2*q^2)/(b*c*d*e*f)]===0); T5401:=(Hyp`q`ph[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},q_,q_]:> Hyp`q`pq[{(a*q^2)/(b*c*d),(a^3*q^3)/(b^2*c^2*d^2)}, {(a^2*q^2)/(b*c*d),(a^2*q^3)/(b^2*c^2*d^2)},-Log[q,simplify[e]],q]* Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),a^(1/2),-a^(1/2),a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)), (a^3*q^(3))/(b^2*c^2*d^2*e),e}, {(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/b,(a*q)/c,(a*q)/d, (a^(3/2)*q^2)/(b*c*d),-((a^(3/2)*q^2)/(b*c*d)), (a^(3/2)*q^(3/2))/(b*c*d),-((a^(3/2)*q^(3/2))/(b*c*d)), (b*c*d*q^(-1)*e)/a,(a^2*q^(2))/(b*c*d*e)},q,q]/; Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0&& Factor[ee-(b^2*c^2*d^2*e*q^(-2))/a^2]===0&& Hyp`q`Private`IntegerTest[e,q]); T121101:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_,g_,h_,i_,j_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_,ii_,jj_},q_,q_]:> Hyp`q`pq[{a*q,(b^2*c^2*d^2)/(a^2*q)},{(b*c*d)/a,b*c*d},-Log[q,simplify[j]],q]* Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q)/(c*d),(a*q)/(b*d),(a*q)/(b*c),j}, {(a*q)/b,(a*q)/c,(a*q)/d,(a^2*q^(2)*j)/(b^2*c^2*d^2)},q,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]===Factor[i*ii-q*a]===Factor[j*jj-q*a]===0&& Factor[e-(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))]=== Factor[-f-(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))]=== Factor[g/q^(1/2)-(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))]=== Factor[-h/q^(1/2)-(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))]===0&& Factor[i-b*c*d/j]===0&& Hyp`q`Private`IntegerTest[j,q]); T5402:=(Hyp`q`ph[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},q_,q_]:> Hyp`q`ph[{q*a^2/(b*c*d),q^(3/2)*a/(b^(1/2)*c^(1/2)*d^(1/2)), -(q^(3/2)*a/(b^(1/2)*c^(1/2)*d^(1/2))),q*a/(c*d), q*a/(b*d),q*a/(b*c),Sqrt[a],-Sqrt[a],q^(1/2)*Sqrt[a], -q^(1/2)*Sqrt[a],e,q^(3)*a^3/(b^2*c^2*d^2*e)}, {q^(1/2)*a/(b^(1/2)*c^(1/2)*d^(1/2)), -(q^(1/2)*a/(b^(1/2)*c^(1/2)*d^(1/2))),q*a/b,q*a/c, q*a/d,q^(2)*a^(3/2)/(b*c*d),-(q^(2)*a^(3/2)/(b*c*d)), q^(3/2)*a^(3/2)/(b*c*d),-(q^(3/2)*a^(3/2)/(b*c*d)), q^(2)*a^2/(b*c*d*e),b*c*d*e*q^(-1)/a},q,q]* Hyp`q`pq[{q^(2)*a^2/(b*c*d*e),q^(3)*a^3/(b^2*c^2*d^2)}, {q^(2)*a^2/(b*c*d),q^(3)*a^3/(b^2*c^2*d^2*e)},-Log[q,simplify[a]],q]/; Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]=== Factor[ee-b^2*c^2*d^2*e/(q^2*a^2)]===0&& Hyp`q`Private`IntegerTest[a,q]); T121102:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,f_,g_,h_,i_,e_,j_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ff_,gg_,hh_,ii_,ee_,jj_},q_,q_]:> Hyp`q`ph[{f^2,(b^(1/2)*q^(1/2)*f)/(c^(1/2)*d^(1/2)), (c^(1/2)*q^(1/2)*f)/(b^(1/2)*d^(1/2)), (d^(1/2)*q^(1/2)*f)/(b^(1/2)*c^(1/2)),e}, {(c^(1/2)*d^(1/2)*q^(1/2)*f)/b^(1/2), (b^(1/2)*d^(1/2)*q^(1/2)*f)/c^(1/2), (b^(1/2)*c^(1/2)*q^(1/2)*f)/d^(1/2),(e*q*f^2)/(b*c*d)},q,q]* Hyp`q`pq[{b^(1/2)*c^(1/2)*d^(1/2)*q^(1/2)*f,(b*c*d)/e}, {(b^(1/2)*c^(1/2)*d^(1/2)*q^(1/2)*f)/e,b*c*d},-Log[q,simplify[f^2]],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]===Factor[i*ii-q*a]===Factor[j*jj-q*a]===0&& Factor[a-b^(1/2)*c^(1/2)*d^(1/2)*h/q]===0&& Factor[j-(b*c*d)/e]===0&& Factor[f+i/q^(1/2)]===Factor[-g+i/q^(1/2)]===Factor[h/q^(1/2)+i/q^(1/2)]===0&& Hyp`q`Private`IntegerTest[f^2,q]); T7601:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_},q_,q_]:> ((1-(a^3*q/e^2)/(b^2*c^2*d^2))* Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)),a^(1/2)*q, -(a^(1/2)*q),(a^3*q)/(b^2*c^2*d^2*e),e}, {(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/b,(a*q)/c,(a*q)/d, (a^(3/2)*q^(3/2))/(b*c*d),-((a^(3/2)*q^(3/2))/(b*c*d)), (a^(3/2)*q)/(b*c*d),-((a^(3/2)*q)/(b*c*d)),(b*c*d*q*e)/a, (a^2*q^(2))/(b*c*d*e)},q,q]* Hyp`q`pq[{a/(b*c*d),(a^3*q)/(b^2*c^2*d^2)}, {(a^2*q^2)/(b*c*d),(a^2*q)/(b^2*c^2*d^2)},-Log[q,simplify[e]],q])/ (1-(a^3*q)/(b^2*c^2*d^2))/; 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[ee-(b^2*c^2*d^2*e)/(a^2)]===0&& Hyp`q`Private`IntegerTest[e,q]); T121103:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_,g_,h_,i_,j_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_,ii_,jj_},q_,q_]:> Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),j},{(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/b,(a*q)/c,(a*q)/d, (a^2*q^(4)*j)/(b^2*c^2*d^2)},q,q]* (1-(b*c*d)/q^2)/(1-b*c*d*q^(-2)/j^2)* Hyp`q`pq[{a*q,(b^2*c^2*d^2)/(a^2*q^3)}, {(b*c*d)/(a*q^2),(b*c*d)/q^2},-Log[q,simplify[j]],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]===Factor[i*ii-q*a]===Factor[j*jj-q*a]===0&& Factor[e+h/q^(1/2)]===Factor[(a*q)/(b^(1/2)*c^(1/2)*d^(1/2))+h/q^(1/2)]=== Factor[-f+h/q^(1/2)]===Factor[g/q^(1/2)+h/q^(1/2)]===0&& Factor[i-b*c*d*q^(-2)/j]===0&& Hyp`q`Private`IntegerTest[j,q]); T10901:=(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`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),e,f,(a^3*q^(2))/(b*c*d*e*f*h),h}, {(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/b,(a*q)/c,(a*q)/d, (a^2*q^2)/(b*c*d*e),(a^2*q^2)/(b*c*d*f),(e*f*h)/(a), (a^2*q^(2))/(b*c*d*h)},q,q]* Hyp`q`pq[{a*q,(a*q)/(e*f),(a^2*q^2)/(b*c*d*e),(a^2*q^2)/(b*c*d*f)}, {(a*q)/e,(a*q)/f,(a^2*q^2)/(b*c*d*e*f),(a^2*q^2)/(b*c*d)}, -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[g-(a^3*q^(2))/(b*c*d*e*f*h)]===0&& Hyp`q`Private`IntegerTest[h,q]); T2161:=(Hyp`q`ph[{a_,b_},{c_},q_,z_]:> Hyp`q`pqinf[{a*b*z/c,q/c},{a*z/c,q/a},q]* Hyp`q`ph[{c/a,c*q/(a*b*z)},{c*q/(a*z)},q,b*q/c]- Hyp`q`pqinf[{b,q/c,c/a,a*z/q,q^2/(a*z)},{c/q,b*q/c,q/a,a*z/c,c*q/(a*z)},q]* Hyp`q`ph[{a*q/c,b*q/c},{q^2/c},q,z]); T2162:=(Hyp`q`ph[{a_,b_},{c_},q_,z_]:> Hyp`q`pqinf[{b,c/a,a*z,q/(a*z)},{c,b/a,z,q/z},q]* Hyp`q`ph[{a,a*q/c},{a*q/b},q,c*q/(a*b*z)]+ Hyp`q`pqinf[{a,c/b,b*z,q/(b*z)},{c,a/b,z,q/z},q]* Hyp`q`ph[{b,b*q/c},{b*q/a},q,c*q/(a*b*z)]); T3261:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`pqinf[{e/b,e/c,c*q/a,q/d},{e,c*q/d,q/a,e/(b*c)},q]* Hyp`q`ph[{c,d/a,c*q/e},{c*q/a,b*c*q/e},q,b*q/d]- Hyp`q`pqinf[{q/d,e*q/d,b,c,d/a,d*e/(b*c*q),b*c*q^2/(d*e)}, {d/q,e,b*q/d,c*q/d,q/a,e/(b*c),b*c*q/e},q]* Hyp`q`ph[{a*q/d,b*q/d,c*q/d},{q^2/d,e*q/d},q,d*e/(a*b*c)]/; Factor[z-d*e/(a*b*c)]===0); T3262:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`pqinf[{e/b,e/c},{e,e/(b*c)},q]*Hyp`q`ph[{d/a,b,c},{d,b*c*q/e},q,q]+ Hyp`q`pqinf[{d/a,b,c,d*e/(b*c)},{d,e,b*c/e,d*e/(a*b*c)},q]* Hyp`q`ph[{e/b,e/c,d*e/(a*b*c)},{d*e/(b*c),e*q/(b*c)},q,q]/; Factor[z-d*e/(a*b*c)]===0); T3263:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_] :> Hyp`q`pqinf[{(d*q)/(b*c),e/c,a,b,(a*b*q)/(d*e),(d*e)/(a*b)}, {(a*q)/e,q/c,d,(a*b)/d,(d*e)/(a*b*c),e},q]* Hyp`q`ph[{q/b,(d*e)/(a*b*c),d/b},{(d*q)/(a*b),(d*q)/(b*c)},q,(b*q)/e] + Hyp`q`pqinf[{(a*q)/c,d/b,d/a,q/e},{(a*q)/e,q/c,d,d/(a*b)},q]* Hyp`q`ph[{(a*q)/d,e/c,a},{(a*b*q)/d,(a*q)/c},q,(b*q)/e]/; Factor[z-(d*e)/(a*b*c)]===0); T3264:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,q_] :> Hyp`q`pqinf[{(b*c*q)/e,q/e},{(c*q)/e,(b*q)/e}, q]*Hyp`q`ph[{d/a,b,c},{d,(b*c*q)/e},q,(a*q)/e] - Hyp`q`pqinf[{q/e,a,b,c,(d*q)/e},{(c*q)/e,(b*q)/e,d,e/q,(a*q)/e},q]* Hyp`q`ph[{(c*q)/e,(b*q)/e,(a*q)/e},{(d*q)/e,q^2/e},q,q]); T3265:=(Hyp`q`ph[{a_,b_,c_},{bb_,cc_},q_,z_]:> Hyp`q`pqinf[{a*(z*b*c/a/q)},{(z*b*c/a/q)},q]* Hyp`q`ph[{Sqrt[a],-Sqrt[a],Sqrt[q*a],-Sqrt[q*a],a*q/(b*c)}, {a*q/b,a*q/c,a*(z*b*c/a/q),q/(z*b*c/a/q)},q,q]+ Hyp`q`pqinf[{a,a*q/(b*c),a*q*(z*b*c/a/q)/b,a*q*(z*b*c/a/q)/c},{a*q/b,a*q/c,a*q*(z*b*c/a/q)/(b*c),(z*b*c/a/q)^(-1)},q]* Hyp`q`ph[{(z*b*c/a/q)*Sqrt[a],-(z*b*c/a/q)*Sqrt[a],(z*b*c/a/q)*Sqrt[q*a],-(z*b*c/a/q)*Sqrt[q*a],a*q*(z*b*c/a/q)/(b*c)}, {a*q*(z*b*c/a/q)/b,a*q*(z*b*c/a/q)/c,(z*b*c/a/q)*q,a*(z*b*c/a/q)^2},q,q]/; Factor[b*bb-q*a]===Factor[c*cc-q*a]===0); T8761:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pqinf[{a*q,a*q/(d*e),a*q/(d*f),a*q/(e*f)},{a*q/d,a*q/e,a*q/f,a*q/(d*e*f)},q]* Hyp`q`ph[{a*q/(b*c),d,e,f},{a*q/b,a*q/c,d*e*f/a},q,q]+ Hyp`q`pqinf[{a*q,a*q/(b*c),d,e,f,a^2*q^2/(b*d*e*f),a^2*q^2/(c*d*e*f)}, {a*q/b,a*q/c,a*q/d,a*q/e,a*q/f,a^2*q^2/(b*c*d*e*f),d*e*f/(a*q)},q]* Hyp`q`ph[{a*q/(d*e),a*q/(d*f),a*q/(e*f),a^2*q^2/(b*c*d*e*f)}, {a^2*q^2/(b*d*e*f),a^2*q^2/(c*d*e*f),a*q^2/(d*e*f)},q,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[z-(a^2*q^2)/(b*c*d*e*f)]===0); T8762:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:> Hyp`q`pqinf[{a*q,a*q/(d*e),a*q/(d*f),a*q/(e*f),e*q/c,f*q/c,b/a,b*e*f/a}, {a*q/d,a*q/e,a*q/f,a*q/(d*e*f),q/c,e*f*q/c,b*e/a,b*f/a},q]* Hyp`q`ph[{e*f/c,q*Sqrt[e*f/c],-q*Sqrt[e*f/c],a*q/(b*c),a*q/(c*d),e*f/a,e,f}, {Sqrt[e*f/c],-Sqrt[e*f/c],b*e*f/a,d*e*f/a,a*q/c,f*q/c,e*q/c},q,b*d/a]- Hyp`q`pqinf[{a*q,b/a,b*q/c,b*q/d,b*q/e,b*q/f,d,e,f,a*q/(b*c), b*d*e*f/a^2,a^2*q/(b*d*e*f)}, {a/b,a*q/c,a*q/d,a*q/e,a*q/f,b*d/a,b*e/a,b*f/a,d*e*f/a,a*q/(d*e*f), q/c,b^2*q/a},q]* Hyp`q`ph[{b^2/a,q*Sqrt[b^2/a],-q*Sqrt[b^2/a],b,b*c/a,b*d/a,b*e/a,b*f/a}, {Sqrt[b^2/a],-Sqrt[b^2/a],b*q/a,b*q/c,b*q/d,b*q/e,b*q/f}, q,a^2*q^2/(b*c*d*e*f)]/; 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[z-(a^2*q^2)/(b*c*d*e*f)]===0); T8763:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_] :> Hyp`q`pqinf[{(c*e*f)/a,(f*q)/d,(e*q)/d,c/a, (a*q)/(e*f),a*q,(a*q)/(b*f),(a*q)/(b*e)}, {(e*f*q)/d,(c*f)/a,(c*e)/a,q/d,(a*q)/f,(a*q)/e,(a*q)/(b*e*f), (a*q)/b},q]*Hyp`q`ph[{(e*f)/d,(e^(1/2)*f^(1/2)*q)/d^(1/2), -((e^(1/2)*f^(1/2)*q)/d^(1/2)),(a*q)/(b*d),(e*f)/a,(a*q)/(c*d),e,f} ,{(e^(1/2)*f^(1/2))/d^(1/2),-((e^(1/2)*f^(1/2))/d^(1/2)),(b*e*f)/a, (a*q)/d,(c*e*f)/a,(f*q)/d,(e*q)/d},q,(b*c)/a] + Hyp`q`pqinf[{a*q,(a^2*q^2)/(b*d*e*f),(c*q)/b,(a*q^2)/(b*d*e), (a*q^2)/(b*d*f),(a*q)/(c*d),e,f,b,(a^2*q^2)/(b*c*e*f), (b*c*e*f)/(a^2*q)},{(c*f)/a,(c*e)/a,q/d,(a*q)/f,(a*q)/e,(a*q)/b, (b*e*f)/(a*q),(a*q)/d,(a^2*q^2)/(b*c*d*e*f),(a*q)/c, (a^2*q^3)/(b^2*d*e*f)},q]* Hyp`q`ph[{(a^2*q^2)/(b^2*d*e*f),(a*q^2)/(b*d^(1/2)*e^(1/2)*f^(1/2)), -((a*q^2)/(b*d^(1/2)*e^(1/2)*f^(1/2))),(a*q)/(b*d),q/b, (a^2*q^2)/(b*c*d*e*f),(a*q)/(b*f),(a*q)/(b*e)}, {(a*q)/(b*d^(1/2)*e^(1/2)*f^(1/2)), -((a*q)/(b*d^(1/2)*e^(1/2)*f^(1/2))),(a*q^2)/(b*e*f), (a^2*q^2)/(b*d*e*f),(c*q)/b,(a*q^2)/(b*d*e),(a*q^2)/(b*d*f)},q, (b*c)/a]/; 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[z-(a^2*q^2)/(b*c*d*e*f)]===0); T10961:=(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`pqinf[{a*q,b/a,c,d,e,f,g,(a^3*q^2)/(b*c*d*e*f*g),(b*q)/c, (b*q)/d,(b*q)/e,(b*q)/f,(b*q)/g,(b^2*c*d*e*f*g)/(a^3*q)}, {(b^2*q)/a,a/b,(a*q)/c,(a*q)/d,(a*q)/e,(a*q)/f,(a*q)/g, (b*c*d*e*f*g)/(a^2*q),(b*c)/a,(b*d)/a,(b*e)/a,(b*f)/a,(b*g)/a, (a^2*q^2)/(c*d*e*f*g)},q]* Hyp`q`ph[{b^2/a,(b*q)/a^(1/2),-((b*q)/a^(1/2)),b,(b*c)/a,(b*d)/a, (b*e)/a,(b*f)/a,(b*g)/a,(a^2*q^2)/(c*d*e*f*g)}, {b/a^(1/2),-(b/a^(1/2)),(b*q)/a,(b*q)/c,(b*q)/d,(b*q)/e,(b*q)/f, (b*q)/g,(b^2*c*d*e*f*g)/(a^3*q)},q,q]+ Hyp`q`pqinf[{a*q,b/a,f,g,(a^3*q^2)/(b*c*d*e*f*g),(b*q)/f,(b*q)/g, (b^2*c*d*e*f*g)/(a^3*q),(a*q)/(d*e),(a*q)/(c*e),(a*q)/(c*d), (b*d*e)/a,(b*c*e)/a,(b*c*d)/a}, {(b^2*c*d*e)/a^2,(a^2*q)/(b*c*d*e),(a*q)/c,(a*q)/d,(a*q)/e, (a*q)/f,(a*q)/g,(b*c*d*e*f*g)/(a^2*q),(b*c)/a,(b*d)/a,(b*e)/a, (b*f)/a,(b*g)/a,(a^2*q^2)/(c*d*e*f*g)},q]* Hyp`q`ph[{(b^2*c*d*e)/(a^2*q),(b*c^(1/2)*d^(1/2)*e^(1/2)*q^(1/2))/a, -((b*c^(1/2)*d^(1/2)*e^(1/2)*q^(1/2))/a),b,(b*c)/a,(b*d)/a, (b*e)/a,(b*c*d*e*f)/(a^2*q),(b*c*d*e*g)/(a^2*q),(a*q)/(f*g)}, {(b*c^(1/2)*d^(1/2)*e^(1/2))/(a*q^(1/2)), -((b*c^(1/2)*d^(1/2)*e^(1/2))/(a*q^(1/2))),(b*c*d*e)/a^2,(b*d*e)/a, (b*c*e)/a,(b*c*d)/a,(b*q)/f,(b*q)/g,(b^2*c*d*e*f*g)/(a^3*q)},q,q]\ +Hyp`q`pqinf[{a*q,b/a,(a^2*q^2)/(c*d*e*f),(a^2*q^2)/(c*d*e*g), (b*f*g)/a,(b*c*d*e*f)/(a^2*q),(b*c*d*e*g)/(a^2*q),(a*q)/(f*g)}, {(a^2*q^2)/(c*d*e),(b*c*d*e)/(a^2*q),(a*q)/f,(a*q)/g, (b*c*d*e*f*g)/(a^2*q),(b*f)/a,(b*g)/a,(a^2*q^2)/(c*d*e*f*g)},q]* Hyp`q`ph[{(a^2*q)/(c*d*e),(a*q^(3/2))/(c^(1/2)*d^(1/2)*e^(1/2)), -((a*q^(3/2))/(c^(1/2)*d^(1/2)*e^(1/2))),b,(a*q)/(d*e),(a*q)/(c*e), (a*q)/(c*d),f,g,(a^3*q^2)/(b*c*d*e*f*g)}, {(a*q^(1/2))/(c^(1/2)*d^(1/2)*e^(1/2)), -((a*q^(1/2))/(c^(1/2)*d^(1/2)*e^(1/2))),(a^2*q^2)/(b*c*d*e), (a*q)/c,(a*q)/d,(a*q)/e,(a^2*q^2)/(c*d*e*f),(a^2*q^2)/(c*d*e*g), (b*f*g)/a},q,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[h-a^3*q^2/(b*c*d*e*f*g)]===0); (* Ex2.2 *) T4308:=(Hyp`q`ph[{a_,aa_,aaa_,b_},{aaaa_,aaaaa_,bb_},q_,t_]:> Hyp`q`pqinf[{a*q,b*t},{t,(a*q)/b},q]*Hyp`q`ph[{b^(-1),t},{b*q*t},q,a*q]/; Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]=== Factor[-aaa/q+aaaaa]===0&& Factor[b*bb-q*a]===0); (* Ex2.2,reversed *) T2109:=(Hyp`q`ph[{a_,b_},{c_},q_,t_]:>Hyp`q`pqinf[{b,a*t},{t,b/a},q]* Hyp`q`ph[{t/q,q^(1/2)*t^(1/2),-(q^(1/2)*t^(1/2)),a^(-1)}, {t^(1/2)/q^(1/2),-(t^(1/2)/q^(1/2)),a*t},q,b]/; Factor[c-(b*q)/a]===0); (* Ex2.13(i) *) T4309:=(Hyp`q`ph[{a_,b_,c_,d_},{bb_,cc_,dd_},q_,z_]:> Hyp`q`pqinf[{(a*q^2)/(b*c*d),(a^3*q^3)/(b^2*c^2*d^2)}, {(a^2*q^2)/(b*c*d),(a^2*q^3)/(b^2*c^2*d^2)},q]* Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),a^(1/2),-a^(1/2), a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c)},{(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a^(3/2)*q^2)/(b*c*d), -((a^(3/2)*q^2)/(b*c*d)),(a^(3/2)*q^(3/2))/(b*c*d), -((a^(3/2)*q^(3/2))/(b*c*d)),(a*q)/b,(a*q)/c,(a*q)/d},q, (a*q^2)/(b*c*d)]/; Factor[z-(a^2*q^3)/(b^2*c^2*d^2)]=== Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]===0); (* Ex2.13(i),reversed *) T10902:=(Hyp`q`ph[{a_,aa_,aaa_,b_,e_,f_,g_,c_,d_, h_},{aaaa_,aaaaa_,bb_,ee_,ff_,gg_,cc_,dd_,hh_},q_, z_]:>Hyp`q`pqinf[{a*q,(a^2*q)/b^4},{(a*q)/b^2,(a^2*q)/b^2},q]* Hyp`q`ph[{b^2,(b^2*c)/a,(b^2*d)/a,(a*q)/(c*d)}, {(a*q)/c,(a*q)/d,(b^2*c*d)/a},q,(a^2*q)/b^4]/; 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+e]===Factor[f+g]===Factor[b^2*q-f^2]=== Factor[h-(a^2*q)/(b^2*c*d)]===Factor[z-(a*q)/b^2]===0); (* Ex2.13(ii) *) T4310:=(Hyp`q`ph[{a_,b_,c_,d_},{bb_,cc_,dd_},q_,z_]:> Hyp`q`pqinf[{a*q,-q,(a^(3/2)*q^2)/(b*c*d),-((a^(3/2)*q^2)/(b*c*d))}, {(a^2*q^2)/(b*c*d),-((a*q^2)/(b*c*d)),a^(1/2)*q,-(a^(1/2)*q)},q]* Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),a^(1/2),-a^(1/2), (a*q)/(c*d),(a*q)/(b*d),(a*q)/(b*c)}, {(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a^(3/2)*q^2)/(b*c*d), -((a^(3/2)*q^2)/(b*c*d)),(a*q)/b,(a*q)/c,(a*q)/d},q,-q]/; Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]=== Factor[z+((a*q^2)/(b*c*d))]===0); (* Ex2.13(ii),reversed *) T8706:=(Hyp`q`ph[{a_,aa_,aaa_,b_,e_,c_,d_,f_}, {aaaa_,aaaaa_,bb_,ee_,cc_,dd_,ff_}, q_,z_]:>Hyp`q`pqinf[{a*q,-((a*q)/b^2),b*q,-(b*q)}, {b^2*q,-q,(a*q)/b,-((a*q)/b)},q]* Hyp`q`ph[{b^2,(b^2*c)/a,(b^2*d)/a,(a*q)/(c*d)}, {(a*q)/c,(a*q)/d,(b^2*c*d)/a},q,-((a*q)/b^2)]/; 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[b+e]===Factor[f-(a^2*q)/(b^2*c*d)]===Factor[q+z]===0); (* Ex2.14(ii) *) T6501:=(Hyp`q`ph[{a_,aa_,b_,c_,d_,e_}, {aaa_,bb_,cc_,dd_,ee_},q_,q_]:> Hyp`q`ph[{(a^2*q)/(b*c*d),(a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),a^(1/2)*q,-a^(1/2),a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)), (a^3*q^(2))/(b^2*c^2*d^2*e),e}, {(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a*q)/b,(a*q)/c,(a*q)/d, (a^(3/2)*q)/(b*c*d),-((a^(3/2)*q^2)/(b*c*d)), (a^(3/2)*q^(3/2))/(b*c*d),-((a^(3/2)*q^(3/2))/(b*c*d)), (b*c*d*e)/(a),(a^2*q^(2))/(b*c*d*e)},q,q]* Hyp`q`pq[{(a*q)/(b*c*d),(a^3*q^2)/(b^2*c^2*d^2),-((a^(3/2)*q^2)/(b*c*d))}, {(a^2*q^2)/(b*c*d),(a^2*q^2)/(b^2*c^2*d^2),-((a^(3/2)*q)/(b*c*d))},-Log[q,simplify[e]], q]/; Factor[aa/q-aaa]===Factor[a^(1/2)-aaa]=== Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]=== Factor[ee-(b^2*c^2*d^2*e*q^(-1))/a^2]===0&& Hyp`q`Private`IntegerTest[e,q]); (* Ex2.14(ii),reversed *) T121104:=(Hyp`q`ph[{a_,aa_,aaa_,c_,d_,e_,b_,f_, g_,h_,i_,j_}, {aaaa_,aaaaa_,cc_,dd_,ee_,bb_,ff_,gg_,hh_,ii_,jj_},q_,q_]:> Hyp`q`ph[{b^2/q^2,b,(b^2*c)/(a*q^2),(b^2*d)/(a*q^2), (a*q)/(c*d),j},{b/q,(a*q)/c,(a*q)/d,(b^2*c*d)/(a*q^2), (b^4*q^(-3)*j)/a^2},q,q]* Hyp`q`pq[{a*q,(a^2*q^4)/b^4,-((a*q)/b)}, {(a*q^2)/b^2,(a^2*q^2)/b^2,-((a*q^2)/b)},-Log[q,simplify[j]],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]===Factor[i*ii-q*a]===Factor[j*jj-q*a]===0&& Factor[e-(a^2*q^3)/(b^2*c*d)]===Factor[b+q*f]===Factor[g+h]=== Factor[b^2-g^2*q]===Factor[i-(a^2*q^2)/b^2/j]===0&& Hyp`q`Private`IntegerTest[j,q]); (* Ex2.15 *) T8764:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_},q_,z_]:>-((a* Hyp`q`pqinf[{a*q,c,b/a,c/a,(b*q)/d,(b*q)/e,(b*q)/f,(a*q)/(b*d), (a*q)/(b*e),(a*q)/(b*f)}, {(a*q)/d,(a*q)/e,(a*q)/f,q/d,q/e,q/f,(b^2*q)/a,(b*c)/a,a/b, c/b},q]*Hyp`q`ph[{b^2/a,(b*q)/a^(1/2),-((b*q)/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,(a^2*q^2)/(b*c*d*e*f)])/b)- (a*Hyp`q`pqinf[{a*q,b,b/a,c/a,(c*q)/d,(c*q)/e,(c*q)/f,(a*q)/(c*d), (a*q)/(c*e),(a*q)/(c*f)}, {(a*q)/d,(a*q)/e,(a*q)/f,q/d,q/e,q/f,(c^2*q)/a,(b*c)/a,a/c, b/c},q]*Hyp`q`ph[{c^2/a,(c*q)/a^(1/2),-((c*q)/a^(1/2)),c,(b*c)/a, (c*d)/a,(c*e)/a,(c*f)/a}, {c/a^(1/2),-(c/a^(1/2)),(c*q)/a,(c*q)/b,(c*q)/d,(c*q)/e, (c*q)/f},q,(a^2*q^2)/(b*c*d*e*f)])/c/; 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[z-(a^2*q^2)/(b*c*d*e*f)]===0); (* Ex2.19 *) T10903:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_,f_,g_,h_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,ff_,gg_, hh_},q_,q_]:>e^(-Log[q,simplify[h]])*Hyp`q`ph[{e*h/(b),(e^(1/2)*q*h^(1/2))/b^(1/2), -((e^(1/2)*q*h^(1/2))/b^(1/2)),e,(a*q)/(b*c),(a*q)/(b*d), (a*q)/(b*f),(a*q)/(b*g),e*h/(a),h}, {e^(1/2)*h^(1/2)/(b^(1/2)),-(e^(1/2)*h^(1/2)/(b^(1/2))),q*h/b, (c*e*h)/(a),(d*e*h)/(a),(e*f*h)/(a),(e*g*h)/(a),(a*q)/b, (e*q)/b},q,q]*Hyp`q`pq[{a*q,(a*q)/(c*e),(a*q)/(d*e),(a*q)/(e*f), (a*q)/(e*g),b},{(a*q)/c,(a*q)/d,(a*q)/e,(a*q)/f,(a*q)/g,b/e},-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]===Factor[g-a^3*q^(2)/(b*c*d*e*f*h)]===0&& Hyp`q`Private`IntegerTest[h,q]); (* 3.2.6 *) T3210:={(Hyp`q`ph[{a_,b_,c_},{e_,d_},q_,z_]:> (d^(-Log[q,simplify[c]])*e^(-Log[q,simplify[c]])* Hyp`q`ph[{a,(a*c*b*q)/(d*e),c},{(a*c*q)/e,(a*c*q)/d},q,q/b]* Hyp`q`pq[{(a*c*q)/d,(a*c*q)/e},{d,e},-Log[q,simplify[c]],q])/ ((a*c)^(-Log[q,simplify[c]])/c)/; Factor[z-(d*e)/(a*b*c)]===0&& Hyp`q`Private`IntegerTest[c,q]), (Hyp`q`ph[{a_,c_,b_},{e_,d_},q_,z_]:> (d^(-Log[q,simplify[c]])*e^(-Log[q,simplify[c]])* Hyp`q`ph[{a,(a*c*b*q)/(d*e),c},{(a*c*q)/e,(a*c*q)/d},q,q/b]* Hyp`q`pq[{(a*c*q)/d,(a*c*q)/e},{d,e},-Log[q,simplify[c]],q])/ ((a*c)^(-Log[q,simplify[c]])/c)/; Factor[z-(d*e)/(a*b*c)]===0&& Hyp`q`Private`IntegerTest[c,q]), (Hyp`q`ph[{b_,c_,a_},{e_,d_},q_,z_]:> (d^(-Log[q,simplify[c]])*e^(-Log[q,simplify[c]])* Hyp`q`ph[{a,(a*c*b*q)/(d*e),c},{(a*c*q)/e,(a*c*q)/d},q,q/b]* Hyp`q`pq[{(a*c*q)/d,(a*c*q)/e},{d,e},-Log[q,simplify[c]],q])/ ((a*c)^(-Log[q,simplify[c]])/c)/; Factor[z-(d*e)/(a*b*c)]===0&& Hyp`q`Private`IntegerTest[c,q])}; (* 3.4.4 *) T5461:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_},{aaaa_,aaaaa_,bb_,cc_}, q_,x_]:>(1-(b^2*c^2*x^2)/(a*q))*Hyp`q`pqinf[{b*c*q*x},{(b*c*x)/(a*q)},q]* Hyp`q`ph[{a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)),a^(1/2)*q,-(a^(1/2)*q), (a*q)/(b*c)},{(a*q)/b,(a*q)/c,b*c*q*x,(a*q^2)/(b*c*x)},q,q]+ Hyp`q`pqinf[{a*q,(a*q)/(b*c),c*x,b*x},{(a*q)/b,(a*q)/c,x,(a*q)/(b*c*x)}, q]*Hyp`q`ph[{(b*c*x)/(a^(1/2)*q^(1/2)),-((b*c*x)/(a^(1/2)*q^(1/2))), (b*c*x)/a^(1/2),-((b*c*x)/a^(1/2)),x}, {c*x,b*x,(b*c*x)/a,(b^2*c^2*x^2)/a},q,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]===0); (* 3.4.4,reversed,first form *) T5462:=(Hyp`q`ph[{a_,d_,e_,f_,g_},{b_,c_,x_,y_},q_, q_]:>(Hyp`q`pqinf[{x/(a^2*q)},{x},q]* Hyp`q`ph[{a^2/q,a*q^(1/2),-(a*q^(1/2)),a^2/b,a^2/c}, {a/q^(1/2),-(a/q^(1/2)),b,c},q,(b*c*x)/(a^4*q)])/ (1-x^2/(a^2*q^2))-(Hyp`q`pqinf[{x/(a^2*q),a^2,(b*c)/a^2,(b*x)/(a^2*q), (c*x)/(a^2*q)},{x,b,c,(b*c*x)/(a^4*q),(a^2*q)/x},q]* Hyp`q`ph[{x/(a*q),-(x/(a*q)),x/(a*q^(1/2)),-(x/(a*q^(1/2))), (b*c*x)/(a^4*q)},{(b*x)/(a^2*q),(c*x)/(a^2*q),x/a^2,x^2/(a^2*q)}, q,q])/(1-x^2/(a^2*q^2))/; Factor[a+d]===Factor[e+f]===Factor[a^2*q-e^2]=== Factor[g-(b*c)/a^2]===Factor[y-(a^2*q^2)/x]===0); (* 3.4.4,reversed,second form *) T5463:=(Hyp`q`ph[{x_,y_,z_,u_,v_},{b_,c_,a_,d_},q_, q_]:>-((1-x^2)*Hyp`q`pqinf[{(q^2*x^2)/a,(b*q)/a,(c*q)/a,(a*b*c)/(q*x^2), q/a},{a/q,(q^2*x^2)/a^2,(b*c)/x^2,b,c},q]* Hyp`q`ph[{(q*x)/a,-((q*x)/a),(q^(3/2)*x)/a,-((q^(3/2)*x)/a),(b*c)/x^2}, {(b*q)/a,(c*q)/a,(q^2*x^2)/a,q^2/a},q,q])+ Hyp`q`pqinf[{(b*q)/a,(c*q)/a,(a*b*c)/(q*x^2),q/a}, {(q^2*x^2)/a^2,(b*c)/x^2,b,c},q]* Hyp`q`ph[{(q*x^2)/a^2,(q^(3/2)*x)/a,-((q^(3/2)*x)/a),(q*x^2)/(a*b), (q*x^2)/(a*c)},{(q^(1/2)*x)/a,-((q^(1/2)*x)/a),(b*q)/a,(c*q)/a},q, (a*b*c)/(q*x^2)]/; Factor[x+y]===Factor[z+u]===Factor[x^2*q-z^2]=== Factor[v-(a*b*c)/(q*x^2)]===Factor[d-q*x^2]===0); (* 3.4.7 *) T2110:={(Hyp`q`ph[{a_,b_},{c_},q_,x_]:>Hyp`q`pqinf[{b*x,(a*b^2*x^2)/q}, {a*b*x,(b^2*x^2)/q},q]*Hyp`q`ph[{(a*b*x)/q,a^(1/2)*b^(1/2)*q^(1/2)*x^(1/2), -(a^(1/2)*b^(1/2)*q^(1/2)*x^(1/2)),(b^2*x)/q,a^(1/2),-a^(1/2), a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2))}, {(a^(1/2)*b^(1/2)*x^(1/2))/q^(1/2),-((a^(1/2)*b^(1/2)*x^(1/2))/q^(1/2)), (a*q)/b,a^(1/2)*b*x,-(a^(1/2)*b*x),(a^(1/2)*b*x)/q^(1/2), -((a^(1/2)*b*x)/q^(1/2))},q,x]/; Factor[c-(a*q)/b]===0), (Hyp`q`ph[{b_,a_},{c_},q_,x_]:>Hyp`q`pqinf[{b*x,(a*b^2*x^2)/q}, {a*b*x,(b^2*x^2)/q},q]*Hyp`q`ph[{(a*b*x)/q,a^(1/2)*b^(1/2)*q^(1/2)*x^(1/2), -(a^(1/2)*b^(1/2)*q^(1/2)*x^(1/2)),(b^2*x)/q,a^(1/2),-a^(1/2), a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2))}, {(a^(1/2)*b^(1/2)*x^(1/2))/q^(1/2),-((a^(1/2)*b^(1/2)*x^(1/2))/q^(1/2)), (a*q)/b,a^(1/2)*b*x,-(a^(1/2)*b*x),(a^(1/2)*b*x)/q^(1/2), -((a^(1/2)*b*x)/q^(1/2))},q,x]/; Factor[c-(a*q)/b]===0)}; (* 3.4.7, reversed *) T8707:=(Hyp`q`ph[{b_,bb_,bbb_,a_,c_,d_,e_,x_}, {bbbb_,bbbbb_,aa_,cc_,dd_,ee_,xx_},q_,z_]:> Hyp`q`pqinf[{b*q,(b^2*q)/a^4},{(b*q)/a^2,(b^2*q)/a^2},q]* Hyp`q`ph[{a^2,(a^2*x)/b},{(b*q)/x},q,(b^2*q)/(a^4*x)]/; Factor[bb/q+bbbbb]===Factor[bbbb+bbbbb]===Factor[b^(1/2)+bbbbb]=== Factor[-bbb/q+bbbbb]===0&& Factor[x*xx-q*b]===Factor[a*aa-q*b]===Factor[d*dd-q*b]=== Factor[e*ee-q*b]===Factor[c*cc-q*b]===0&& Factor[a+c]===Factor[d+e]===Factor[a^2*q-d^2]=== Factor[z-(b^2*q)/(a^4*x)]===0); (* 3.4.8 *) T4311:=(Hyp`q`ph[{a_,aa_,aaa_,b_},{aaaa_,aaaaa_,bb_},q_,x_]:> Hyp`q`pqinf[{a*b^2*q^2*x^2,b*x},{a*b*q^2*x,b^2*q*x^2},q]* Hyp`q`ph[{a*b*q*x,a^(1/2)*b^(1/2)*q^(3/2)*x^(1/2), -(a^(1/2)*b^(1/2)*q^(3/2)*x^(1/2)),a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)), a^(1/2)*q,-(a^(1/2)*q),b^2*q*x}, {a^(1/2)*b^(1/2)*q^(1/2)*x^(1/2),-(a^(1/2)*b^(1/2)*q^(1/2)*x^(1/2)), a^(1/2)*b*q^(3/2)*x,-(a^(1/2)*b*q^(3/2)*x),a^(1/2)*b*q*x, -(a^(1/2)*b*q*x),(a*q)/b},q,x]/; Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]=== Factor[-aaa/q+aaaaa]===0&& Factor[b*bb-q*a]===0); (* 3.4.8, reversed *) T8708:=(Hyp`q`ph[{b_,bb_,bbb_,a_,c_,d_,e_,x_}, {bbbb_,bbbbb_,aa_,cc_,dd_,ee_,xx_},q_,z_]:> Hyp`q`pqinf[{b*q,(b^2*q)/a^4},{(b^2*q)/a^2,b/a^2},q]* Hyp`q`ph[{a^2/q,a*q^(1/2),-(a*q^(1/2)),(a^2*x)/(b*q)}, {a/q^(1/2),-(a/q^(1/2)),(b*q)/x},q,(b^2*q)/(a^4*x)]/; Factor[bb/q+bbbbb]===Factor[bbbb+bbbbb]===Factor[b^(1/2)+bbbbb]=== Factor[-bbb/q+bbbbb]===0&& Factor[x*xx-q*b]===Factor[a*aa-q*b]===Factor[d*dd-q*b]=== Factor[e*ee-q*b]===Factor[c*cc-q*b]===0&& Factor[a+c]===Factor[d+e]===Factor[a^2*q-d^2]=== Factor[z-(b^2*q)/(a^4*x)]===0); (* 3.5.2 *) T3266:=(Hyp`q`ph[{a_,x_,y_},{d_,e_},q_,b_]:> Hyp`q`pqinf[{b/q^(1/2)},{(a*b)/q^(1/2)},q]* Hyp`q`pqinf[{a^(1/2),-((a^(1/2)*b)/q^(1/2))},{-1,b/q^(1/2)},q^(1/2)]* Hyp`q`ph[{-a^(1/2),-((b^(1/2)*x^(1/2))/q^(1/4)),(b^(1/2)*x^(1/2))/q^(1/4), -((b^(1/2)*y^(1/2))/q^(1/4)),(b^(1/2)*y^(1/2))/q^(1/4)}, {-q^(1/2),-((a^(1/2)*b)/q^(1/2)),-((b^(1/2)*x^(1/2)*y^(1/2))/q^(1/4)), (b^(1/2)*x^(1/2)*y^(1/2))/q^(1/4)},q^(1/2),q^(1/2)]+ Hyp`q`pqinf[{b/q^(1/2)},{(a*b)/q^(1/2)},q]* Hyp`q`pqinf[{-a^(1/2),(a^(1/2)*b)/q^(1/2)},{-1,b/q^(1/2)},q^(1/2)]* Hyp`q`ph[{a^(1/2),(b^(1/2)*x^(1/2))/q^(1/4),-((b^(1/2)*x^(1/2))/q^(1/4)), (b^(1/2)*y^(1/2))/q^(1/4),-((b^(1/2)*y^(1/2))/q^(1/4))}, {-q^(1/2),(a^(1/2)*b)/q^(1/2),(b^(1/2)*x^(1/2)*y^(1/2))/q^(1/4), -((b^(1/2)*x^(1/2)*y^(1/2))/q^(1/4))},q^(1/2),q^(1/2)]/; Factor[d-(a*b)/q^(1/2)]===Factor[e-(b*x*y)/q^(1/2)]===0); (* 3.5.2,reversed *) T5464:=(Hyp`q`ph[{a_,x_,xx_,y_,yy_},{c_,b_,d_,dd_},q_,q_]:> Hyp`q`pqinf[{a*b},{b/a},q^2]*Hyp`q`pqinf[{-1,b/a},{-a,b},q]* Hyp`q`ph[{a^2,(a*x^2)/b,(a*y^2)/b},{a*b,(a*x^2*y^2)/b},q^2,(b*q)/a]- Hyp`q`pqinf[{a,-b},{-a,b},q]*Hyp`q`ph[{-a,-x,x,-y,y}, {-q,-b,-((a^(1/2)*x*y)/b^(1/2)),(a^(1/2)*x*y)/b^(1/2)},q,q]/; Factor[x+xx]===Factor[y+yy]===Factor[c+q]=== Factor[d-(a^(1/2)*x*y)/b^(1/2)]===Factor[d+dd]===0); (* 3.5.4 *) T2111:=(Hyp`q`ph[{a_,b_},{c_},q_,x_]:>Hyp`q`pqinf[{(a^(1/2)*q^(1/2))/b,(b*x)/q^(1/2)}, {(a*q^(1/2))/b,(a^(1/2)*b*x)/q^(1/2)},q^(1/2)]* Hyp`q`pqinf[{(a*b*x)/q^(1/2),a*x},{(b*x)/q^(1/2),x},q]* Hyp`q`ph[{(a^(1/2)*b*x)/q,a^(1/4)*b^(1/2)*x^(1/2),-(a^(1/4)*b^(1/2)*x^(1/2)), a^(1/2),(b*x^(1/2))/q^(1/2),-((b*x^(1/2))/q^(1/2)), (b^(1/2)*x^(1/2))/q^(1/4),-((b^(1/2)*x^(1/2))/q^(1/4))}, {(a^(1/4)*b^(1/2)*x^(1/2))/q^(1/2),-((a^(1/4)*b^(1/2)*x^(1/2))/q^(1/2)), (b*x)/q^(1/2),a^(1/2)*x^(1/2),-(a^(1/2)*x^(1/2)), (a^(1/2)*b^(1/2)*x^(1/2))/q^(1/4),-((a^(1/2)*b^(1/2)*x^(1/2))/q^(1/4))}\ ,q^(1/2),(a^(1/2)*q^(1/2))/b]/; Factor[c-a*q/b]===0); (* 3.5.4,reversed *) T8709:=(Hyp`q`ph[{b_,bb_,bbb_,x_,y_,d_,e_,a_}, {bbbb_,bbbbb_,xx_,yy_,dd_,ee_,aa_},q_,z_]:> Hyp`q`pqinf[{(b*q)/a,(b^2*q^2)/(a^2*x^2)},{a*b*q,(b^2*q^2)/x^2},q^2]* Hyp`q`pqinf[{(a*b*q)/x^2,b*q},{(b*q)/x^2,(b*q)/a},q]* Hyp`q`ph[{a^2,(a*x^2)/b},{(a*b*q^2)/x^2},q^2,(b^2*q^2)/(a^2*x^2)]/; Factor[bb/q+bbbbb]===Factor[bbbb+bbbbb]===Factor[b^(1/2)+bbbbb]=== Factor[-bbb/q+bbbbb]===0&& Factor[x*xx-q*b]===Factor[a*aa-q*b]===Factor[d*dd-q*b]=== Factor[e*ee-q*b]===Factor[y*yy-q*b]===0&& Factor[x+y]===Factor[d+e]===Factor[d^2-(b*q)/a]=== Factor[z-(b*q)/x^2]===0); (* 3.5.7 *) T10962:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,f_,d_,g_,e_,h_}, {aaaa_,aaaaa_,bb_,cc_,ff_,dd_,gg_,ee_,hh_},q_,z_]:> Hyp`q`pqinf[{a*q^(1/2),(a*q^(1/2))/(c*d),(a*q^(1/2))/(c*e), (a*q^(1/2))/(d*e)},{(a*q^(1/2))/c,(a*q^(1/2))/d,(a*q^(1/2))/e, (a*q^(1/2))/(c*d*e)},q^(1/2)]* Hyp`q`ph[{(a^(1/2)*q^(1/4))/b^(1/2),-((a^(1/2)*q^(1/4))/b^(1/2)),c,d,e}, {a^(1/2)*q^(1/4),-(a^(1/2)*q^(1/4)),(a*q^(1/2))/b,(c*d*e)/a}, q^(1/2),q^(1/2)]+Hyp`q`pqinf[{a*q,(a^3*q^(3/2))/(c^2*d^2*e^2)}, {(a*q)/b,(a^3*q^(3/2))/(b*c^2*d^2*e^2)},q]* Hyp`q`pqinf[{c,d,e,(a^2*q)/(b*c*d*e)}, {(a*q^(1/2))/c,(a*q^(1/2))/d,(a*q^(1/2))/e,(c*d*e)/(a*q^(1/2))}, q^(1/2)]*Hyp`q`ph[{(a^(3/2)*q^(3/4))/(b^(1/2)*c*d*e), -((a^(3/2)*q^(3/4))/(b^(1/2)*c*d*e)),(a*q^(1/2))/(c*d), (a*q^(1/2))/(c*e),(a*q^(1/2))/(d*e)}, {(a^(3/2)*q^(3/4))/(c*d*e),-((a^(3/2)*q^(3/4))/(c*d*e)), (a^2*q)/(b*c*d*e),(a*q)/(c*d*e)},q^(1/2),q^(1/2)]/; 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[f-c*q^(1/2)]===Factor[g-d*q^(1/2)]===Factor[h-e*q^(1/2)]=== Factor[z-(a^3*q^(3/2))/(b*c^2*d^2*e^2)]===0); (* 3.5.7,reversed *) T5465:=(Hyp`q`ph[{a_,aa_,c_,d_,e_},{b_,bb_,x_,y_},q_,q_]:> -(Hyp`q`pqinf[{b^2*q,b^6/(c^2*d^2*e^2)},{a^2*q,(a^2*b^4)/(c^2*d^2*e^2)},q^2]* Hyp`q`pqinf[{c,d,e,(a^2*b^2)/(c*d*e),b^2/(c*d*e)}, {(c*d*e)/b^2,b^2,b^2/(c*d),b^2/(c*e),b^2/(d*e)},q]* Hyp`q`ph[{(a*b^2)/(c*d*e),-((a*b^2)/(c*d*e)),b^2/(c*d),b^2/(c*e), b^2/(d*e)},{b^3/(c*d*e),-(b^3/(c*d*e)),(a^2*b^2)/(c*d*e), (b^2*q)/(c*d*e)},q,q])+ Hyp`q`pqinf[{b^2/c,b^2/d,b^2/e,b^2/(c*d*e)}, {b^2,b^2/(c*d),b^2/(c*e),b^2/(d*e)},q]* Hyp`q`ph[{b^2/q,b*q^(3/2),-(b*q^(3/2)),b^2/a^2,c,c*q,d,d*q,e,e*q}, {b/q^(1/2),-(b/q^(1/2)),a^2*q,(b^2*q)/c,b^2/c,(b^2*q)/d,b^2/d, (b^2*q)/e,b^2/e},q^2,(a^2*b^4)/(c^2*d^2*e^2)]/; Factor[a+aa]===Factor[b+bb]===Factor[x-a^2]=== Factor[y-(c*d*e*q)/b^2]===0); (* 3.5.10 *) T8710:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,f_,d_,g_}, {aaaa_,aaaaa_,bb_,cc_,ff_,dd_,gg_},q_,z_]:> Hyp`q`pqinf[{a*q^(1/2),(a*q^(1/2))/(b*c),(a*q^(1/2))/(c*d), -((a*q^(1/2))/(c*d)),(a*q^(1/2))/(b^(1/2)*d), -((a*q^(1/2))/(b^(1/2)*d))}, {(a*q^(1/2))/b,(a*q^(1/2))/c,(a*q^(1/2))/d,-((a*q^(1/2))/d), (a*q^(1/2))/(b^(1/2)*c*d),-((a*q^(1/2))/(b^(1/2)*c*d))},q^(1/2)]* Hyp`q`ph[{-(a/d),(I*a^(1/2)*q^(1/2))/d^(1/2),(-I*a^(1/2)*q^(1/2))/d^(1/2),c, b^(1/2),-b^(1/2),(a^(1/2)*q^(1/4))/d,-((a^(1/2)*q^(1/4))/d)}, {(I*a^(1/2))/d^(1/2),(-I*a^(1/2))/d^(1/2),-((a*q^(1/2))/(c*d)), -((a*q^(1/2))/(b^(1/2)*d)),(a*q^(1/2))/(b^(1/2)*d),-(a^(1/2)*q^(1/4)), a^(1/2)*q^(1/4)},q^(1/2),(a*q^(1/2))/(b*c)]/; 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[f*ff-q*a]===Factor[g*gg-q*a]===0&& Factor[f-c*q^(1/2)]===Factor[g-d*q^(1/2)]=== Factor[z-(a^2*q)/(b*c^2*d^2)]===0); (* 3.5.10, reversed *) T8711:=(Hyp`q`ph[{a_,aa_,aaa_,b_,e_,d_,f_,c_}, {aaaa_,aaaaa_,bb_,ee_,dd_,ff_,cc_},q_, z_]:>Hyp`q`pqinf[{(a^2*q^2)/(b^2*d^2),(a^2*q^2)/(c*d^2), -(a*q),a*q,-((a*q)/(b*c)),(a*q)/(b*c)}, {(a^2*q^2)/d^2,(a^2*q^2)/(b^2*c*d^2),-((a*q)/c),(a*q)/c,-((a*q)/b), (a*q)/b},q]*Hyp`q`ph[{(a^2*q)/d^2,-((a*q^(5/2))/d),(a*q^(5/2))/d,b^2,c, c*q,-((a*q)/d^2),-((a*q^2)/d^2)}, {-((a*q^(1/2))/d),(a*q^(1/2))/d,(a^2*q^3)/(b^2*d^2),(a^2*q^3)/(c*d^2), (a^2*q^2)/(c*d^2),-(a*q^2),-(a*q)},q^2,(a^2*q^2)/(b^2*c^2)]/; 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[b+e]===Factor[d+f]=== Factor[z-(a^2*q^2)/(b^2*c*d^2)]===0); (* 3.10.4 *) T10904:=(Hyp`q`ph[{a_,aa_,aaa_,b_,x_,u_,y_,v_,c_,d_}, {aaaa_,aaaaa_,bb_,xx_,uu_,yy_,vv_,cc_,dd_},q_,z_]:> Hyp`q`ph[{d^2,x^2,y^2,-((a*q)/b),-((a*q^2)/b)}, {(x^2*y^2*d^2)/(a^2),(a^2*q^2)/b^2,-(a*q),-(a*q^2)},q^2,q^2]* Hyp`q`pq[{a^2*q^2,(a^2*q^2)/(x^2*y^2)},{(a^2*q^2)/x^2,(a^2*q^2)/y^2}, -Log[q,simplify[d]],q^2]/; 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[x*xx-q*a]===Factor[y*yy-q*a]===Factor[u*uu-q*a]=== Factor[v*vv-q*a]===0&& Factor[x+u]===Factor[y+v]===Factor[c+d]=== Factor[z+((a^3*q^(3))/(b*x^2*y^2*d^2))]===0&& Hyp`q`Private`IntegerTest[d,q]); (* 3.10.4,reversed *) T5403:=(Hyp`q`ph[{x_,y_,a_,c_,d_},{e_,b_,f_,g_},q_, q_]:>Hyp`q`ph[{-(b/q^(1/2)),I*b^(1/2)*q^(1/4),-I*b^(1/2)*q^(1/4),b/a, x^(1/2),-x^(1/2),y^(1/2),-y^(1/2),-d^(1/2),d^(1/2)}, {(I*b^(1/2))/q^(1/4),(-I*b^(1/2))/q^(1/4),-a,-(b/x^(1/2)),b/x^(1/2), -(b/y^(1/2)),b/y^(1/2),b/d^(1/2),-(b/d^(1/2))},q^(1/2), (a*b^2)/(x*y*d)]*Hyp`q`pq[{b^2/x,b^2/y},{b^2,b^2/(x*y)},-Log[q,simplify[d]],q]/; Factor[c-a*q^(1/2)]===Factor[e-a^2]===Factor[f-b*q^(1/2)]=== Factor[g-(q*d*x*y)/b^2]===0&& Hyp`q`Private`IntegerTest[d,q]); T5404:=(Hyp`q`ph[{a_,e_,ee_,dd_,d_}, {b_,c_,y_,z_},q_,q_]:> Hyp`q`pqinf[{q/z},{q*d^2/z},q]* Hyp`q`ph[{d^2,q*d^2/b,q*d^2/c},{b,c},q,(b*c)/(z*d^2)]/; Factor[a-b*c*q^(-1)/d^2]===Factor[y-q*d^2/z]=== Factor[d+dd]===Factor[e+ee]===Factor[e^2-q*d^2]===0&& Hyp`q`Private`IntegerTest[d^2,q]); T5405:=(Hyp`q`ph[{a_,b_,c_,z_,y_}, {d_,e_,f_,g_},q_,q_]:> Hyp`q`ph[{a^(1/2),b^(1/2),z,(a*b)/z}, {a^(1/2)*b^(1/2)*q^(1/2),-(a^(1/2)*b^(1/2)*q^(1/2)), -(a^(1/2)*b^(1/2))},q,q]^2/; Factor[c-a^(1/2)*b^(1/2)]===Factor[y-(a*b)/z]===Factor[d+e]=== Factor[g-a*b]===Factor[d^2-a*b*q]===Factor[f+(a^(1/2)*b^(1/2))]===0&& (Hyp`q`Private`IntegerTest[Sqrt[a],q]||Hyp`q`Private`IntegerTest[Sqrt[b],q]||Hyp`q`Private`IntegerTest[z,q]||Hyp`q`Private`IntegerTest[y,q])); (* Ex3.1 *) T3211:=(Hyp`q`ph[{a_,b_,z_},{c_,d_},q_,q_]:> Hyp`q`ph[{a,b,z^2},{a*b*q,0},q^2,q^2]/; Factor[c+d]===Factor[c^2-a*b*q]===0&& (Hyp`q`Private`IntegerTest[Sqrt[a],q]||Hyp`q`Private`IntegerTest[Sqrt[b],q]||Hyp`q`Private`IntegerTest[z,q])); (* Ex3.1,reversed *) T3212:={(Hyp`q`ph[{a_,b_,z_},{c_,0},q_,q_]:> Hyp`q`ph[{a,b,z^(1/2)},{a^(1/2)*b^(1/2)*q^(1/4),-(a^(1/2)*b^(1/2)*q^(1/4))}, q^(1/2),q^(1/2)]/; Factor[c-a*b*q^(1/2)]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[z,q])), (Hyp`q`ph[{a_,b_,z_},{0,c_},q_,q_]:> Hyp`q`ph[{a,b,z^(1/2)},{a^(1/2)*b^(1/2)*q^(1/4),-(a^(1/2)*b^(1/2)*q^(1/4))}, q^(1/2),q^(1/2)]/; Factor[c-a*b*q^(1/2)]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[z,q]))}; (* Ex3.2(i) *) T3213:=(Hyp`q`ph[{a_,b_,bb_},{c_,d_},q_,z_]:> Hyp`q`pqinf[{-z},{-a*z},q]*Hyp`q`ph[{a,a*q},{b^2*q},q^2,z^2]/; Factor[b+bb]===Factor[c-b^2]===Factor[d+a*z]===0); (* Ex3.2(i),reversed *) T2112:={(Hyp`q`ph[{a_,aa_},{b_},q_,z_]:> Hyp`q`pqinf[{a*z^(1/2)},{z^(1/2)},q^(1/2)]*Hyp`q`ph[{a,(b/q^(1/2))^(1/2),-(b/q^(1/2))^(1/2)},{b/q^(1/2),a*z^(1/2)},q^(1/2),-z^(1/2)]/; Factor[aa-a*q^(1/2)]===0), (Hyp`q`ph[{aa_,a_},{b_},q_,z_]:> Hyp`q`pqinf[{a*z^(1/2)},{z^(1/2)},q^(1/2)]*Hyp`q`ph[{a,(b/q^(1/2))^(1/2),-(b/q^(1/2))^(1/2)},{b/q^(1/2),a*z^(1/2)},q^(1/2),-z^(1/2)]/; Factor[aa-a*q^(1/2)]===0)}; (* Ex3.2(ii) *) T3214:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> (Hyp`q`pqinf[a*z^2,q^2]*Hyp`q`ph[{a,b^2/a},{b^2*q,a*z^2},q^2,a*q*z^2])/ (Hyp`q`pqinf[z,q]*Hyp`q`pqinf[-(a*z),q])/; Factor[b+c]===Factor[d-b^2]===Factor[e+(a*z)]===0); (* Ex3.2(ii),reversed *) T2202:={(Hyp`q`ph[{a_,b_},{c_,d_},q_,z_]:> (Hyp`q`pqinf[z^(1/2)/(a^(1/2)*q^(1/4)),q^(1/2)]* Hyp`q`pqinf[-((a*z)^(1/2)/q^(1/4)),q^(1/2)]* Hyp`q`ph[{a,(a*b)^(1/2),-(a*b)^(1/2)},{a*b,-((a*z)^(1/2)/q^(1/4))}, q^(1/2),z^(1/2)/(a^(1/2)*q^(1/4))])/Hyp`q`pqinf[z/q^(1/2),q]/; Factor[c-a*b*q^(1/2)]===Factor[d-z/q^(1/2)]===0), (Hyp`q`ph[{a_,b_},{d_,c_},q_,z_]:> (Hyp`q`pqinf[z^(1/2)/(a^(1/2)*q^(1/4)),q^(1/2)]* Hyp`q`pqinf[-((a*z)^(1/2)/q^(1/4)),q^(1/2)]* Hyp`q`ph[{a,(a*b)^(1/2),-(a*b)^(1/2)},{a*b,-((a*z)^(1/2)/q^(1/4))}, q^(1/2),z^(1/2)/(a^(1/2)*q^(1/4))])/Hyp`q`pqinf[z/q^(1/2),q]/; Factor[c-a*b*q^(1/2)]===Factor[d-z/q^(1/2)]===0)}; (* Ex3.3 *) T3215:={(Hyp`q`ph[{a_,b_,z_},{c_,d_},q_,q_]:> Hyp`q`pqinf[{-1,-((q*z)/c)},{-(q/c),-z},q]* Hyp`q`ph[{c/a,(a*c)/q,z^2},{c^2,0},q^2,q^2]/; Factor[b*a-q]===Factor[d+q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[z,q])&& (Hyp`q`Private`IntegerTest[c/a,q^2]||Hyp`q`Private`IntegerTest[c/b,q^2]||Hyp`q`Private`IntegerTest[z,q])), (Hyp`q`ph[{a_,b_,z_},{d_,c_},q_,q_]:> Hyp`q`pqinf[{-1,-((q*z)/c)},{-(q/c),-z},q]* Hyp`q`ph[{c/a,(a*c)/q,z^2},{c^2,0},q^2,q^2]/; Factor[b*a-q]===Factor[d+q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[z,q])&& (Hyp`q`Private`IntegerTest[d/a,q^2]||Hyp`q`Private`IntegerTest[d/b,q^2]||Hyp`q`Private`IntegerTest[z,q]))}; (* Ex3.3,reversed *) T3216:={(Hyp`q`ph[{c_,b_,z_},{a_,0},q_,q_]:> Hyp`q`pqinf[{-(q^(1/2)/a^(1/2)),-z^(1/2)},{-1,-((q*z)^(1/2)/a^(1/2))}, q^(1/2)]*Hyp`q`ph[{a^(1/2)/c,(c*q^(1/2))/a^(1/2),z^(1/2)}, {a^(1/2),-q^(1/2)},q^(1/2),q^(1/2)]/; Factor[b-a/(c*q^(1/2))]===0&& (Hyp`q`Private`IntegerTest[c,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[z,q])&& (Hyp`q`Private`IntegerTest[a/c^2,q]||Hyp`q`Private`IntegerTest[c^2*q/a,q^2]||Hyp`q`Private`IntegerTest[z,q])), (Hyp`q`ph[{c_,b_,z_},{0,a_},q_,q_]:> Hyp`q`pqinf[{-(q^(1/2)/a^(1/2)),-z^(1/2)},{-1,-((q*z)^(1/2)/a^(1/2))}, q^(1/2)]*Hyp`q`ph[{a^(1/2)/c,(c*q^(1/2))/a^(1/2),z^(1/2)}, {a^(1/2),-q^(1/2)},q^(1/2),q^(1/2)]/; Factor[b-a/(c*q^(1/2))]===0&& (Hyp`q`Private`IntegerTest[c,q]||Hyp`q`Private`IntegerTest[b,q]||Hyp`q`Private`IntegerTest[z,q])&& (Hyp`q`Private`IntegerTest[a/c^2,q]||Hyp`q`Private`IntegerTest[c^2*q/a,q^2]||Hyp`q`Private`IntegerTest[z,q]))}; T3217:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`ph[{(d*e)/(a*q),(d^(1/2)*e^(1/2)*q^(1/2))/a^(1/2), -((d^(1/2)*e^(1/2)*q^(1/2))/a^(1/2)),e/a,d/a,b,c}, {(d^(1/2)*e^(1/2))/(a^(1/2)*q^(1/2)), -((d^(1/2)*e^(1/2))/(a^(1/2)*q^(1/2))),d,e,(d*e)/(a*b), (d*e)/(a*c),0},q,(d*e)/(b*c)]* Hyp`q`pqinf[{(d*e)/(a*b),(d*e)/(a*c)},{(d*e)/a,(d*e)/(a*b*c)},q]/; Factor[z-(d*e)/(a*b*c)]===0); T7701:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,e_}, {aaaa_,aaaaa_,bb_,cc_,dd_,ee_,0},q_,z_]:> Hyp`q`ph[{(a*q)/(b*c),d,e},{(a*q)/b,(a*q)/c},q, (a*q)/(d*e)]*Hyp`q`pqinf[{a*q,(a*q)/(d*e)},{(a*q)/d,(a*q)/e},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]===0&& Factor[z-(a^2*q^2)/(b*c*d*e)]===0); (* Ex3.4 *) T4312:=(Hyp`q`ph[{a_,aa_,cc_,c_},{d_,dd_,b_},q_,q_]:> a^(-Log[q,simplify[c^2]])*Hyp`q`ph[{a,b^(1/2)/q^(1/4),-(b^(1/2)/q^(1/4)),c}, {(a*cc)/d,b/q^(1/2)},q^(1/2),-(q^(1/2)/d)]* Hyp`q`pq[{d/a},{d},-Log[q,simplify[c^2]],q^(1/2)]/; Factor[aa-a*q^(1/2)]===Factor[dd-d*q^(1/2)]=== Factor[cc-c*q^(1/2)]===0&& Hyp`q`Private`IntegerTest[c^2,q]); (* Ex3.4,reversed *) T4201:=(Hyp`q`ph[{a_,b_,c_,e_},{f_,g_},q_,d_]:> (Hyp`q`ph[{a,a*q,e*q,e},{-(q/d),-(q^2/d),b^2*q},q^2,q^2]* Hyp`q`pq[{-(q/d)},{-(q/(a*d))},-Log[q,simplify[e]],q])/a^(-Log[q,simplify[e]])/; Factor[b+c]===Factor[f+(a*d*e)]===Factor[g-b^2]===0&& Hyp`q`Private`IntegerTest[e,q]); (* Ex8.15 *) T4313:={(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,z_]:> (Hyp`q`pqinf[{a/d,b q/d,c q/d,a b c/d},{q/d,a b/d,a c/d,b c q/d},q]* Hyp`q`W[b c/d,{Sqrt[b c q/a/d],-Sqrt[b c q/a/d],q Sqrt[b c/a/d], -q Sqrt[b c/a/d],a b/d,a c/d,a,b,c},q,q/a])/; Factor[a^2*z-q^2]=== Factor[e*a-b*q]===Factor[f*a-c*q]===Factor[g*a-d*q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q])), (Hyp`q`ph[{a_,b_,c_,d_},{e_,g_,f_},q_,z_]:> (Hyp`q`pqinf[{a/d,b q/d,c q/d,a b c/d},{q/d,a b/d,a c/d,b c q/d},q]* Hyp`q`W[b c/d,{Sqrt[b c q/a/d],-Sqrt[b c q/a/d],q Sqrt[b c/a/d], -q Sqrt[b c/a/d],a b/d,a c/d,a,b,c},q,q/a])/; Factor[a^2*z-q^2]=== Factor[e*a-b*q]===Factor[f*a-c*q]===Factor[g*a-d*q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q])), (Hyp`q`ph[{a_,b_,c_,d_},{f_,e_,g_},q_,z_]:> (Hyp`q`pqinf[{a/d,b q/d,c q/d,a b c/d},{q/d,a b/d,a c/d,b c q/d},q]* Hyp`q`W[b c/d,{Sqrt[b c q/a/d],-Sqrt[b c q/a/d],q Sqrt[b c/a/d], -q Sqrt[b c/a/d],a b/d,a c/d,a,b,c},q,q/a])/; Factor[a^2*z-q^2]=== Factor[e*a-b*q]===Factor[f*a-c*q]===Factor[g*a-d*q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q])), (Hyp`q`ph[{a_,b_,c_,d_},{f_,g_,e_},q_,z_]:> (Hyp`q`pqinf[{a/d,b q/d,c q/d,a b c/d},{q/d,a b/d,a c/d,b c q/d},q]* Hyp`q`W[b c/d,{Sqrt[b c q/a/d],-Sqrt[b c q/a/d],q Sqrt[b c/a/d], -q Sqrt[b c/a/d],a b/d,a c/d,a,b,c},q,q/a])/; Factor[a^2*z-q^2]=== Factor[e*a-b*q]===Factor[f*a-c*q]===Factor[g*a-d*q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q])), (Hyp`q`ph[{a_,b_,c_,d_},{g_,f_,e_},q_,z_]:> (Hyp`q`pqinf[{a/d,b q/d,c q/d,a b c/d},{q/d,a b/d,a c/d,b c q/d},q]* Hyp`q`W[b c/d,{Sqrt[b c q/a/d],-Sqrt[b c q/a/d],q Sqrt[b c/a/d], -q Sqrt[b c/a/d],a b/d,a c/d,a,b,c},q,q/a])/; Factor[a^2*z-q^2]=== Factor[e*a-b*q]===Factor[f*a-c*q]===Factor[g*a-d*q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q])), (Hyp`q`ph[{a_,b_,c_,d_},{g_,e_,f_},q_,z_]:> (Hyp`q`pqinf[{a/d,b q/d,c q/d,a b c/d},{q/d,a b/d,a c/d,b c q/d},q]* Hyp`q`W[b c/d,{Sqrt[b c q/a/d],-Sqrt[b c q/a/d],q Sqrt[b c/a/d], -q Sqrt[b c/a/d],a b/d,a c/d,a,b,c},q,q/a])/; Factor[a^2*z-q^2]=== Factor[e*a-b*q]===Factor[f*a-c*q]===Factor[g*a-d*q]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q]))}; (* Ex3.6 *) T3267:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,q_]:>Hyp`q`pqinf[{q/e,(a*b*q)/e,(a*c*q)/e,d/a}, {d,(a*q)/e,(b*q)/e,(c*q)/e},q]* Hyp`q`ph[{a,(a*q)/e,(a*b*c*q)/(d*e)},{(a*b*q)/e,(a*c*q)/e},q,d/a]- Hyp`q`pqinf[{q/e,a,b,c,(d*q)/e},{e/q,(a*q)/e,(b*q)/e,(c*q)/e,d},q]* Hyp`q`ph[{(a*q)/e,(b*q)/e,(c*q)/e},{q^2/e,(d*q)/e},q,q]); (* Ex3.6,reversed *) T3268:=(Hyp`q`ph[{a_,b_,c_},{d_,e_},q_,z_]:> Hyp`q`pqinf[{(d*e)/(b*c),b,d/a,e/a},{b/a,d,e,(d*e)/(a*b*c)},q]* Hyp`q`ph[{a,d/b,e/b},{(d*e)/(b*c),(a*q)/b},q,q]+ Hyp`q`pqinf[{a,d/b,e/b,(d*e)/(a*c)},{d,e,(d*e)/(a*b*c),a/b},q]* Hyp`q`ph[{b,d/a,e/a},{(b*q)/a,(d*e)/(a*c)},q,q]/; Factor[z-(d*e)/(a*b*c)]===0); (* Ex3.8 *) T2163:=(Hyp`q`ph[{a_,b_},{c_},q_,x_]:>Hyp`q`pqinf[{b,c/a,a*x},{b/a,c,x},q]* Hyp`q`ph[{a,c/b,0},{(a*q)/b,a*x},q,q]+ Hyp`q`pqinf[{a,c/b,b*x},{a/b,c,x},q]*Hyp`q`ph[{b,c/a,0},{(b*q)/a,b*x},q,q]); (* Ex3.8,reversed *) T3269:={(Hyp`q`ph[{a_,b_,0},{c_,x_},q_,q_]:>Hyp`q`pqinf[{q/c,(a*b*q)/c,x/a}, {(a*q)/c,(b*q)/c,x},q]*Hyp`q`ph[{a,(a*q)/c},{(a*b*q)/c},q,x/a]- Hyp`q`pqinf[{a,b,(q*x)/c,q/c},{c/q,(a*q)/c,(b*q)/c,x},q]* Hyp`q`ph[{(a*q)/c,(b*q)/c,0},{q^2/c,(q*x)/c},q,q]), (Hyp`q`ph[{a_,0,b_},{c_,x_},q_,q_]:>Hyp`q`pqinf[{q/c,(a*b*q)/c,x/a}, {(a*q)/c,(b*q)/c,x},q]*Hyp`q`ph[{a,(a*q)/c},{(a*b*q)/c},q,x/a]- Hyp`q`pqinf[{a,b,(q*x)/c,q/c},{c/q,(a*q)/c,(b*q)/c,x},q]* Hyp`q`ph[{(a*q)/c,(b*q)/c,0},{q^2/c,(q*x)/c},q,q]), (Hyp`q`ph[{0,a_,b_},{c_,x_},q_,q_]:>Hyp`q`pqinf[{q/c,(a*b*q)/c,x/a}, {(a*q)/c,(b*q)/c,x},q]*Hyp`q`ph[{a,(a*q)/c},{(a*b*q)/c},q,x/a]- Hyp`q`pqinf[{a,b,(q*x)/c,q/c},{c/q,(a*q)/c,(b*q)/c,x},q]* Hyp`q`ph[{(a*q)/c,(b*q)/c,0},{q^2/c,(q*x)/c},q,q])}; (* Ex3.16 *) T4361:=(Hyp`q`ph[{a_,aa_,b_,c_},{aaa_,bb_,cc_},q_,x_]:> (1-(b*c*x)/(a^(1/2)*q))*Hyp`q`pqinf[{b*c*x},{(b*c*x)/(a*q)},q]* Hyp`q`ph[{a^(1/2),-(a^(1/2)*q),(a*q)^(1/2),-(a*q)^(1/2),(a*q)/(b*c)}, {(a*q)/b,(a*q)/c,(a*q^2)/(b*c*x),b*c*x},q,q]+ (1-a^(1/2))*Hyp`q`pqinf[{a*q,(a*q)/(b*c),c*x,b*x}, {(a*q)/b,(a*q)/c,x,(a*q)/(b*c*x)},q]* Hyp`q`ph[{(b*c*x)/(a^(1/2)*q),-((b*c*x)/a^(1/2)),(b*c*x)/(a*q)^(1/2), -((b*c*x)/(a*q)^(1/2)),x},{c*x,b*x,(b*c*x)/a,(b^2*c^2*x^2)/(a*q)}, q,q]/; Factor[aa/q-aaa]===Factor[a^(1/2)+aaa]=== Factor[b*bb-q*a]===Factor[c*cc-q*a]===0); T4362:=(Hyp`q`ph[{a_,b_,c_,d_},{e_,f_,g_},q_,q_] :> -(Hyp`q`pqinf[{(e*f)/(a*b*c*d),a,b,c,d,(e^2*f)/(a*b*c*d), (e*f^2)/(a*b*c*d)},{(e*f)/(a*b*c),(e*f)/(a*b*d),(e*f)/(a*c*d),e, f,(e*f)/(b*c*d),(a*b*c*d)/(e*f)},q]* Hyp`q`ph[{(e*f)/(a*b*c),(e*f)/(a*b*d),(e*f)/(a*c*d),(e*f)/(b*c*d)}, {(e^2*f)/(a*b*c*d),(e*f^2)/(a*b*c*d),(e*f*q)/(a*b*c*d)},q,q])+ Hyp`q`pqinf[{(e*f)/(a*b),(e*f)/(a*c),(e*f)/(a*d),(e*f)/(a*b*c*d)}, {(e*f)/a,(e*f)/(a*b*c),(e*f)/(a*b*d),(e*f)/(a*c*d)},q]* Hyp`q`ph[{(e*f)/(a*q),(e^(1/2)*f^(1/2)*q^(1/2))/a^(1/2), -((e^(1/2)*f^(1/2)*q^(1/2))/a^(1/2)),f/a,e/a,b,c,d}, {(e^(1/2)*f^(1/2))/(a^(1/2)*q^(1/2)), -((e^(1/2)*f^(1/2))/(a^(1/2)*q^(1/2))),e,f,(e*f)/(a*b),(e*f)/(a*c), (e*f)/(a*d)},q,(e*f)/(b*c*d)]/; Factor[g-(a*b*c*d*q)/(e*f)]===0); (* Ex3.16,reversed,first form *) T5466:=(Hyp`q`ph[{a_,d_,aa_,aaa_,e_}, {b_,c_,x_,y_},q_,q_]:> (Hyp`q`pqinf[{q/x},{(a^2*q^2)/x},q]* Hyp`q`ph[{a^2,-(a*q),(a^2*q)/b,(a^2*q)/c},{-a,b,c},q,(b*c)/(a^2*x)])/ (1-(a*q)/x)-((1-a)*Hyp`q`pqinf[{q/x,a^2*q,(b*c)/(a^2*q),(b*q)/x, (c*q)/x},{(a^2*q^2)/x,b,c,(b*c)/(a^2*x),x/q},q]* Hyp`q`ph[{(a*q)/x,-((a*q^2)/x),(a*q^(3/2))/x,-((a*q^(3/2))/x), (b*c)/(a^2*x)},{(b*q)/x,(c*q)/x,q^2/x,(a^2*q^3)/x^2},q,q])/ (1-(a*q)/x)/; Factor[d+a*q]===Factor[aa+aaa]===Factor[aa^2-a^2*q]=== Factor[e-(b*c)/(a^2*q)]===Factor[y-(a^2*q^2)/x]===0); (* Ex3.16,reversed,second form *) T5467:=(Hyp`q`ph[{a_,d_,aa_,aaa_,e_}, {b_,c_,x_,y_},q_,q_]:>(Hyp`q`pqinf[{(b*q)/x,(c*q)/x, (b*c*x)/(a^2*q^2),q/x},{(a^2*q^3)/x^2,(b*c)/(a^2*q),b,c},q]* Hyp`q`ph[{(a^2*q^2)/x^2,-((a*q^2)/x),(a^2*q^2)/(b*x),(a^2*q^2)/(c*x)}, {-((a*q)/x),(b*q)/x,(c*q)/x},q,(b*c*x)/(a^2*q^2)])/(1-(a*q)/x)- ((1-a)*Hyp`q`pqinf[{(a^2*q^2)/x,(b*q)/x,(c*q)/x,(b*c*x)/(a^2*q^2),q/x}, {x/q,(a^2*q^3)/x^2,(b*c)/(a^2*q),b,c},q]* Hyp`q`ph[{(a*q)/x,-((a*q^2)/x),(a*q^(3/2))/x,-((a*q^(3/2))/x), (b*c)/(a^2*q)},{(b*q)/x,(c*q)/x,q^2/x,(a^2*q^2)/x},q,q])/ (1-(a*q)/x)/; Factor[d+a*q]===Factor[aa+aaa]===Factor[aa^2-a^2*q]=== Factor[e-(b*c*x)/(a^2*q^2)]===Factor[y-a^2*q]===0); (* Ex3.21(iii) *) T10905:=(Hyp`q`ph[{a_,aa_,aaa_,b_,c_,d_,C_,D_,B_,AA_}, {aaaa_,aaaaa_,bb_,cc_,dd_,CC_,DD_, BB_,A_},q_,q_]:>Hyp`q`ph[{AA/(A),q*AA^(1/2)/A^(1/2), -(q*AA^(1/2)/A^(1/2)),B/A,C/A,A*AA/(B*C),c*AA/(a),AA/(b*c), b*AA/(a),AA},{AA^(1/2)/(A^(1/2)),-(AA^(1/2)/(A^(1/2))), q*AA/B,q*AA/C,(B*C*q)/A^2,AA/(c),(b*c*AA)/(a), AA/(b),AA/(a)},q,q]* Hyp`q`pq[{a*q,b*q,c*q,(a*q)/(b*c),q*AA/B,q*AA/C,(B*C*q)/A^2}, {q*AA/A,(B*q)/A,(C*q)/A,(A*q*AA)/(B*C),(a*q)/b,(a*q)/c, b*c*q},-Log[q,simplify[AA]],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[B*BB-A*AA]===Factor[C*CC-A*AA]===Factor[D*DD-A*AA]=== Factor[d-a/(b*c)]===Factor[D-A^2*AA/(B*C)]===Factor[BB-A*AA/(B)]=== Factor[CC-A*AA/(C)]===Factor[DD-(B*C)/A]===0&& Hyp`q`Private`IntegerTest[AA,q]); (* Rahman/Verma 7.7 *) T121105:=(Hyp`q`ph[{a_,aa_,aaa_,c_,cc_,d_,dd_,e_,ee_, f_,g_,h_}, {aaaa_,aaaaa_,ccc_,cccc_,ddd_,dddd_,eee_,eeee_,ff_,gg_,hh_},q_,q_]:> Hyp`q`ph[{a/h^(1/2),a^(1/2)*q^(1/2)/h^(1/4), -(a^(1/2)*q^(1/2)/h^(1/4)),c,d,e,a^(1/2)*q^(1/4)/h^(1/2), -(a^(1/2)*q^(1/4)/h^(1/2)),(a^2*q^(1/2))/(c*d*e*h^(1/2)),h^(1/2)}, {a^(1/2)/h^(1/4),-(a^(1/2)/h^(1/4)),a*q^(1/2)/(c*h^(1/2)), (a*q^(1/2))/(d*h^(1/2)),(a*q^(1/2))/(e*h^(1/2)),a^(1/2)*q^(1/4), -(a^(1/2)*q^(1/4)),(c*d*e)/a,a*q^(1/2)/h},q^(1/2),-q^(1/2)/h^(1/2)]* Hyp`q`pq[{a*q^(1/2),(a*q^(1/2))/(c*d),(a*q^(1/2))/(c*e),(a*q^(1/2))/(d*e)}, {(a*q^(1/2))/c,(a*q^(1/2))/d,(a*q^(1/2))/e,(a*q^(1/2))/(c*d*e)},-Log[q,simplify[h]], q^(1/2)]/; Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]=== Factor[-aaa/q+aaaaa]===0&& Factor[cc*cccc-q*a]===Factor[c*ccc-q*a]===Factor[d*ddd-q*a]=== Factor[e*eee-q*a]===Factor[f*ff-q*a]===Factor[g*gg-q*a]=== Factor[h*hh-q*a]===Factor[dd*dddd-q*a]===Factor[ee*eeee-q*a]===0&& Factor[cc-c*q^(1/2)]===Factor[dd-d*q^(1/2)]===Factor[ee-e*q^(1/2)]=== Factor[f-(a^2*q^(1/2))/(c*d*e*h^(1/2))]=== Factor[g-(a^2*q)/(c*d*e*h^(1/2))]===0&& Hyp`q`Private`IntegerTest[h,q]); (* Rahman/Verma 7.7,reversed *) T10906:=(Hyp`q`ph[{a_,aa_,aaa_,c_,d_,e_,f_, g_,h_,i_}, {aaaa_,aaaaa_,cc_,dd_,ee_,ff_,gg_,hh_,ii_},q_,z_]:> Hyp`q`ph[{a*i,a^(1/2)*q^(2)*i^(1/2),-(a^(1/2)*q^(2)*i^(1/2)),i^2,c,c*q, d,d*q,e,e*q,(a^2*q*i)/(c*d*e),(a^2*q^(2)*i)/(c*d*e)}, {a^(1/2)*i^(1/2),-(a^(1/2)*i^(1/2)),a*q^(2)/i,(a*q^(2)*i)/c, (a*q*i)/c,(a*q^(2)*i)/d,(a*q^(1)*i)/d,(a*q^(2)*i)/e, (a*q*i)/e,(c*d*e*q)/a,(c*d*e)/a},q^2,q^2]* Hyp`q`pq[{(a*q*i)/c,(a*q*i)/d,(a*q*i)/e, (a*q*i)/(c*d*e)},{a*q*i,(a*q*i)/(c*d), (a*q*i)/(c*e),(a*q*i)/(d*e)},-Log[q,simplify[i]],q]/; Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]=== Factor[-aaa/q+aaaaa]===0&& 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]===Factor[i*ii-q*a]===0&& Factor[f-a^(1/2)*q^(1/2)/i^(1/2)]===Factor[f+g]=== Factor[h-(a^2*q*i)/(c*d*e)]===Factor[z+q/i]===0&& Hyp`q`Private`IntegerTest[i,q]); (* 7.8 *) T121106:=(Hyp`q`ph[{a_,aa_,aaa_,e_,c_,cc_,d_,dd_, f_,g_,hh_,h_}, {aaaa_,aaaaa_,ee_,ccc_,cccc_,ddd_,dddd_,ff_,gg_,hhhh_,hhh_},q_,q_]:> Hyp`q`ph[{a/e^(1/2),(a*q)^(1/2)/e^(1/4),-((a*q)^(1/2)/e^(1/4)), (a^(1/2)*q^(1/4))/e^(1/2),-((a^(1/2)*q^(1/4))/e^(1/2)),c,d, e^(1/2),(a^2*q^(1/2))/(c*d*e^(1/2)*h),h}, {a^(1/2)/e^(1/4),-(a^(1/2)/e^(1/4)),a^(1/2)*q^(1/4), -(a^(1/2)*q^(1/4)),(a*q^(1/2))/(c*e^(1/2)),(a*q^(1/2))/(d*e^(1/2)), (a*q^(1/2))/e,(c*d*h)/(a),a*q^(1/2)/e^(1/2)/h},q^(1/2), -(q^(1/2)/e^(1/2))]*Hyp`q`pq[{a*q^(1/2),(a*q^(1/2))/(c*d), (a*q^(1/2))/(c*e^(1/2)),(a*q^(1/2))/(d*e^(1/2))}, {(a*q^(1/2))/c,(a*q^(1/2))/d,(a*q^(1/2))/e^(1/2), (a*q^(1/2))/(c*d*e^(1/2))},-Log[q,simplify[h^2]],q^(1/2)]/; Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]=== Factor[-aaa/q+aaaaa]===0&& Factor[cc*cccc-q*a]===Factor[c*ccc-q*a]===Factor[d*ddd-q*a]=== Factor[e*ee-q*a]===Factor[f*ff-q*a]===Factor[g*gg-q*a]=== Factor[h*hhh-q*a]===Factor[dd*dddd-q*a]===Factor[hh*hhhh-q*a]===0&& Factor[cc-c*q^(1/2)]===Factor[dd-d*q^(1/2)]===Factor[hh-h*q^(1/2)]=== Factor[f-(a^2*q^(1/2))/(c*d*e^(1/2)*h)]=== Factor[g-(a^2*q)/(c*d*e^(1/2)*h)]===0&& Hyp`q`Private`IntegerTest[h^2,q]); (* Ex.8.15 *) T121107:=(Hyp`q`ph[{d_,dd_,ddd_,e_,ee_,f_,ff_,g_, h_,a_,b_,c_}, {dddd_,ddddd_,eee_,eeee_,fff_,ffff_,gg_,hh_,aa_,bb_,cc_},q_,z_]:> Hyp`q`ph[{a,b,c,(b*c)/d},{(b*q)/a,(c*q)/a,(b*c*q)/(a*d)},q,q^2/a^2]* Hyp`q`pqinf[{(d*q)/(b*c),(a*d)/c,(a*d)/b,d*q},{(a*d)/(b*c),(d*q)/c,(d*q)/b, a*d},q]/; Factor[dd/q+ddddd]===Factor[dddd+ddddd]===Factor[d^(1/2)+ddddd]=== Factor[-ddd/q+ddddd]===0&& Factor[e*eee-q*d]===Factor[ee*eeee-q*d]===Factor[f*fff-q*d]=== Factor[ff*ffff-q*d]===Factor[g*gg-q*d]===Factor[h*hh-q*d]=== Factor[a*aa-q*d]===Factor[b*bb-q*d]===Factor[c*cc-q*d]===0&& Factor[e^2*a-(d*q)]===Factor[e+ee]=== Factor[f^2*a-q^2*d]===Factor[f+ff]=== Factor[g*c-a*d]===Factor[h*b-a*d]===0&& (Hyp`q`Private`IntegerTest[a,q]||Hyp`q`Private`IntegerTest[b,q]|| Hyp`q`Private`IntegerTest[c,q])); (* Rahman/Verma,7.8,reversed *) T10907:=(Hyp`q`ph[{a_,aa_,aaa_,f_, g_,c_,d_,e_,h_,i_}, {aaaa_,aaaaa_,ff_,gg_,cc_,dd_,ee_,hh_,ii_},q_,z_]:> Hyp`q`ph[{a*e,(a*e)^(1/2)*q^2,-((a*e)^(1/2)*q^2),e^2,c,c*q,d,d*q, (a^2*e*q)/(c*d*i),(a^2*e*q^(2))/(c*d*i),q*i,i}, {(a*e)^(1/2),-(a*e)^(1/2),(a*q^2)/e,(a*e*q^2)/c,(a*e*q)/c, (a*e*q^2)/d,(a*e*q)/d,(c*d*q*i)/a,(c*d*i)/(a), a*e*q/i,a*e*q^(2)/i},q^2,q^2]* Hyp`q`pq[{(a*e*q)/c,(a*e*q)/d,a*q,(a*q)/(c*d)}, {a*e*q,(a*e*q)/(c*d),(a*q)/c,(a*q)/d},-Log[q,simplify[i]],q]/; Factor[aa/q+aaaaa]===Factor[aaaa+aaaaa]===Factor[a^(1/2)+aaaaa]=== Factor[-aaa/q+aaaaa]===0&& 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]===Factor[i*ii-q*a]===0&& Factor[f-(a*q)^(1/2)/e^(1/2)]===Factor[f+g]=== Factor[h-(a^2*e*q)/(c*d*i)]===Factor[z+(q/e)]===0&& Hyp`q`Private`IntegerTest[i,q]); (* Ex2.25,T! *) T5468:=(Hyp`q`ph[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_}, q_,q_]:>-(Hyp`q`pqinf[{a,b,c,d,e,(a^2*q^3)/(b^2*c^2*d^2*e), (a^3*q^4)/(b^3*c^2*d^2*e),(a^3*q^4)/(b^2*c^3*d^2*e), (a^3*q^4)/(b^2*c^2*d^3*e)}, {(a*q)/b,(a*q)/c,(a*q)/d,(b^2*c^2*d^2*e)/(a^2*q^3), (a^3*q^3)/(b^2*c^2*d^2*e),(a^2*q^3)/(b*c^2*d^2*e), (a^2*q^3)/(b^2*c*d^2*e),(a^2*q^3)/(b^2*c^2*d*e), (a^2*q^3)/(b^2*c^2*d^2)},q]* Hyp`q`ph[{(a^2*q^3)/(b^2*c^2*d^2),(a^3*q^3)/(b^2*c^2*d^2*e), (a^2*q^3)/(b*c^2*d^2*e),(a^2*q^3)/(b^2*c*d^2*e), (a^2*q^3)/(b^2*c^2*d*e)}, {(a^2*q^4)/(b^2*c^2*d^2*e),(a^3*q^4)/(b^3*c^2*d^2*e), (a^3*q^4)/(b^2*c^3*d^2*e),(a^3*q^4)/(b^2*c^2*d^3*e)},q,q])+ Hyp`q`pqinf[{(a*q^2)/(b*c*d),(a^2*q^2)/(b*c*d*e),(a^3*q^3)/(b^2*c^2*d^2), (a^2*q^3)/(b^2*c^2*d^2*e)}, {(a^2*q^2)/(b*c*d),(a^3*q^3)/(b^2*c^2*d^2*e),(a^2*q^3)/(b^2*c^2*d^2), (a*q^2)/(b*c*d*e)},q]*Hyp`q`ph[{(a^2*q)/(b*c*d), (a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(3/2))/(b^(1/2)*c^(1/2)*d^(1/2))),a^(1/2),-a^(1/2), a^(1/2)*q^(1/2),-(a^(1/2)*q^(1/2)),(a*q)/(c*d),(a*q)/(b*d), (a*q)/(b*c),e,(a^3*q^3)/(b^2*c^2*d^2*e)}, {(a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2)), -((a*q^(1/2))/(b^(1/2)*c^(1/2)*d^(1/2))),(a^(3/2)*q^2)/(b*c*d), -((a^(3/2)*q^2)/(b*c*d)),(a^(3/2)*q^(3/2))/(b*c*d), -((a^(3/2)*q^(3/2))/(b*c*d)),(a*q)/b,(a*q)/c,(a*q)/d, (a^2*q^2)/(b*c*d*e),(b*c*d*e)/(a*q)},q,q]+ Hyp`q`pqinf[{a,e,(a*q)/(c*d),(a*q)/(b*d),(a*q)/(b*c), (a^2*q^3)/(b^2*c^2*d^2*e),(a^2*q^3)/(b^2*c*d*e), (a^2*q^3)/(b*c^2*d*e),(a^2*q^3)/(b*c*d^2*e), (a^5*q^7)/(b^4*c^4*d^4*e^2)}, {(a*q)/b,(a*q)/c,(a*q)/d,(a^3*q^3)/(b^2*c^2*d^2*e), (a^2*q^3)/(b*c^2*d^2*e),(a^2*q^3)/(b^2*c*d^2*e), (a^2*q^3)/(b^2*c^2*d*e),(a^2*q^3)/(b^2*c^2*d^2),(b*c*d*e)/(a*q^2), (a^4*q^6)/(b^3*c^3*d^3*e^2)},q]* Hyp`q`ph[{(a^4*q^5)/(b^3*c^3*d^3*e^2), (a^2*q^(7/2))/(b^(3/2)*c^(3/2)*d^(3/2)*e), -((a^2*q^(7/2))/(b^(3/2)*c^(3/2)*d^(3/2)*e)),(a^(3/2)*q^2)/(b*c*d*e), -((a^(3/2)*q^2)/(b*c*d*e)),(a^(3/2)*q^(5/2))/(b*c*d*e), -((a^(3/2)*q^(5/2))/(b*c*d*e)),(a*q^2)/(b*c*d), (a^3*q^3)/(b^2*c^2*d^2*e),(a^2*q^3)/(b*c^2*d^2*e), (a^2*q^3)/(b^2*c*d^2*e),(a^2*q^3)/(b^2*c^2*d*e)}, {(a^2*q^(5/2))/(b^(3/2)*c^(3/2)*d^(3/2)*e), -((a^2*q^(5/2))/(b^(3/2)*c^(3/2)*d^(3/2)*e)), (a^(5/2)*q^4)/(b^2*c^2*d^2*e),-((a^(5/2)*q^4)/(b^2*c^2*d^2*e)), (a^(5/2)*q^(7/2))/(b^2*c^2*d^2*e), -((a^(5/2)*q^(7/2))/(b^2*c^2*d^2*e)),(a^3*q^4)/(b^2*c^2*d^2*e^2), (a*q^3)/(b*c*d*e),(a^2*q^3)/(b^2*c*d*e),(a^2*q^3)/(b*c^2*d*e), (a^2*q^3)/(b*c*d^2*e)},q,q]/; Factor[b*bb-q*a]===Factor[c*cc-q*a]===Factor[d*dd-q*a]=== Factor[ee-(b^2*c^2*d^2*e)/(a^2*q^2)]===0); T5469:=(Hyp`q`ph[{a_,d_,e_,f_,g_},{b_,c_,x_,y_},q_,q_] :> Hyp`q`pqinf[{x/a^2},{x},q]* Hyp`q`ph[{a^2,(a^2*q)/b,(a^2*q)/c},{b,c},q,(b*c*x)/(a^4*q)] - Hyp`q`pqinf[{x/a^2,a^2,(b*c)/(a^2*q),b*x/a^2,c*x/a^2},{x,b,c,(b*c*x)/(a^4*q),(x/a^2)^(-1)}, q]*Hyp`q`ph[{x/a,-x/a,q^(1/2)*x/a,-q^(1/2)*x/a, (b*c*x/a^2)/(a^2*q)},{b*x/a^2,c*x/a^2,q*x/a^2,x^2/a^2},q,q]/; Factor[a+d]===Factor[e+f]===Factor[a^2*q-e^2]=== Factor[g-(b*c)/e^2]===Factor[y-(a^2*q)/x]===0); (* Ex2.25,R! *) T121161:=(Hyp`q`ph[{a_,aa_,aaa_,b_,f_,g_,h_,c_,d_, i_,e_,j_}, {aaaa_,aaaaa_,bb_,ff_,gg_,hh_,cc_,dd_,ii_,ee_,jj_}, q_,q_]:>-Hyp`q`pqinf[{a*q,(a*q)/(b^2*e),b^2,e,c,d,(a^2*q)/(b^2*c*d), (a^2*q^2)/(b^2*c*e),(a^2*q^2)/(b^2*d*e),(c*d*q)/e, (a^4*q^3)/(b^6*e^2)},{(a*q)/b^2,(a*q)/e,(a^2*q)/b^2,(a*q)/c, (a*q)/d,(b^2*c*d)/a,(a*c*q)/(b^2*e),(a*d*q)/(b^2*e), (a^3*q^2)/(b^4*c*d*e),(b^2*e)/(a*q),(a^3*q^3)/(b^4*e^2)},q]* Hyp`q`ph[{(a^3*q^2)/(b^4*e^2),(a^(3/2)*q^2)/(b^2*e), -((a^(3/2)*q^2)/(b^2*e)),(a*q)/(b*e),-((a*q)/(b*e)), (a*q^(3/2))/(b*e),-((a*q^(3/2))/(b*e)),(a*q)/b^2,(a^2*q)/(b^2*e), (a*c*q)/(b^2*e),(a*d*q)/(b^2*e),(a^3*q^2)/(b^4*c*d*e)}, {(a^(3/2)*q)/(b^2*e),-((a^(3/2)*q)/(b^2*e)),(a^2*q^2)/(b^3*e), -((a^2*q^2)/(b^3*e)),(a^2*q^(3/2))/(b^3*e), -((a^2*q^(3/2))/(b^3*e)),(a^2*q^2)/(b^2*e^2),(a*q^2)/(b^2*e), (a^2*q^2)/(b^2*c*e),(a^2*q^2)/(b^2*d*e),(c*d*q)/e},q,q]+ Hyp`q`pqinf[{a*q,(a^2*q)/(b^2*e),(a^2*q)/b^4,(a*q)/(b^2*e)}, {(a*q)/b^2,(a*q)/e,(a^2*q)/b^2,(a^2*q)/(b^4*e)},q]* Hyp`q`ph[{b^2,(b^2*c)/a,(b^2*d)/a,(a*q)/(c*d),e}, {(a*q)/c,(a*q)/d,(b^2*c*d)/a,(b^4*e)/a^2},q,q]+ Hyp`q`pqinf[{a*q,(a*q)/(b^2*e),b^2,(b^2*c)/a,(b^2*d)/a,(a*q)/(c*d),e, (a^3*q^2)/(b^4*c*e),(a^3*q^2)/(b^4*d*e),(a*c*d*q)/(b^2*e)}, {(a*q)/b^2,(a*q)/e,(a^2*q)/b^2,(a*q)/c,(a*q)/d,(b^2*c*d)/a, (b^4*e)/(a^2*q),(a*c*q)/(b^2*e),(a*d*q)/(b^2*e), (a^3*q^2)/(b^4*c*d*e)},q]* Hyp`q`ph[{(a^2*q)/b^4,(a^2*q)/(b^2*e),(a*c*q)/(b^2*e),(a*d*q)/(b^2*e), (a^3*q^2)/(b^4*c*d*e)},{(a^2*q^2)/(b^4*e),(a^3*q^2)/(b^4*c*e), (a^3*q^2)/(b^4*d*e),(a*c*d*q)/(b^2*e)},q,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]===Factor[i*ii-q*a]===Factor[j*jj-q*a]===0&& Factor[b+f]===Factor[g^2-b^2*q]===Factor[g+h]=== Factor[i-(a^2*q)/(b^2*c*d)]===Factor[j-(a^2*q)/(b^2*e)]===0) (* Ex 2.30,T! *) T10963:=(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`pqinf[{(b*q)/f,(b*q)/g,(b^2*c*d*e*f*g)/(a^3*q),a*q,c,d,e,f,g, (a^3*q^2)/(b*c*d*e*f*g),b/a,(b*q)/c,(b*q)/d,(b*q)/e}, {(a*q)/f,(a*q)/g,(b*c*d*e*f*g)/(a^2*q),(b^2*q)/a,(b*c)/a,(b*d)/a, (b*e)/a,(b*f)/a,(b*g)/a,(a^2*q^2)/(c*d*e*f*g),a/b,(a*q)/c, (a*q)/d,(a*q)/e},q]*Hyp`q`ph[{b^2/a,(b*q)/a^(1/2),-((b*q)/a^(1/2)),b, (b*c)/a,(b*d)/a,(b*e)/a,(b*f)/a,(b*g)/a,(a^2*q^2)/(c*d*e*f*g)}, {b/a^(1/2),-(b/a^(1/2)),(b*q)/a,(b*q)/c,(b*q)/d,(b*q)/e,(b*q)/f, (b*q)/g,(b^2*c*d*e*f*g)/(a^3*q)},q,q])+ Hyp`q`pqinf[{(b*e*g)/a,(b*f*g)/a,a*q,b/a,(a^3*q^2)/(b*c*d*e*f*g), (b^2*c*d*e*f*g)/(a^3*q),(a*q)/(c*g),(a*q)/(d*g),(a*q)/(e*g), (a*q)/(f*g),(b*c*g)/a,(b*d*g)/a}, {(b*e)/a,(b*f)/a,(b^2*c*d*e*f*g^2)/(a^3*q),(b*g)/a, (a^3*q^2)/(b*c*d*e*f*g^2),(a*q)/g,(a*q)/c,(a*q)/d,(a*q)/e,(a*q)/f, (b*c)/a,(b*d)/a},q]*Hyp`q`ph[{(b^2*c*d*e*f*g^2)/(a^3*q^2), (b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g)/a^(3/2), -((b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g)/a^(3/2)),b, (b*d*e*f*g)/(a^2*q),(b*c*e*f*g)/(a^2*q),(b*c*d*f*g)/(a^2*q), (b*c*d*e*g)/(a^2*q),(b*g)/a,g}, {(b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g)/(a^(3/2)*q), -((b*c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g)/(a^(3/2)*q)), (b*c*d*e*f*g^2)/(a^3*q),(b*c*g)/a,(b*d*g)/a,(b*e*g)/a,(b*f*g)/a, (b*c*d*e*f*g)/(a^2*q),(b^2*c*d*e*f*g)/(a^3*q)},q,q]+ Hyp`q`pqinf[{(a^2*q^2)/(c*d*f*g),(a^2*q^2)/(c*d*e*g),a*q,b/a,g,(b*q)/g, (b*d*e*f*g)/(a^2*q),(b*c*e*f*g)/(a^2*q),(b*c*d*f*g)/(a^2*q), (b*c*d*e*g)/(a^2*q),(a^2*q^2)/(d*e*f*g),(a^2*q^2)/(c*e*f*g)}, {(b*e)/a,(b*f)/a,(a^3*q^3)/(c*d*e*f*g^2),(a^2*q^2)/(c*d*e*f*g), (b*c*d*e*f*g^2)/(a^3*q^2),(b*c*d*e*f*g)/(a^2*q),(a*q)/c,(a*q)/d, (a*q)/e,(a*q)/f,(b*c)/a,(b*d)/a},q]* Hyp`q`ph[{(a^3*q^2)/(c*d*e*f*g^2), (a^(3/2)*q^2)/(c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g), -((a^(3/2)*q^2)/(c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g)),b,(a*q)/(c*g), (a*q)/(d*g),(a*q)/(e*g),(a*q)/(f*g),(a^2*q^2)/(c*d*e*f*g), (a^3*q^2)/(b*c*d*e*f*g)}, {(a^(3/2)*q)/(c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g), -((a^(3/2)*q)/(c^(1/2)*d^(1/2)*e^(1/2)*f^(1/2)*g)), (a^3*q^3)/(b*c*d*e*f*g^2),(a^2*q^2)/(d*e*f*g),(a^2*q^2)/(c*e*f*g), (a^2*q^2)/(c*d*f*g),(a^2*q^2)/(c*d*e*g),(a*q)/g,(b*q)/g},q,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]===Factor[h-(a^3*q^2)/(b*c*d*e*f*g)]===0); T8810:={ Hyp`q`ps[{aa_, aaa_, b_, c_, d_, e_, f_, g_}, {a_, aaaa_, bb_, cc_, dd_, ee_, ff_, gg_},q_, z_]:> Hyp`q`pqinf[{f, g, f/a^2, g/a^2, q*a^2, q/a^2}, {bb, cc, dd, ee, q/b, q/c, q/d, q/e},q]* Hyp`q`pqinf[{q, q*a^2/b/f, q*a^2/c/f, q*a^2/d/f, q*a^2/e/f, q*f/b, q*f/c, q*f/d, q*f/e}, {f, q/f, ff, f/a^2, g/f, f*g/a^2, q*f^2/a^2},q]* Hyp`q`ph[{f^2/a^2, q*f/a, -q*f/a, f*b/a^2, f*c/a^2, f*d/a^2, f*e/a^2, f*g/a^2}, {f/a, -f/a, f*q/b, f*q/c, f*q/d, f*q/e, f*q/g}, q, z]+ Hyp`q`pqinf[{f, g, f/a^2, g/a^2, q*a^2, q/a^2}, {bb, cc, dd, ee, q/b, q/c, q/d, q/e},q]* Hyp`q`pqinf[{q, q*a^2/b/g, q*a^2/c/g, q*a^2/d/g, q*a^2/e/g, q*g/b, q*g/c, q*g/d, q*g/e}, {g, q/g, gg, g/a^2, f/g, g*f/a^2, q*g^2/a^2},q]* Hyp`q`ph[{g^2/a^2, q*g/a, -q*g/a, g*b/a^2, g*c/a^2, g*d/a^2, g*e/a^2, g*f/a^2}, {g/a, -g/a, g*q/b, g*q/c, g*q/d, g*q/e, g*q/f}, q, z]/; Factor[aa*a-q*a^2]===Factor[aaa*aaaa-aa*a]===Factor[aaa*aaaa-b*bb]=== Factor[b*bb-c*cc]=== Factor[c*cc-d*dd]===Factor[d*dd-e*ee]===Factor[e*ee-f*ff]=== Factor[f*ff-g*gg]===Factor[z-q^2*a^6/b/c/d/e/f/g]===0}; T101010:= {Hyp`q`ps[{aa_, aaa_, b_, c_, d_, e_, f_, g_, h_, k_}, {a_, aaaa_, bb_, cc_, dd_, ee_, ff_, gg_, hh_, kk_}, q_, z_]:> Hyp`q`ph[{k^2/(a^2), (k*q)/(a^2)^(1/2), -((k*q)/(a^2)^(1/2)), (b*k)/(a^2), (c*k)/(a^2), (d*k)/(a^2), (e*k)/(a^2), (f*k)/(a^2), (h*k)/(a^2), (g*k)/(a^2)}, {k/(a^2)^(1/2), -(k/(a^2)^(1/2)), (k*q)/b, (k*q)/c, (k*q)/d, (k*q)/e, (k*q)/f, (k*q)/h, (k*q)/g}, q, ((a^2)^4*q^3)/(b*c*d*e*f*g*h*k)]* Hyp`q`pqinf[{g, h, g/(a^2), h/(a^2), (a^2)*q, q/(a^2), q, ((a^2)*q)/(b*k), ((a^2)*q)/(c*k), ((a^2)*q)/(d*k), ((a^2)*q)/(e*k), ((a^2)*q)/(f*k), (k*q)/b, (k*q)/c, (k*q)/d, (k*q)/e, (k*q)/f}, {((a^2)*q)/b, ((a^2)*q)/c, ((a^2)*q)/d, ((a^2)*q)/e, ((a^2)*q)/f, q/b, q/c, q/d, q/e, q/f, (h*k)/(a^2), (g*k)/(a^2), h/k, g/k, q/k, ((a^2)*q)/k, (k^2*q)/(a^2)}, q] + Hyp`q`ph[{h^2/(a^2), (h*q)/(a^2)^(1/2), -((h*q)/(a^2)^(1/2)), (b*h)/(a^2), (c*h)/(a^2), (d*h)/(a^2), (e*h)/(a^2), (f*h)/(a^2), (g*h)/(a^2), (h*k)/(a^2)}, {h/(a^2)^(1/2), -(h/(a^2)^(1/2)), (h*q)/b, (h*q)/c, (h*q)/d, (h*q)/e, (h*q)/f, (h*q)/g, (h*q)/k}, q, ((a^2)^4*q^3)/(b*c*d*e*f*g*h*k)]* Hyp`q`pqinf[{g, k, g/(a^2), k/(a^2), (a^2)*q, q/(a^2), q, ((a^2)*q)/(b*h), ((a^2)*q)/(c*h), ((a^2)*q)/(d*h), ((a^2)*q)/(e*h), ((a^2)*q)/(f*h), (h*q)/b, (h*q)/c, (h*q)/d, (h*q)/e, (h*q)/f}, {((a^2)*q)/b, ((a^2)*q)/c, ((a^2)*q)/d, ((a^2)*q)/e, ((a^2)*q)/f, q/b, q/c, q/d, q/e, q/f, (g*h)/(a^2), (h*k)/(a^2), g/h, k/h, q/h, ((a^2)*q)/h, (h^2*q)/(a^2)}, q] + Hyp`q`ph[{g^2/(a^2), (g*q)/(a^2)^(1/2), -((g*q)/(a^2)^(1/2)), (b*g)/(a^2), (c*g)/(a^2), (d*g)/(a^2), (e*g)/(a^2), (f*g)/(a^2), (g*h)/(a^2), (g*k)/(a^2)}, {g/(a^2)^(1/2), -(g/(a^2)^(1/2)), (g*q)/b, (g*q)/c, (g*q)/d, (g*q)/e, (g*q)/f, (g*q)/h, (g*q)/k}, q, ((a^2)^4*q^3)/(b*c*d*e*f*g*h*k)]* Hyp`q`pqinf[{h, k, h/(a^2), k/(a^2), (a^2)*q, q/(a^2), q, ((a^2)*q)/(b*g), ((a^2)*q)/(c*g), ((a^2)*q)/(d*g), ((a^2)*q)/(e*g), ((a^2)*q)/(f*g), (g*q)/b, (g*q)/c, (g*q)/d, (g*q)/e, (g*q)/f}, {((a^2)*q)/b, ((a^2)*q)/c, ((a^2)*q)/d, ((a^2)*q)/e, ((a^2)*q)/f, q/b, q/c, q/d, q/e, q/f, (g*h)/(a^2), (g*k)/(a^2), h/g, k/g, q/g, ((a^2)*q)/g, (g^2*q)/(a^2)}, q] /; Factor[aa*a-q*a^2]===Factor[aa*a-aaa*aaaa]===Factor[b*bb-c*cc]=== Factor[c*cc-d*dd]=== Factor[d*dd-e*ee]===Factor[e*ee-f*ff]===Factor[f*ff-g*gg]=== Factor[g*gg-h*hh]===Factor[h*hh-k*kk]=== Factor[z*b*c*d*e*f*g*h*k/a^8-q^3]===0}; Regel[Global`rs01]:=Transfor`q`Trs01; Regel[2101]:=Transfor`q`T2101; Regel[2102]:=Transfor`q`T2102; Regel[2103]:=Transfor`q`T2103; Regel[2104]:=Transfor`q`T2104; Regel[2105]:=Transfor`q`T2105; Regel[2106]:=Transfor`q`T2106; Regel[2107]:=Transfor`q`T2107; Regel[2108]:=Transfor`q`T2108; Regel[2109]:=Transfor`q`T2109; Regel[2110]:=Transfor`q`T2110; Regel[2111]:=Transfor`q`T2111; Regel[2112]:=Transfor`q`T2112; Regel[2161]:=Transfor`q`T2161; Regel[2162]:=Transfor`q`T2162; Regel[2163]:=Transfor`q`T2163; Regel[2201]:=Transfor`q`T2201; Regel[2202]:=Transfor`q`T2202; Regel[3101]:=Transfor`q`T3101; Regel[3201]:=Transfor`q`T3201; Regel[3202]:=Transfor`q`T3202; Regel[3203]:=Transfor`q`T3203; Regel[3204]:=Transfor`q`T3204; Regel[3205]:=Transfor`q`T3205; Regel[3206]:=Transfor`q`T3206; Regel[3207]:=Transfor`q`T3207; Regel[3208]:=Transfor`q`T3208; Regel[3209]:=Transfor`q`T3209; Regel[3210]:=Transfor`q`T3210; Regel[3211]:=Transfor`q`T3211; Regel[3212]:=Transfor`q`T3212; Regel[3213]:=Transfor`q`T3213; Regel[3214]:=Transfor`q`T3214; Regel[3215]:=Transfor`q`T3215; Regel[3216]:=Transfor`q`T3216; Regel[3217]:=Transfor`q`T3217; Regel[3261]:=Transfor`q`T3261; Regel[3262]:=Transfor`q`T3262; Regel[3263]:=Transfor`q`T3263; Regel[3264]:=Transfor`q`T3264; Regel[3265]:=Transfor`q`T3265; Regel[3266]:=Transfor`q`T3266; Regel[3267]:=Transfor`q`T3267; Regel[3268]:=Transfor`q`T3268; Regel[3269]:=Transfor`q`T3269; Regel[4201]:=Transfor`q`T4201; Regel[4301]:=Transfor`q`T4301; Regel[4302]:=Transfor`q`T4302; Regel[4303]:=Transfor`q`T4303; Regel[4304]:=Transfor`q`T4304; Regel[4305]:=Transfor`q`T4305; Regel[4306]:=Transfor`q`T4306; Regel[4307]:=Transfor`q`T4307; Regel[4308]:=Transfor`q`T4308; Regel[4309]:=Transfor`q`T4309; Regel[4310]:=Transfor`q`T4310; Regel[4311]:=Transfor`q`T4311; Regel[4312]:=Transfor`q`T4312; Regel[4313]:=Transfor`q`T4313; Regel[4314]:=Transfor`q`T4314; Regel[4315]:=Transfor`q`T4315; Regel[4316]:=Transfor`q`T4316; Regel[4361]:=Transfor`q`T4361; Regel[4362]:=Transfor`q`T4362; Regel[4363]:=Transfor`q`T4363; Regel[4364]:=Transfor`q`T4364; Regel[4365]:=Transfor`q`T4365; Regel[4366]:=Transfor`q`T4366; Regel[4367]:=Transfor`q`T4367; Regel[4368]:=Transfor`q`T4368; Regel[4369]:=Transfor`q`T4369; Regel[5401]:=Transfor`q`T5401; Regel[5402]:=Transfor`q`T5402; Regel[5403]:=Transfor`q`T5403; Regel[5404]:=Transfor`q`T5404; Regel[5405]:=Transfor`q`T5405; Regel[5406]:=Transfor`q`T5406; Regel[5407]:=Transfor`q`T5407; Regel[5408]:=Transfor`q`T5408; Regel[5409]:=Transfor`q`T5409; Regel[5410]:=Transfor`q`T5410; Regel[5411]:=Transfor`q`T5411; Regel[5412]:=Transfor`q`T5412; Regel[5413]:=Transfor`q`T5413; Regel[5414]:=Transfor`q`T5414; Regel[5415]:=Transfor`q`T5415; Regel[5416]:=Transfor`q`T5416; Regel[5417]:=Transfor`q`T5417; Regel[5461]:=Transfor`q`T5461; Regel[5462]:=Transfor`q`T5462; Regel[5463]:=Transfor`q`T5463; Regel[5464]:=Transfor`q`T5464; Regel[5465]:=Transfor`q`T5465; Regel[5466]:=Transfor`q`T5466; Regel[5467]:=Transfor`q`T5467; Regel[5468]:=Transfor`q`T5468; Regel[5469]:=Transfor`q`T5469; Regel[6501]:=Transfor`q`T6501; Regel[6502]:=Transfor`q`T6502; Regel[6503]:=Transfor`q`T6503; Regel[6504]:=Transfor`q`T6504; Regel[6505]:=Transfor`q`T6505; Regel[6506]:=Transfor`q`T6506; Regel[6507]:=Transfor`q`T6507; Regel[6508]:=Transfor`q`T6508; Regel[6509]:=Transfor`q`T6509; Regel[6510]:=Transfor`q`T6510; Regel[6511]:=Transfor`q`T6511; Regel[6512]:=Transfor`q`T6512; Regel[6513]:=Transfor`q`T6513; Regel[6514]:=Transfor`q`T6514; Regel[6515]:=Transfor`q`T6515; Regel[6516]:=Transfor`q`T6516; Regel[6561]:=Transfor`q`T6561; Regel[6562]:=Transfor`q`T6562; Regel[6563]:=Transfor`q`T6563; Regel[6564]:=Transfor`q`T6564; Regel[6565]:=Transfor`q`T6565; Regel[6566]:=Transfor`q`T6566; Regel[6567]:=Transfor`q`T6567; Regel[6568]:=Transfor`q`T6568; Regel[6569]:=Transfor`q`T6569; Regel[7601]:=Transfor`q`T7601; Regel[7602]:=Transfor`q`T7602; Regel[7603]:=Transfor`q`T7603; Regel[7604]:=Transfor`q`T7604; Regel[7605]:=Transfor`q`T7605; Regel[7606]:=Transfor`q`T7606; Regel[7607]:=Transfor`q`T7607; Regel[7608]:=Transfor`q`T7608; Regel[7609]:=Transfor`q`T7609; Regel[7610]:=Transfor`q`T7610; Regel[7611]:=Transfor`q`T7611; Regel[7612]:=Transfor`q`T7612; Regel[7613]:=Transfor`q`T7613; Regel[7614]:=Transfor`q`T7614; Regel[7615]:=Transfor`q`T7615; Regel[7616]:=Transfor`q`T7616; Regel[7661]:=Transfor`q`T7661; Regel[7662]:=Transfor`q`T7662; Regel[7663]:=Transfor`q`T7663; Regel[7664]:=Transfor`q`T7664; Regel[7665]:=Transfor`q`T7665; Regel[7666]:=Transfor`q`T7666; Regel[7667]:=Transfor`q`T7667; Regel[7668]:=Transfor`q`T7668; Regel[7669]:=Transfor`q`T7669; Regel[7701]:=Transfor`q`T7701; Regel[8701]:=Transfor`q`T8701; Regel[8702]:=Transfor`q`T8702; Regel[8703]:=Transfor`q`T8703; Regel[8704]:=Transfor`q`T8704; Regel[8705]:=Transfor`q`T8705; Regel[8706]:=Transfor`q`T8706; Regel[8707]:=Transfor`q`T8707; Regel[8708]:=Transfor`q`T8708; Regel[8709]:=Transfor`q`T8709; Regel[8710]:=Transfor`q`T8710; Regel[8711]:=Transfor`q`T8711; Regel[8712]:=Transfor`q`T8712; Regel[8713]:=Transfor`q`T8713; Regel[8714]:=Transfor`q`T8714; Regel[8715]:=Transfor`q`T8715; Regel[8716]:=Transfor`q`T8716; Regel[8761]:=Transfor`q`T8761; Regel[8762]:=Transfor`q`T8762; Regel[8763]:=Transfor`q`T8763; Regel[8764]:=Transfor`q`T8764; Regel[8765]:=Transfor`q`T8765; Regel[8766]:=Transfor`q`T8766; Regel[8767]:=Transfor`q`T8767; Regel[8768]:=Transfor`q`T8768; Regel[8769]:=Transfor`q`T8769; Regel[10901]:=Transfor`q`T10901; Regel[10902]:=Transfor`q`T10902; Regel[10903]:=Transfor`q`T10903; Regel[10904]:=Transfor`q`T10904; Regel[10905]:=Transfor`q`T10905; Regel[10906]:=Transfor`q`T10906; Regel[10907]:=Transfor`q`T10907; Regel[10908]:=Transfor`q`T10908; Regel[10909]:=Transfor`q`T10909; Regel[10910]:=Transfor`q`T10910; Regel[10911]:=Transfor`q`T10911; Regel[10912]:=Transfor`q`T10912; Regel[10913]:=Transfor`q`T10913; Regel[10914]:=Transfor`q`T10914; Regel[10915]:=Transfor`q`T10915; Regel[10916]:=Transfor`q`T10916; Regel[10961]:=Transfor`q`T10961; Regel[10962]:=Transfor`q`T10962; Regel[10963]:=Transfor`q`T10963; Regel[10964]:=Transfor`q`T10964; Regel[10965]:=Transfor`q`T10965; Regel[10966]:=Transfor`q`T10966; Regel[10967]:=Transfor`q`T10967; Regel[10968]:=Transfor`q`T10968; Regel[10969]:=Transfor`q`T10969; Regel[121101]:=Transfor`q`T121101; Regel[121102]:=Transfor`q`T121102; Regel[121103]:=Transfor`q`T121103; Regel[121104]:=Transfor`q`T121104; Regel[121105]:=Transfor`q`T121105; Regel[121106]:=Transfor`q`T121106; Regel[121107]:=Transfor`q`T121107; Regel[121108]:=Transfor`q`T121108; Regel[121109]:=Transfor`q`T121109; Regel[121110]:=Transfor`q`T121110; Regel[121111]:=Transfor`q`T121111; Regel[121112]:=Transfor`q`T121112; Regel[121113]:=Transfor`q`T121113; Regel[121114]:=Transfor`q`T121114; Regel[121115]:=Transfor`q`T121115; Regel[121116]:=Transfor`q`T121116; Regel[121161]:=Transfor`q`T121161; Regel[121162]:=Transfor`q`T121162; Regel[121163]:=Transfor`q`T121163; Regel[121164]:=Transfor`q`T121164; Regel[121165]:=Transfor`q`T121165; Regel[121166]:=Transfor`q`T121166; Regel[121167]:=Transfor`q`T121167; Regel[121168]:=Transfor`q`T121168; Regel[121169]:=Transfor`q`T121169; Regel[8810]:=Transfor`q`T8810; Regel[101010]:=Transfor`q`T101010; End[] Protect[ Trs01, T2101, T2102, T2103, T2104, T2105, T2201, T3201, T2106, T2107, T2108, T3202, T3203, T3101, T3204, T3205, T3206, T3207, T3208, T3209, T4301, T4302, T8701, T8702, T4303, T4304, T8703, T4305, T4306, T8704, T8705, T5401, T121101, T5402, T121102, T7601, T7701, T121103, T10901, T2161, T2162, T3261, T3262, T3263, T3264, T3265, T8761, T8762, T8763, T10961, T4308, T2109, T4309, T10902, T4310, T8706, T6501, T121104, T8764, T10903, T3210, T5461, T5462, T5463, T2110, T8707, T4311, T8708, T3266, T5464, T2111, T8709, T10962, T5465, T8710, T8711, T10904, T5403, T5404, T5405, T3211, T3212, T3213, T2112, T3214, T2202, T3215, T3216, T3217, T4312, T4313, T4201, T3267, T3268, T2163, T3269, T4361, T4362, T5466, T5467, T10905, T121105, T10906, T121106, T121107, T10907, T5468, T5469, T121161, T10963, T8810, T101010, TListe, TransListe ] EndPackage[] If[$VersionNumber>=2.,$Messages=OutputStream["stdout",1],$Messages={"stdout"}]; If[$VersionNumber>=5.,$Messages={OutputStream["stdout",1]},Null];