(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 612485, 16616]*) (*NotebookOutlinePosition[ 636088, 17359]*) (* CellTagsIndexPosition[ 630345, 17175]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["TARCER 1.97", "Title", TextAlignment->Center, CellTags->"T1.1"], Cell[TextData[{ "A ", StyleBox["Mathematica", FontSlant->"Italic"], " program for the reduction of two-loop propagator integrals " }], "Text", TextAlignment->Center], Cell[TextData[{ "Rolf Mertig\n", ButtonBox["Mertig Research & Consulting\n", ButtonData:>{ URL[ "http://www.mertig.com"], None}, ButtonStyle->"Hyperlink"], "and\nRainer Scharf\n", ButtonBox["Universit\[ADoubleDot]t Leipzig", ButtonData:>{ URL[ "http://www.physik.uni-leipzig.de/~scharf/"], None}, ButtonStyle->"Hyperlink"] }], "Text", Editable->False, TextAlignment->Center, CellTags->"T1.2"], Cell["18th September, 2003", "Text", TextAlignment->Center], Cell["\<\ COMMENTS (RM 18.9.2003): Fixed things for 5.0, eliminated a TVI \ symmetry (causing infinite recursion) and added TFI decomposition into products of TAI's (was somehow missing but shows up \ in, e.g., the 2-loop Higss selfenergy). Putting TFI back into the Tarcer context, because the fcloops context created \ trouble ... Changed default of $Comment to False.\ \>", "Text"], Cell["\<\ COMMENTS (FO 8.9.2002.): Changed context of TFI to \ HighEnergyPhysics`fcloops`TFI` and updated other HighEnergyPhysics`* \ contexts.\ \>", "Text"], Cell["\<\ COMMENTS (FO 15.3.2001.): Changed PreFactor into Prefactor1 to \ avoid conflict with FeynArts and FeynCalc.\ \>", "Text"], Cell["\<\ COMMENTS (FO 15.3.2001.): Changed context of Zeta2 and made \ definition dependent on not having loaded FeynCalc.\ \>", "Text"], Cell[TextData[{ "COMMENTS (RM 25.4.): ", ButtonBox["TFISimplify", ButtonData:>"T1.7.1.1", ButtonStyle->"Hyperlink"], " (like TFIRecurse, but without trule[9])." }], "Text"], Cell[TextData[{ "COMMENTS (RM 23.4.): bug fixed in ", ButtonBox["tlrule[17]", ButtonData:>"tlrule17", ButtonStyle->"Hyperlink"], "." }], "Text"], Cell[TextData[{ "COMMENTS (RM 6.4.): ", ButtonBox["special TVR relations", ButtonData:>"specialTVR", ButtonStyle->"Hyperlink"], " added to TVR." }], "Text"], Cell[TextData[{ "COMMENTS (RM 22.3.): ", ButtonBox["TVI Symmetry", ButtonData:>"Tsymmetry", ButtonStyle->"Hyperlink"], " added to TVR." }], "Text"], Cell[TextData[{ "COMMENTS (RM 18.3.): More rules added to ", ButtonBox["$TTable", ButtonData:>"$TTable", ButtonStyle->"Hyperlink"], ". " }], "Text"], Cell[TextData[{ "COMMENTS (RM 18.2.): More rules added to ", ButtonBox["$TTable", ButtonData:>"$TTable", ButtonStyle->"Hyperlink"], ". " }], "Text"], Cell[TextData[{ "COMMENTS (RM 21.2.): Included ", ButtonBox["$TTable", ButtonData:>"$TTable", ButtonStyle->"Hyperlink"], ". added tlrule[25]" }], "Text"], Cell["\<\ COMMENTS (RM 20.2.): $RankLimit = {0,6} ; Changed TarcerRecurse \ such that special TJR and TVR (reducing D -> D-2) are used first.\ \>", "Text"], Cell["\<\ COMMENTS (RM 15.2.): $RankLimit = {0,8} ; The following test now works: Print[\"test 1 : TFI[D, pp, \ {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1,MW}}] = \", Timing[t1 \ =TarcerRecurse[TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, \ MZ}, {1,MW}}]] ] // \ InputForm ] Print[\"test 2 : TFI[d, \ pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}] = \", Timing[t2 \ =TarcerRecurse[TFI[D, pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}]]; ] // \ InputForm ] \ \>", "Text"], Cell["\<\ COMMENTS (RM 13.2.): tlrule[11] and trule[12] made more \ restrictive: inhibiting thus a recursion if {n5,m5} equals {0,0}.\ \>", "Text"], Cell["\<\ COMMENTS (RM 12.2.): tlrule[15] made safer (in order to not get 0 \ :> 0 ); TFIRecurse made safer (to not \ get into a recursion); There is still something \ wrong with the tlrule's ; since TFIRecurse[TFI[D, pp, {0, 0, 0, 1, \ 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1, MW}}]] doesn't work ..\ \>", "Text"], Cell["\<\ COMMENTS (RM 5.2.): tlrule[10] slightly changed to cover more \ cases.\ \>", "Text"], Cell["\<\ COMMENTS (RM 2.2.): FunctionExpand added in tlrule[9]. 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Putting Unset[$Post] behind $Post=(#:)&; will produce a lot of typsetted reduction formulae.\ \>", "Text"], Cell[BoxData[ \(Unset[$Post]; \)], "Input"], Cell[BoxData[ \($Post\ = \ \((#; )\) &; \)], "Input"], Cell[BoxData[ \(If[$Notebooks =!= True, $Post\ = \ \((#; )\) &]; \)], "Input"], Cell[BoxData[ \($HistoryLength = 0; \)], "Input"], Cell["\<\ This determines the directory into which the resulting file \ tarcer.mx is written.\ \>", "Text"], Cell[BoxData[ \(If[$Notebooks, SetDirectory[ ToFileName[ First["\" /. NotebookInformation[InputNotebook[]]]]]]\)], "Input"], Cell[TextData[{ "Somehow ", StyleBox["Mathematica", FontSlant->"Italic"], " crashes on my (R.M.) good old NeXTStation if I don't open all cells first \ ...; this opens all cells automatically:" }], "SmallText"], Cell[BoxData[ \(If[$System === "\", SelectionMove[EvaluationNotebook[], All, Notebook]; FrontEndExecute[{FrontEnd`FrontEndToken[ EvaluationNotebook[], "\"]}]]\)], "Input"], Cell[BoxData[ \(Off[General::spell]; \)], "Input"], Cell[BoxData[ \(Off[General::spell1]; \)], "Input"], Cell[CellGroupData[{ Cell["Creating the tarcerij.mx file", "Subsubsection", CellTags->"T1.2.1.1"], Cell[TextData[{ "Running this notebook will produce a tarcerij.mx file where ij will be \ replaced by \nthe two number set by the variable $RankLimit (default 33). \n\ In the same directory as this notebook which can be loaded into ", StyleBox["Mathematica", FontSlant->"Italic"], " by <"Italic"], "as \nmyshellprompt> math -initfile tarcer33.mx" }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Usages", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.2.1"], Cell[BoxData[""], "Input"], Cell[BoxData[ \(\(BeginPackage["\"];\)\)], "Input"], Cell[BoxData[ \(TarcerRecurse::usage = "\"; \)], \ "Input"], Cell[BoxData[ \(TarcerExpand::usage = "\ (4+e), order] or \ TarcerExpand[epxr, d -> (4-e), order] or TarcerExpand[expr, d -> (4 - 2 \ om)substitutes integrals as specified by the option TarcerRules, and does a \ Laurent expansion in the variable around 0 at the right hand side of the \ second argument (i.e., you can use whatever convention you like ...). The \ same effect as TarcerExpand[TarcerRecurse[expr], ...] can be achieved by \ setting the option TarcerRecurse of TarcerExpand to True. TarcerExpand[expr, \ d -> (4+e)] is equivalent to TarcerExpand[expr, d -> (4+e), 0].\>"; \)], \ "Input"], Cell[BoxData[ \(TarcerReduce::usage = "\"; \)], "Input"], Cell[BoxData[ \(Cayley::usage = "\"; \)], "Input"], Cell[BoxData[ \(Cayleyu::usage = "\"; \)], "Input"], Cell[BoxData[ \(CayleyD::usage = "\"; \)], "Input"], Cell[BoxData[ \(Prefactor1::usage = "\"; \)], "Input"], Cell[BoxData[ \(SEpsilon::usage = "\"; \)], "Input"], Cell["\<\ TFI::\"usage\" = \"TFI[d, pp, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] is the 2-loop d-dimensional integral 1/( (q1^2 - m1^2)^n1 (q2^2 - m2^2)^n2 ((q1-p)^2 - m3^2)^n3 * ((q2-p)^2 - m4^2)^n4 ((q1-q2)^2 - m5^2)^n5 ) . TFI[d, pp, {x,y,z,v,w}, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] has as additional factors in the numerator (q1^2)^x*(q2^2)^y*(q1.p)^z* (q2.p)^v*(q1.q2)^w . 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(important for the \ palette and OperatorApply).\ \>", "Text"], Cell[BoxData[ \(MakeBoxes[Schiebe[i_, pm_String]\ , fmt_] := InterpretationBox[ StyleBox[SuperscriptBox[i, pm], FontWeight -> "\"], Schiebe[i, pm], Editable -> True]\)], "Input"], Cell[BoxData[ \(CayleyD /: MakeBoxes[\(CayleyD[i_Integer]\)[args_], fmt_] := FractionBox[ SubscriptBox["\<\[CapitalDelta]\>", \ i], "\<\[CapitalDelta]\>"]; \)], "Input"], Cell[BoxData[ \(CayleyD /: MakeBoxes[\(CayleyD[i_Integer, j_Integer]\)[args_], fmt_] := FractionBox[ SubscriptBox["\<\[CapitalDelta]\>", 10\ i + j], "\<\[CapitalDelta]\>"]; \)], "Input"], Cell[BoxData[ \(CayleyD /: MakeBoxes[\(CayleyD[i_Integer, j_Integer, k_Integer]\)[args_], fmt_] := FractionBox[ SubscriptBox["\<\[CapitalDelta]\>", 100\ \ i + 10 j + k], "\<\[CapitalDelta]\>"]; \)], "Input"], Cell[BoxData[ \(Cayley /: MakeBoxes[\(Cayley[i_Integer]\)[args_], fmt_] := SubscriptBox["\<\[CapitalDelta]\>", \ i]; \)], "Input"], Cell[BoxData[ \(Cayley /: MakeBoxes[\(Cayley[i_Integer, j_Integer]\)[args_], fmt_] := SubscriptBox["\<\[CapitalDelta]\>", 10\ i + j]; \)], "Input"], Cell[BoxData[ \(Cayley /: MakeBoxes[\(Cayley[i_Integer, j_Integer, k_Integer]\)[args_], fmt_] := SubscriptBox["\<\[CapitalDelta]\>", 100\ \ i + 10 j + k]; \)], "Input"], Cell[BoxData[ \(Cayleyu /: MakeBoxes[\(Cayleyu[i_Integer, j_Integer, k_Integer]\)[args_], fmt_] := SubscriptBox["\", 100\ \ i + 10 j + k]; \)], "Input"], Cell["\<\ MakeBoxes[PP, fm_] := InterpretationBox[SuperscriptBox[p, 2], PP]; MakeBoxes[m1^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 1, p], m1^p]; \ MakeBoxes[m2^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 2, p], m2^p]; \ MakeBoxes[m3^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 3, p], m3^p]; \ MakeBoxes[m4^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 4, p], m4^p]; \ MakeBoxes[m5^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 5, p], m5^p]; \ m6 = Sqrt[PP]; \ \>", "Input"], Cell[BoxData[ \(MakeBoxes[m1, _] := InterpretationBox[SubscriptBox[m, 1], m1]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[m2, _] := InterpretationBox[SubscriptBox[m, 2], m2]; 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\)], "Input"], Cell[BoxData[ \(redblue[z_ + 1] := StyleBox[mbt[z], FontColor \[Rule] RGBColor[0, 0, 1]]; \)], "Input"], Cell[BoxData[ \(redblue[z_ + 2] := StyleBox[OverscriptBox[mbt[z], "\<_\>"], FontColor \[Rule] RGBColor[0, 0, 1]]; \)], "Input"], Cell[BoxData[ \(redblue[z_Subscript + 2] := StyleBox[SubscriptBox[ OverscriptBox[ z\[LeftDoubleBracket]1\[RightDoubleBracket], "\<_\>"], z\[LeftDoubleBracket]2\[RightDoubleBracket]], FontColor \[Rule] RGBColor[0, 0, 1]]; \)], "Input"], Cell[BoxData[ \(TFI /: MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", ur}]], \n\t\tTFI[d, pp, {ur}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TFI /: MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], fmt_] := \n\t\(\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", Apply[Sequence, Flatten[{any}]]}]], \n\t\tTFI[d, pp, dp, any, {den}], Editable -> True})\) /; 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Hold[TVI] -> TVI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)], "Input"], Cell[BoxData[ \({TVI[d, {\[Alpha], \[Beta], \[Gamma], \[Delta]}], TVI[d, {\[Alpha] + 1, \[Beta], \[Gamma], \[Delta]}], TVI[d, {\[Alpha] - 1, \[Beta], \[Gamma], \[Delta]}]}\)], "Input"], Cell[BoxData[ \(TJI /: MakeBoxes[TJI[d_, 0, {den__}], fmt_] := \t\((\n\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[ TJI]\)[d, 0, {den}], Editable -> True})\) /. Hold[TJI] -> TJI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\n\t)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TJI /: MakeBoxes[TJI[dpp__, {den__}], fmt_] := \t\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([\)\(1\)\(]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJI]\)[ dpp, {den}], Editable -> True})\) /. Hold[TJI] -> TJI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TKI /: MakeBoxes[TKI[d_, pp___, {den__}], fmt_] := \n\t\((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TKI /: MakeBoxes[TKI[dpp__, {den__}], fmt_] := \t\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([\)\(1\)\(]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TKI]\)[ dpp, {den}], Editable -> True})\) /. Hold[TKI] -> TKI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \({TKI[d, {\[Alpha], \[Beta], \[Gamma]}], TKI[d, {\[Alpha] + 1, \[Beta], \[Gamma]}], TKI[d, {\[Alpha] - 1, \[Beta], \[Gamma]}]}\)], "Input"], Cell[BoxData[ \(TBI /: MakeBoxes[TBI[d_, pp___, {den__}], fmt_] := \n\t\((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TBI /: MakeBoxes[TBI[d_, pp___, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\tTBI[d, pp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \({TBI[d, {\[Alpha], \[Beta]}], TBI[d, {\[Alpha] + 1, \[Beta]}], TBI[d, {\[Alpha] - 1, \[Beta]}]}\)], "Input"], Cell[BoxData[ \(TAI /: MakeBoxes[TAI[d_, pp___, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\tTAI[ d, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \({TAI[d, {\[Alpha]}], TAI[d, {\[Alpha] + 1}], TAI[d, {\[Alpha] - 1}]}\)], "Input"], Cell["\<\ T*IC are just like T*I , but used only for commentary in the recursion (TComment).\ \>", "Text"], Cell[BoxData[ \(TFIC /: MakeBoxes[TFIC[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", i, "\<0\>"}]], \n\t\tTFIC[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TFIC /: MakeBoxes[TFIC[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", "\<0\>", i}]], \n\t\tTFIC[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TFIC /: MakeBoxes[TFIC[dpp__, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[First[{dpp}], TraditionalForm], "\<)\>"}]], \n\t\tTFIC[dpp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)], "Input"], Cell[BoxData[ \(TVIC /: MakeBoxes[TVIC[dpp__, {den__}], fmt_] := \n\((\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([\)\(1\)\(]\)], TraditionalForm], "\<)\>"}]], \n\t\(Hold[TVIC]\)[ dpp, {den}], Editable -> True})\) /. Hold[TVIC] -> TVIC)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)], "Input"], Cell[BoxData[ \(TJIC /: MakeBoxes[TJIC[d_, 0, {den__}], fmt_] := \t\((\n\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[ TJIC]\)[d, 0, {den}], Editable -> True})\) /. Hold[TJIC] -> TJIC)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\n\t)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TJIC /: MakeBoxes[TJIC[dpp__, {den__}], fmt_] := \t\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([\)\(1\)\(]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJIC]\)[ dpp, {den}], Editable -> True})\) /. Hold[TJIC] -> TJIC)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TBIC /: MakeBoxes[TBIC[d_, pp___, {den__}], fmt_] := \n\t\((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TBIC /: MakeBoxes[TBIC[d_, pp___, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\tTBIC[d, pp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TAIC /: MakeBoxes[TAIC[d_, pp___, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\tTAIC[ d, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TFR /: MakeBoxes[TFR[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", i, "\<0\>"}]], \n\t\tTFR[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TFR /: MakeBoxes[TFR[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", "\<0\>", i}]], \n\t\tTFR[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TFR /: MakeBoxes[TFR[dpp__, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[First[{dpp}], TraditionalForm], "\<)\>"}]], \n\t\tTFR[dpp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)], "Input"], Cell[BoxData[ \(TVR /: MakeBoxes[TVR[dpp__, {den__}], fmt_] := \n\((\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([\)\(1\)\(]\)], TraditionalForm], "\<)\>"}]], \n\t\(Hold[TVR]\)[ dpp, {den}], Editable -> True})\) /. Hold[TVR] -> TVR)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)], "Input"], Cell[BoxData[ \(TJR /: MakeBoxes[TJR[d_, 0, {den__}], fmt_] := \t\((\n\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[ TJR]\)[d, 0, {den}], Editable -> True})\) /. Hold[TJR] -> TJR)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\n\t)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TJR /: MakeBoxes[TJR[dpp__, {den__}], fmt_] := \t\((\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([\)\(1\)\(]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJR]\)[ dpp, {den}], Editable -> True})\) /. Hold[TJR] -> TJR)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TBR /: MakeBoxes[TBR[d_, pp___, {den__}], fmt_] := \n\t\((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TBR /: MakeBoxes[TBR[d_, pp___, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\tTBR[d, pp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(TAR /: MakeBoxes[TAR[d_, pp___, {den__}], fmt_] := \n\t\((InterpretationBox @@ {SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox @@ {\((redblue /@ {den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\tTAR[ d, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)], "Input"], Cell[BoxData[ \(n1 /: MakeBoxes[n1, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 1]; \)], "Input"], Cell[BoxData[ \(n2 /: MakeBoxes[n2, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 2]; \)], "Input"], Cell[BoxData[ \(n3 /: MakeBoxes[n3, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 3]; \)], "Input"], Cell[BoxData[ \(n4 /: MakeBoxes[n4, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 4]; \)], "Input"], Cell[BoxData[ \(n5 /: MakeBoxes[n5, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 5]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[ParD[i_]\^j_, TraditionalForm] := SubsuperscriptBox["\<\[PartialD]\>", i, j]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[ParD[i_], TraditionalForm] ^= SubscriptBox["\<\[PartialD]\>", i]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[DPlus, TraditionalForm] := StyleBox[SuperscriptBox["\", "\<+\>"], FontWeight \[Rule] "\", SingleLetterItalics \[Rule] False]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[TpD[_, b_], TraditionalForm] := MakeBoxes[b, TraditionalForm]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["The Palettes", "Subsection", CellTags->"T1.3.2.1"], Cell[BoxData[ \(If[$PutPalettes === True, \n\t\(\(tobut[a_]\ := \ ButtonBox[ToBoxes[a, StandardForm], \ ButtonStyle -> "\"]; \)\(\n\)\(\ \)\(If[ Head[pal1] === NotebookObject, \n\t NotebookClose[pal1]]; \)\(\n\)\(\t\)\(pal1 = NotebookPut[ Notebook[{Cell[ BoxData[ GridBox[\n\t\t\t\t\t\t\tJoin[ Transpose@{\n\t\t\t\t\t\t\t\t\tTable[ tobut@\(m\_j\^2\), {j, 5}], \n\t\t\t\t\t\t\t\t\tTable[ tobut@\[Nu]\_j, {j, 5}], \n\t\t\t\t\t\t\t\t\tTable[ tobut@Schiebe[i, "\<+\>"], {i, 5}], \n\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Table[tobut@Schiebe[i, "\<-\>"], {i, 5}]}, \n\t\t\t\t\t\t\t\(\({\t tobut /@ {PP, \[CapitalDelta]\_\[Placeholder], u\_\[Placeholder], \[ScriptCapitalC]\ }}\)\(\n\ \)\)\t\t\t\t\t\t\t], RowSpacings -> 0, \n\ \ \ \ \ \ ColumnSpacings -> 0]], NotebookDefault]}, \n\tEditable -> True, \n WindowToolbars -> {}, \nWindowSize -> {Fit, \ Fit}, \n WindowMargins -> {{0, \ Automatic}, \ {0, Automatic}}, \n WindowFrame -> "\", \nWindowElements -> {}, \n WindowFrameElements -> "\", \n WindowClickSelect -> False, \n ScrollingOptions -> {"\" -> True}, \n ShowCellBracket -> False, \n CellMargins -> {{0, \ 0}, \ {0, \ 0}}, \nActive -> True, \n CellOpen -> True, \nShowCellLabel -> False, \n ShowCellTags -> False, \n ImageMargins -> {{0, \ 0}, \ {0, \ 0}}, \nMagnification -> 2, Visible -> True]]; \)\(\n\)\(SetOptions[pal1, WindowMargins -> {{0, Automatic}, {Automatic, 0}}]; \)\(\n\)\(SetOptions[pal1, Visible -> True, WindowSize -> {Fit, Fit}]; \)\(\n\)\(\ \)\(If[ Head[pal2] === NotebookObject, \n\t NotebookClose[pal2]]; \)\(\n\)\(\t\)\(pal2 = NotebookPut[ Notebook[{Cell[ BoxData[ GridBox[\n\t\t\t\t\t\t\tJJJ = Join[{tobut /@ {TFI[ d + 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\ \_4, \[Nu]\_5}], TVI[d + 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\_4}], TJI[d + 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TKI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TBI[d, {\[Nu]\_1, \[Nu]\_2}], TAI[ d, {\[Nu]\_1}]}}, \n\t\t\t\t\t\t\t\t\ \(\({tobut /@ {TFI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\_4, \[Nu]\_5}], TVI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \ \[Nu]\_4}], TJI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TKI[d - 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TBI[d - 2, {\[Nu]\_1, \[Nu]\_2}], TAI[d - 2, {\[Nu]\_1}]}}\)\(\n\)\)\t\t\t\t\t\t\t\ ], RowSpacings -> 0, \n\ \ \ \ \ \ ColumnSpacings -> 0]], NotebookDefault]}, \n\tEditable -> True, \n WindowToolbars -> {}, \nWindowSize -> {FitAll, \ FitAll}, \n WindowMargins -> {{0, Automatic}, \ {0, Automatic}}, \n WindowFrame -> "\", \nWindowElements -> {}, \n WindowFrameElements -> "\", \n WindowClickSelect -> False, \n ScrollingOptions -> {"\" -> True}, \n ShowCellBracket -> False, \n CellMargins -> {{0, 0}, \ {0, 0}}, \nActive -> True, \n CellOpen -> True, \nShowCellLabel -> False, \n ShowCellTags -> False, \n ImageMargins -> {{0, 0}, \ {0, \ 0}}, \nMagnification -> 2, Visible -> True]]; \)\(\n\)\(SetOptions[pal2, WindowMargins -> {{Automatic, 15}, {Automatic, 4}}]; \)\(\n\)\(SetOptions[pal2, Visible -> True, WindowSize -> {Fit, Fit}]; \)\(\n\)\(\t\)\(SetOptions[pal2, WindowSize -> {Fit, Fit}]\)\(\n\)\)\t]; \)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["OperatorApply", "Subsection", CellTags->"T1.3.3.1"], Cell[BoxData[ \(OperatorApplyF[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TFI[ d_, {n15__}] :> \n\t\t\t\t\tTFI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TFI[ d_, {n15__}] :> \n\t\t\t\t\tTFI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TFI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"], Cell[BoxData[ \(OperatorApplyV[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TVI[ d_, {n15__}] :> \n\t\t\t\t\tTVI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TVI[ d_, {n15__}] :> \n\t\t\t\t\tTVI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TVI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"], Cell[BoxData[ \(OperatorApplyJ[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TJI[ d_, {n15__}] :> \n\t\t\t\t\tTJI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TJI[ d_, {n15__}] :> \n\t\t\t\t\tTJI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TJI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"], Cell[BoxData[ \(OperatorApplyK[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TKI[ d_, {n15__}] :> \n\t\t\t\t\tTKI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TKI[ d_, {n15__}] :> \n\t\t\t\t\tTKI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TKI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"], Cell[BoxData[ \(OperatorApplyK[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TKI[ d_, {n15__}] :> \n\t\t\t\t\tTKI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TKI[ d_, {n15__}] :> \n\t\t\t\t\tTKI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TKI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"], Cell[BoxData[ \(OperatorApplyB[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TBI[ d_, {n15__}] :> \n\t\t\t\t\tTBI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TBI[ d_, {n15__}] :> \n\t\t\t\t\tTBI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TBI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"], Cell[BoxData[ \(OperatorApplyA[x_ == y_] := Block[{sch}, \n\t\tsch\ = \ {Schiebe[i_, "\<+\>"]\^ni_. \ TAI[ d_, {n15__}] :> \n\t\t\t\t\tTAI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] + ni, i]], \n\t\t\t\t\(\(Schiebe[i_, "\<-\>"]\^ni_. \ TAI[ d_, {n15__}] :> \n\t\t\t\t\tTAI[d, ReplacePart[{n15}, {n15}[\([\)\(i\)\(]\)] - ni, i]]\)\(\n\)\)\t\t\t}; Map[Collect[Expand[#] //. sch, TAI[__], Factor] &, \n\t\t\tx == y]]; \)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["MassDerivative", "Subsection", CellTags->"T1.3.4.1"], Cell[BoxData[ RowBox[{ RowBox[{\(MassDerivative[ STLI[any__, {\n\ \ \ \ \ \ \ {al_, m1_}, {be_, m2_}, {ga_, m3_}, {de_, m4_}, {ep_, m5_}}], {{0, d1_}, {0, d2_}, \ {0, d3_}, \ {0, d4_}, \ {0, d5_}}]\), StyleBox[" ", FontWeight->"Plain"], StyleBox[":=", FontWeight->"Plain"], "\n", \(\((\ \(Pochhammer[al, d1]\ Pochhammer[be, d2]\ Pochhammer[ga, d3]\)*\n\ \ Pochhammer[de, d4]\ Pochhammer[ep, d5]\ )\)\ *\n\ STLI[any, {{al + d1, m1}, \ {be + d2, m2}, \ {ga + d3, m3}, \ {de + d4, m4}, \ {ep + d5, m5}}]\)}], ";"}]], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["TarasovT", "Subsection", CellTags->"T1.3.5.1"], Cell["\<\ TarasovT[abrs__, qq_ /; Head[qq] =!= List] := TarasovT[abrs, qq, {\"g\", \"g\", \"g\", \"g\", \"g\"}]\ \>", "Input"], Cell[BoxData[ \(TarasovT[r_, \ s_, \ qq_, \ {alp1_, alp2_, \ alp3_, alp4_, alp5_}]\ := \n Block[{\ al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22, dum1, dum2}, \n\ \(If[alp1\ === \ 0, \ al1\ = \ 0]; \ If[alp2\ === \ 0, \ al2\ = \ 0]; \)\n\ \(If[alp3\ === \ 0, \ al3\ = \ 0]; \)\n\(If[alp4\ === \ 0, \ al4\ = \ 0]; \ If[alp5\ === \ 0, \ al5\ = \ 0]; \)\n\ \(alrul\ = \ Select[{al1 :> I\ ParD[1], \ al2 :> I\ ParD[2], \ al3 :> I\ ParD[3], \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ al4 :> I\ ParD[4], \ al5 :> I\ ParD[5]}, \ \(! MatchQ[#, \ 0 :> _]\) &]; \)\n\ \(Q1\ = \ al3\ al5\ + \ al4\ al5\ + \ al2\ al3\ + \ al3\ al4; \)\n\ \(Q2\ = \ al4\ al5\ + \ al3\ al5\ + \ al1\ al4\ + \ al3\ al4; \)\n\ \(Q11\ = 1/\((\(-4\))\)\ \((\ al2\ + \ al4\ + \ al5\ )\); \)\n\ \(Q22\ = 1/\((\(-4\))\)\ \((\ al1\ + \ al3\ + \ al5\ )\); \)\n\ \(Q12\ = 1/\((\(-2\))\)\ al5; \)\n\t\t\(new = \n\ I^\((\(-r\) - s)\) \((\ D[\ Exp[\ I\ qq\ \((\n\ \ \ \ be1\ Q1\ + \ be2\ Q2\ + be1^2\ Q11\ + be2^2\ Q22\ + \ be1\ be2\ Q12\n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ )\)\ rho\ ], {be1, r}, {be2, s}\n\t\t\t\t]\ )\) /. \n\ \((\ Join[alrul, \ {be1\ :> \ 0, be2\ :> \ 0, \ rho\ :> \ \(-Pi^2\)/ Pi^2\ DPlus\ }])\); \(\(Map[\((Select[#, \ \((FreeQ[#, ParD] && FreeQ[#, DPlus])\) &]\ TpD[qq, Select[#, \((\(! \((FreeQ[#, ParD] && FreeQ[#, DPlus])\)\))\) &]])\) &, \(\((Expand[new, ParD] + \ dum1\ dum2)\)\(\n\)\)\t\t] /. {dum1 :> 0, dum2 :> 0}\)\(\n\)\)\)\t\t]; \)], "Input"], Cell[BoxData[ \(\(\(\n\)\(TarasovT[r_, \ s_, \ pp_, \ dp_ /; Head[dp] =!= List]\ := \ TarasovT[r, s, pp, dp, {"\", "\", "\", "\", "\"}]\)\)\)], "Input"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\((\[CapitalDelta]\ q\_1)\)\^a\)]], Cell[BoxData[ \(TraditionalForm\`\((\[CapitalDelta]\ q\_2)\)\^b\)]], Cell[BoxData[ \(TraditionalForm\`\((p\ q\_1)\)\^r\)]], Cell[BoxData[ \(TraditionalForm\`\((p\ q\_2)\)\^s\)]] }], "Text"], Cell[BoxData[ \(\(\(\n\)\(TarasovT[a_, b_, r_, s_, pp_, dp_, {alp1_, alp2_, alp3_, alp4_, alp5_}] := Block[{al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22, dum1, dum2}, If[alp1 === 0, al1 = 0]; If[alp2 === 0, al2 = 0]; If[alp3 === 0, al3 = 0]; If[alp4 === 0, al4 = 0]; If[alp5 === 0, al5 = 0]; alrul = Select[{al1 \[RuleDelayed] I\ ParD[1], al2 \[RuleDelayed] I\ ParD[2], al3 \[RuleDelayed] I\ ParD[3], al4 \[RuleDelayed] I\ ParD[4], al5 \[RuleDelayed] I\ ParD[5]}, \(\(\[InvisibleSpace]\)\(! \((MatchQ[#1, 0 \[RuleDelayed] _])\)\)\) &]; Q1 = al3\ al5 + al4\ al5 + al2\ al3 + al3\ al4; Q2 = al4\ al5 + al3\ al5 + al1\ al4 + al3\ al4; Q11 = \(-\(1\/4\)\)\ \((al2 + al4 + al5)\); Q22 = \(-\(1\/4\)\)\ \((al1 + al3 + al5)\); Q12 = \(-\(al5\/2\)\); new = I\^\(\(-r\) - s - a - b\)\ \[PartialD]\_\({be1, r}, {be2, s}, \ {ga1, a}, {ga2, b}\)Exp[ I\ \((\((be1\ pp + ga1\ dp)\)\ Q1 + \((be2\ pp + ga2\ dp)\)\ Q2 + be1\ \((be1\ pp + 2\ ga1\ dp)\)\ Q11 + be2\ \((be2\ pp + 2\ ga2\ dp)\)\ Q22 + \((be1\ be2\ pp + \((be1\ \ ga2 + be2\ ga1)\)\ dp)\)\ Q12)\)\ rho] /. Join[alrul, {be1 \[RuleDelayed] 0, be2 \[RuleDelayed] 0, ga1 :> 0, ga2 :> 0, rho \[RuleDelayed] \(-\(\(\[Pi]\^2\ DPlus\)\/\[Pi]\^2\)\)}]; \ \((Select[#1, FreeQ[#1, ParD] && FreeQ[#1, DPlus] &]\ TpD[pp, Select[#1, \(\(\[InvisibleSpace]\)\(! \((FreeQ[#1, ParD] && FreeQ[#1, DPlus])\)\)\) &]] &)\) /@ \((Expand[ new] + dum1\ dum2)\) /. {dum1 \[RuleDelayed] 0, dum2 \[RuleDelayed] 0}]; \)\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["ApplyTarasovT", "Subsection", CellTags->"T1.3.6.1"], Cell[BoxData[ \(ApplyTarasovT[tij_, \ exp_] := Block[{dump}, \n\t\tdump = Product[ParD[j]^dummy, {j, 5}]; \n\t\tExpand[ tij\ exp] /. \n\((STLI[de_, pp_, pe__List]\ TpD[tpp_, DPlus^i_. \ t_])\) :> \n\t MassDerivative[ STLI[\ de /. de :> \((de\ + \ 2\ i)\), pp, pe], \n\t\t\t\t\t\t\t\(\(t\ dump\ /. Times -> List\) /. Power[_, n_] :> {0, n}\) /. dummy -> 0]]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Misc", "Subsection", CellTags->"T1.3.7.1"], Cell[BoxData[ \(Prefactor1 /: \t\tPrefactor1[a_]^n_ := Prefactor1[a^n]\)], "Input"], Cell[CellGroupData[{ Cell["Colors", "Subsubsection", CellTags->"T1.3.7.1.1"], Cell[TextData[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], " ", StyleBox["TVI ", FontColor->RGBColor[0.2, 0.4, 0.8]], StyleBox["TFR ", FontColor->RGBColor[0, 0.6, 0]], StyleBox["TVR ", FontColor->RGBColor[0.2, 0.8, 1]], StyleBox["MakeFun ", FontColor->RGBColor[1, 0.6, 0.6]], StyleBox["Cayley ", FontColor->RGBColor[1, 0, 0.4]], StyleBox["CayleyD ", FontColor->RGBColor[1, 0.2, 1]], StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], StyleBox[" ", FontColor->RGBColor[1, 0.2, 1]], StyleBox["IFF ", FontColor->RGBColor[0.6, 0.4, 1]], StyleBox["ToArgs ", FontColor->RGBColor[0.2, 0.6, 1]], StyleBox["Block", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]] }], "Text"], Cell[BoxData[ \(MakeBoxes[Block, StandardForm] := StyleBox["\", FontSize \[Rule] 16, FontWeight \[Rule] "\", FontColor \[Rule] RGBColor[1, 0.2, 0.2]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[Cayley, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[1, 0, 0.4]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[CayleyD, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[1, 0.2, 1]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[Cayleyu, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[0.8, 0.8, 0.4]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[IFF, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[0.6, 0.4, 1]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[MakeFun, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[1, 0.6, 0.6]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[TFI, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[1, 0.6, 0]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[TFR, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[0, 0.6, 0]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[ToArgs, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[0.2, 0.6, 1]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[TVI, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[0.2, 0.4, 0.8]]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[TVR, StandardForm] := StyleBox["\", FontColor \[Rule] RGBColor[0.2, 0.8, 1]]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["PQ", "Subsubsection", CellTags->"T1.3.7.2.1"], Cell[BoxData[ \(PQ[_Integer?Positive]\ := \ True; \)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["PNQ", "Subsubsection", CellTags->"T1.3.7.3.1"], Cell[BoxData[ \(PNQ[0] = True; \)], "Input"], Cell[BoxData[ \(PNQ[_Integer?Positive]\ := \ True; \)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["FactorC", "Subsubsection", CellTags->"T1.3.7.4.1"], Cell[BoxData[ \(FactorC[z_] := \(FactorC[z] = Factor[z]\)\)], "Input"], Cell["\<\ TFI[depp__,{a___,b_Integer,c___}]:=TFI[depp,{a,{b,0},c}]; TFI[depp__,{a___,{0,m_/;m=!=0},b___}]:=TFI[depp,{a,{0,0},b}]; TFI[a__,{0,0},b__List]:=TFI[a,b]; TFI[d_,pp_,dp_,{0,0},{x1_,x2_,x3_,x4_,x5_},list_List]:= TFI[d,pp,{x1,x2,x3,x4,x5},list]; TFI[d_,pp_,dp_,{a_,b_},{0,0,0,0,0},list_List]:=TFI[d,pp,dp,{a,b},list]; TFI[d_,pp_,dp_/;Head[dp]=!=List,{0,0,0,0,0},list_List]:=TFI[d,pp,list]; TFI[d_,pp_,dp_/;Head[dp]=!=List,list_List]:=TFI[d,pp,list]; TFI[d_,pp_,dp_/;Head[dp]=!=List,{x1_,x2_,x3_,x4_,x5_},list_List]:= TFI[d,pp,{x1,x2,x3,x4,x5},list]; TFI[__,{{_,_},{0,0},{_,_},{0,0},{_,0}}]:=0; TFI[__,{{0,0},{_,_},{0,0},{_,_},{_,0}}]:=0; TFI[__,{{0,0},{_,_},{_,0},{_,_},{0,0}}]:=0; TFI[__,{{_,0},{_,_},{0,0},{_,_},{0,0}}]:=0; TFI[__,{{_,_},{_,0},{_,_},{0,0},{0,0}}]:=0; TFI[__,{{_,_},{0,0},{_,_},{_,0},{0,0}}]:=0; TFI[__,{{0,0},{0,0},{0,0},{_,0},{_,_}}]:=0; TFI[__,{{0,0},{0,0},{_,0},{0,0},{_,_}}]:=0; TFI[__,{{0,0},{_,0},{0,0},{0,0},{_,_}}]:=0; TFI[__,{{_,0},{0,0},{0,0},{0,0},{_,_}}]:=0; TFI[__,{{_,_},{_,0},{0,0},{0,0},{0,0}}]:=0; TFI[__,{{_,0},{_,_},{0,0},{0,0},{0,0}}]:=0; TFI[__,{{_,_},{0,0},{0,0},{_,0},{0,0}}]:=0; TFI[__,{{_,0},{0,0},{0,0},{_,_},{0,0}}]:=0; TFI[__,{{0,0},{_,0},{_,_},{0,0},{0,0}}]:=0; TFI[__,{{0,0},{_,_},{_,0},{0,0},{0,0}}]:=0; TFI[__,{{0,0},{0,0},{_,_},{_,0},{0,0}}]:=0; TFI[__,{{0,0},{0,0},{_,0},{_,_},{0,0}}]:=0; If[$Notebooks, mbt[z_] := ToBoxes[z, TraditionalForm]; redblue[z_ /; Head[z] =!= Plus] := mbt[z]; redblue[(z_) - 1] := StyleBox[mbt[z], FontColor -> RGBColor[1, 0, 0]]; redblue[(z_Subscript) - 2] := StyleBox[SubscriptBox[OverscriptBox[z[[1]], \"_\"], z[[2]]], FontColor -> RGBColor[1, 0, 0]]; redblue[(z_) - 2] := StyleBox[OverscriptBox[mbt[z], \"_\"], FontColor -> RGBColor[1, 0, 0]]; redblue[(z_) - 3] := StyleBox[UnderscriptBox[OverscriptBox[mbt[z], \"_\"], \"_\"], FontColor -> RGBColor[1, 0, 0]]; redblue[(z_) + 1] := StyleBox[mbt[z], FontColor -> RGBColor[0, 0, 1]]; redblue[(z_) + 2] := StyleBox[OverscriptBox[mbt[z], \"_\"], FontColor -> RGBColor[0, 0, 1]]; redblue[(z_Subscript) + 2] := StyleBox[SubscriptBox[OverscriptBox[z[[1]], \"_\"], z[[2]]], FontColor -> RGBColor[0, 0, 1]]; TFI/: MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], TraditionalForm] := InterpretationBox @@ {SubsuperscriptBox[StyleBox[\"F\", Rule[SingleLetterItalics, False], Rule[FontWeight, \"Bold\"]], RowBox @@ {redblue /@ {den}}, RowBox[{\"(\", ToBoxes[d, TraditionalForm], \")\", \" \", ur}]], TFI[d, pp, {ur}, {den}], Editable -> True} /; MemberQ[{StandardForm, TraditionalForm}, TraditionalForm]; TFI/: MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], TraditionalForm] := (InterpretationBox @@ {SubsuperscriptBox[StyleBox[\"F\", Rule[SingleLetterItalics, False], Rule[FontWeight, \"Bold\"]], RowBox @@ {redblue /@ {den}}, RowBox[{\"(\", ToBoxes[d, TraditionalForm], \")\", \" \", Sequence @@ Flatten[{any}]}]], TFI[d, pp, dp, any, {den}], Editable -> True}) /; Head[dp] =!= List; TFI/: MakeBoxes[TFI[dpp__, {den__}], TraditionalForm] := InterpretationBox @@ {SubsuperscriptBox[StyleBox[\"F\", Rule[SingleLetterItalics, False], Rule[FontWeight, \"Bold\"]], RowBox @@ {redblue /@ {den}}, RowBox[{\"(\", ToBoxes[First[{dpp}], TraditionalForm], \")\"}]], TFI[dpp, {den}], Editable -> True} /; MemberQ[{StandardForm, TraditionalForm}, TraditionalForm] && Head[Last[{dpp}]] =!= List; ];\ \>", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["TJI", "Subsubsection", CellTags->"T1.3.7.6.1"], Cell[BoxData[ \(TJI[de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}, {n3_Integer, m3_}}] := \((TJI[de, pp, {{n1, m1}, {n2, m2}, {n3, m3}}] = TJI[de, pp, Reverse[Sort[{{n1, m1}, {n2, m2}, {n3, m3}}]]])\) /; \(\(\[InvisibleSpace]\)\(! \ \((OrderedQ[{{n3, m3}, {n2, m2}, {n1, m1}}])\)\)\)\)], "Input"], Cell[BoxData[ \(TJI[d, pp, {{1, m1}, {1, m2}, {1, m3}}]\)], "Input"], Cell[BoxData[ \(TJI[d_, 0, {{_, 0}, {_, 0}, {_, 0}}] := 0\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["TBI", "Subsubsection", CellTags->"T1.3.7.7.1"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["TBI", FontColor->RGBColor[1, 0.6, 0]], "[", \(de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}}\), "]"}], ":=", RowBox[{ RowBox[{"(", RowBox[{\(TJI[de, pp, {{n1, m1}, {n2, m2}}]\), "=", RowBox[{ StyleBox["TBI", FontColor->RGBColor[1, 0.6, 0]], "[", \(de, pp, Reverse@\(Sort@{{n1, m1}, {n2, m2}}\)\), "]"}]}], ")"}], "/;", "\[InvisibleSpace]", \(! \((OrderedQ[{{n2, m2}, {n1, m1}}])\)\)}]}]], "Input"], Cell[BoxData[ \(TBI[d_, 0, {{_, 0}, {_, 0}}] := 0\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["TAI", "Subsubsection", CellTags->"T1.3.7.8.1"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["TAI", FontColor->RGBColor[1, 0.6, 0]], "[", \(de_, pp_, {{n1_Integer, 0}}\), "]"}], ":=", "0"}], ";"}]], "Input"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Definitions and notation", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.4.1"], Cell[BoxData[ RowBox[{ RowBox[{"\[CapitalDelta]\[ScriptCapitalC]", "=", RowBox[{\(-\(1\/2\)\), RowBox[{"Det", "[", " ", RowBox[{"(", GridBox[{ {"0", "1", "1", "1", "1"}, {"1", "0", \(\[Mu]\_6\), \(\[Mu]\_4\), \(\[Mu]\_3\)}, {"1", \(\[Mu]\_6\), "0", \(\[Mu]\_2\), \(\[Mu]\_1\)}, {"1", \(\[Mu]\_4\), \(\[Mu]\_2\), "0", \(\[Mu]\_5\)}, {"1", \(\[Mu]\_3\), \(\[Mu]\_1\), \(\[Mu]\_5\), "0"} }], ")"}], "]"}]}]}], ";"}]], "Input"], Cell[BoxData[ \(checkli\ = \ {\n\t\t\[ScriptCapitalC] -> \[CapitalDelta]\ \[ScriptCapitalC], \n\[CapitalDelta]\_i_ :> \[PartialD]\_\(\[Mu]\_i\)\ \[CapitalDelta]\[ScriptCapitalC], \n\t\t\[Mu]\_6 :> PP, \[Mu]\_i_ :> ToExpression["\" <> ToString[i]]^2, \n\t\tm\_1 :> \@m1\^2, m\_2 :> \@m2\^2, m\_3 :> \@m3\^2, m\_4 :> \@m4\^2, m\_5 :> \@m5\^2, \n\[CapitalDelta]\_\(i_, j_, k_\) :> \[Mu]\_i\%2 + \ \[Mu]\_j\%2 + \[Mu]\_k\%2 - 2 \((\(\[Mu]\_i\) \[Mu]\_j + \(\[Mu]\_j\) \[Mu]\_k + \(\[Mu]\_k\) \ \[Mu]\_i)\), \n u\_\(i_, j_, k_\) :> \[Mu]\_i - \[Mu]\_j - \[Mu]\_k, \n\ \[CapitalSigma]\_i_ :> 3\ d\ - 2\ \((\[Sum]\_\(j = 1\)\%i \[Nu]\_j)\) - 2, \n\t\[Nu]\_1 \[RuleDelayed] n1, \[Nu]\_2 \[RuleDelayed] n2, \[Nu]\_3 \[RuleDelayed] n3, \[Nu]\_4 \[RuleDelayed] n4, \[Nu]\_5 \[RuleDelayed] n5}; 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TVIC -> TVIkernel, {1, 2, 1, 1, 2}])\) - Extract[expr /. TVI -> TVIkernel, {1, 2, 1, 2}])\); \n If[\ {TVIkernel} === Union[Head /@ Cases[rel, ff_[__] /; Context[ff] =!= "\", 4]], \t\n rel = Collect[Numerator[Together[rel]], \ TVI[__], Factor]; \n kern = rel /. TVIkernel -> TVIKernel; \n kern = kern /. {PP -> \(-1\), m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3], m4 -> Sqrt[z4]}; \n kern = PowerExpand[kern]; \nkern = Expand[kern]; \n kern = kern /. {\(z1\^\(s1 + w1_. \)\) \(z2\^\(s2 + w2_. \)\) \(z3\^\(s3 + w3_. \)\) \(z4\^\(s4 + w4_. \)\) fac_ :> \((fac /. {s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3, s4 -> s4 - w4})\)}\ ; \n kern = \(\(kern /. TVIpsi -> TVIPsi\) /. {gamma[zz_] :> gamma[Expand[zz]]}\) /. {gamma[zz_ + nn_Integer] :> gamma[zz] Pochhammer[zz, nn]}; \n\t\t\t\tKERN = kern; \n kern = kern /. {gamma[zz_] :> 1}; \n kern = \(kern /. {\((\(-1\))\)\^\(nn_ + ww_Integer\) :> \ \((\(-1\))\)\^ww}\) /. {\((\(-1\))\)\^nn_ :> 1}; \n nkern = Table[\n\t\t\tkern /. Thread[{d, \ n1, \ n2, \ n3, n4, s1, s2, \ s3, s4} -> Table[Random[], {9}]], {3}]; \n nkern\ \ , \n\t\tPrint["\"]\ ]\ ], \n\t\t\ If[$Notebooks, Print["\"]]]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["CheckTJIRecursion", "Subsubsection", CellTags->"T1.5.3.2.1"], Cell[BoxData[ \(TJIKernel[d_, PP, \ lis_] := \n\(\((\(-PP\))\)\^\(d - n1 - n2 - n3\)\) \(\((m1\^2\/\(-PP\))\)\^s1\) \ \(\((m2\^2\/\(-PP\))\)\^s2\) \((m3\^2\/\(-PP\))\)\^s3* TJIpsi\ [ d, \ \((lis /. {m1 -> s1, m2 -> s2, m3 -> s3})\)]; \)], "Input"], Cell[BoxData[ \(TJIPsi\ [d_, {{n1_, \ s1_}, \ {n2_, s2_}, {n3_, s3_}}] := Evaluate[TVIPsi[d, \n\t{{n1, \ s1}, \ {n2, s2}, {n3, s3}, {0, 0}}]/ gamma[0]]\)], "Input"], Cell[BoxData[ \(Clear[CheckTJIRecursion]; \)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[expr_] := \ If[\ $CheckRecursion === True, \n\t Block[{rel, kern, nkern}, \n rel = \((\((Extract[ expr /. TJIC -> TJIkernel, {1, 2, 1, 1, 2}])\) - Extract[ expr /. 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{(n2_)?PQ, m2_}, {(n3_)?PQ, m3_}, {(n4_)?PQ, m4_}, {(n5_)?PQ, m5_}}] := (TComment[\"(50)\", TFIC[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}]]; Block[{r1 = 3 - d, r2 = 4 - d, r3 = -(m1^2*m2^2*m3^2) + m2^4*m3^2 + m2^2*m3^4 + m1^4*m4^2 - m1^2*m2^2*m4^2 - m1^2*m3^2*m4^2 - m2^2*m3^2*m4^2 + m1^2*m4^4 + m1^2*m2^2*m5^2 - m2^2*m3^2*m5^2 - m1^2*m4^2*m5^2 + m3^2*m4^2*m5^2 + m1^2*m3^2*PP - m2^2*m3^2*PP - m1^2*m4^2*PP + m2^2*m4^2*PP - m1^2*m5^2*PP - m2^2*m5^2*PP - m3^2*m5^2*PP - m4^2*m5^2*PP + m5^4*PP + m5^2*PP^2, r4 = -4 + d, r5 = -3 + d, r6 = -7 + 2*d, r7 = -(m2^2*r4) + m3^2*r5 - m5^2*r5 + m4^2*r6, r8 = -10 + 3*d, r9 = -m3^2 + m4^2, r10 = -11 + 3*d, r11 = -(m4^2*r10) - 3*m5^2*r5 + m3^2*r6, r12 = m2^2*r11 + m5^4*r5 + m2^4*r8 + m4^2*r4*r9 + m5^2*r5*r9, r13 = -6 + d, r14 = -(m4^2*r13) + m5^2*r5, r15 = -3*m3^2 - m4^2*r10 + m5^2*r5, r16 = m3^2*r14 + m2^2*r15 + m2^4*r4 - 2*m3^4*r5 - 3*m4^2*m5^2*r5 + m5^4*r5 + m4^4*r8, r17 = m3^2 + 2*m4^2, r18 = -1 + d, r19 = -(m3^2*r13) - 2*m4^2*r18 + 2*m5^2*r5, r20 = 2*m2^4 - 3*m3^4 + d*m3^4 - 3*m3^2*m4^2 + 2*m4^4 + m2^2*r19 - 2*m5^4*r5 + m5^2*r17*r5, r21 = 2 + d, r22 = 2*m5^2 - m4^2*r21 + m2^2*r4 - m3^2*r4, r23 = -7 + d, r24 = 6*m4^2 - 4*m5^2, r25 = 3*m3^2 + m4^2*r18 + m5^2*r23, r26 = -6*m4^4 - 2*m4^2*m5^2*r23 + m3^2*r24 + 2*m2^2*r25 - 2*m2^4*r4 - m3^4*r4, r27 = m3^4 + m3^2*m4^2 - 2*m4^4, r28 = m3^2 + m4^2*r23, r29 = -2*m4^2*r18 + m3^2*r21 + 2*m5^2*r23, r30 = -6*m2^4 + 2*m5^2*r28 - m2^2*r29 + r27*r4, r31 = m1^4*r22 + m1^2*r26 + m3^2*r30 + m1^6*r4, r32 = m3 - m4, r33 = m3 + m4, r34 = 2*m3^2 + m4^2, r35 = -17 + 3*d, r36 = m3^2*r23 + m4^2*r35, r37 = -9 + d, r38 = 17 - 3*d, r39 = 5*m3^2 + m4^2*r37 + m5^2*r38, r40 = 1 + d, r41 = 5*m4^2 - m5^2*r23 + m2^2*r4 - m3^2*r40, r42 = m5^4*r35 - m5^2*r36 + m2^2*r39 - 2*m1^4*r4 + m2^4*r4 - r32*r33*r34*r4 + m1^2*r41, r43 = m1^2 - m2^2 + m3^2 - m4^2, r44 = 2*m5^2*r13 + r4*r43, r45 = m3^4*r12 + m1^4*r16 + m1^2*m3^2*r20 + PP*r31 + PP^2*r42 + PP^3*r44 + m1^6*r7, r46 = m2^2 + m4^2, r47 = 13 - 3*d, r48 = m4^2*r47 - m5^2*r5 + m3^2*r6, r49 = m5^4*r5 + m5^2*r32*r33*r5 + m4^2*r4*r9, r50 = -18 + 4*d, r51 = -(m4^2*r13) - 3*m5^2*r5, r52 = 2*m3^4*r5 + m4^2*m5^2*r5 + m5^4*r5 + m4^4*r50 + m3^2*r51, r53 = -3*m4^2 + 2*m5^2*r5, r54 = m4^4*r47 + 2*m3^4*r5 + m4^2*m5^2*r5 - 2*m5^4*r5 + m3^2*r53, r55 = m4^2*r13 + 6*m3^2*r5 - 2*m5^2*r5, r56 = 3*m4^2 + m3^2*r5 - m5^2*r5, r57 = 7 - 2*d, r58 = m3^2*r5 + 3*m5^2*r5 + m4^2*r57, r59 = m2^6*r4 + m2^2*m4^2*r55 + m2^4*r56 + m4^4*r58, r60 = m4^2 - m3^2*r5, r61 = 10 - 3*d, r62 = 2*m5^2 + 3*m4^2*r4 + m3^2*r61, r63 = m4^2 + m5^2*r5, r64 = -4*m4^2*m5^2 + 3*m4^4*r4 - 2*m3^4*r5 + 2*m3^2*r63, r65 = m4^2 + m3^2*r5 - m5^2*r5, r66 = 2*m3^2*r5 + 2*m5^2*r5 + m4^2*r61, r67 = 3*m2^4*r4 + 2*m2^2*r65 + m4^2*r66, r68 = -3*m2^6*r4 - 2*m1^4*m4^2*r5 + 2*m4^2*m5^2*r60 + m2^4*r62 + m2^2*r64 + m1^2*r67 - 3*m4^4*r4*r9, r69 = -13 + 3*d, r70 = m3^2*r5 + m4^2*r69, r71 = m4^2 - 3*m2^2*r4 - m3^2*r5 + m5^2*r5, r72 = -5 + d, r73 = m3^2 + m5^2*r69 + m4^2*r72, r74 = 3*m2^4*r4 - m5^4*r5 + m5^2*r70 + m1^2*r71 + m2^2*r73 + 3*m4^2*r4*r9, r75 = m1^2 - m2^2 + m3^2 - m4^2 - 2*m5^2, r76 = m2^8*r4 + m2^6*r48 + m4^4*r49 + 2*m1^4*m4^2*r46*r5 + m2^4*r52 + m2^2*m4^2*r54 - m1^2*r59 + PP*r68 + PP^2*r74 + PP^3*r4*r75, r77 = m3^2 - m4^2 + m5^2, r78 = -2*m2^2 + m4^2 + m5^2, r79 = -2*m1^2 - m3^2 - m4^2 + m5^2, r80 = m1^4 + PP^2 - m1^2*r77 + m3^2*r78 + PP*r79, r81 = m3^2 + m4^2, r82 = m3^2 + m4^2 + m5^2, r83 = m1^2 + m3^2 - m5^2, r84 = m1^4 + 2*m3^2*m4^2 - m4^4 + PP^2 - m2^2*r77 + m5^2*r81 - m1^2*r82 - 2*PP*r83, r85 = m1 - m3, r86 = -PP + r85^2, r87 = m1 + m3, r88 = -PP + r87^2, r89 = m2 - m4, r90 = m2 + m4, r91 = -m1^2 - m2^2 - m3^2 - m4^2 + 2*m5^2, r92 = PP^2 + r85*r87*r89*r90 + PP*r91, r93 = m2^2 - 3*m4^2, r94 = m4 - m5, r95 = m4 + m5, r96 = 2*m3^2 - m4^2 + m5^2, r97 = -m1^2 - m2^2 - 2*m3^2 + 3*m5^2, r98 = PP^2 + m1^2*r93 + m2^2*r94*r95 + m4^2*r96 + PP*r97, r99 = -2 + d, r100 = -m1^2 + m2^2, r101 = m2^2 + m1^2*r72, r102 = m3^2*r101 - 2*m3^4*r4 + m2^2*r100*r4, r103 = 9 - 2*d, r104 = m2^2*r23 + m3^2*r72, r105 = 2*m1^4 + m2^4*r103 + m1^2*r104 + m2^2*m3^2*r5, r106 = -9 + 2*d, r107 = m1 - m2, r108 = m1 + m2, r109 = -(r106*r107*r108) + m3^2*r4, r110 = m2^2*r102 + m4^2*r105 + m4^4*r109 - m4^6*r4, r111 = m1^2 + m2^2, r112 = m2^2*r4 - 2*m1^2*r72, r113 = -19 + 5*d, r114 = m3^2*r112 + m3^4*r113 + m2^2*r111*r4, r115 = m3^2*r5 + m2^2*r6, r116 = 2*m1^4 + 2*m1^2*r115 + m2^4*r13 + m3^4*r72 - 2*m2^2*m3^2*r99, r117 = m2^2*r106 + m3^2*r4 - m1^2*r99, r118 = m2^2*r114 - m4^2*r116 + m4^4*r117 - m4^6*r6, r119 = -(m2^2*r5) + 2*m3^2*r57 + m1^2*r72, r120 = m1^2*r18 + 2*m3^2*r4 - m2^2*r5, r121 = m2^2*r119 + m4^2*r120 + 2*m4^4*r5, r122 = m3^2*r5 + m4^2*r72, r123 = -2*m2^2*r4 - m4^2*r69 + m3^2*r72, r124 = m2^2*r122 + m1^2*r123 + 2*m2^4*r4 + 2*m4^2*r32*r33*r4, r125 = -3*m4^2 + m2^2*r4 - m3^2*r72, r126 = m3^2 - m4^2*r72, r127 = -2*m3^2*m4^2 - 2*m1^2*r125 - 2*m2^2*r126 + m4^4*r18 - 4*m2^4*r4 + m3^4*r72, r128 = -(m2^2*r18) + 2*m4^2*r5 + m1^2*r72 + 2*m3^2*r72, r129 = m5^2*r127 - m5^4*r128 - r124*r32*r33 + m5^6*r72, r130 = -m1^2 + m2^2 + m3^2 - m4^2, r131 = -14 + 3*d, r132 = -(m3^2*r13) + m4^2*r131 + m1^2*r4 + 5*m2^2*r4, r133 = -2*m5^4 + m5^2*r132 + r130*r32*r33*r4, r134 = m5^2*r118 + m5^4*r121 + PP*r129 + PP^2*r133 + r110*r32*r33 - 2*m5^2*PP^3*r4 + m5^6*r5*r89*r90, r135 = m3 - m4 - m5, r136 = m3 + m4 - m5, r137 = m3 - m4 + m5, r138 = m3 + m4 + m5, r139 = -10 + d, r140 = 13 - 2*d, r141 = d*m4^2 + 2*m3^2*r5, r142 = -8 + d, r143 = m4^2*r142 - m3^2*r99 + m5^2*r99, r144 = m3^2*m4^2*r139 + m4^4*r140 - m5^2*r141 + m2^2*r143 + m3^4*r5 + m5^4*r5, r145 = 3*m3^4 - 12*m3^2*m4^2 + 7*m4^4, r146 = 3*m3^2 + 4*m4^2, r147 = m3^2 - 11*m4^2, r148 = 7*m3^4 + 10*m3^2*m4^2 - 17*m4^4 - 5*m5^4 - 2*m5^2*r147, r149 = m2^2 + 2*m3^2 + m4^2, r150 = -m2^4 + m2^2*m3^2 + m3^4 + 3*m2^2*m4^2 + m3^2*m4^2 - m4^4 + m5^4 - m5^2*r149, r151 = 3*m3^6 + 6*m3^4*m4^2 - 17*m3^2*m4^4 + 8*m4^6 + 3*m5^6 - m5^2*r145 - m5^4*r146 + m2^2*r148 - d*r150*r77 + 6*m2^4*r94*r95, r152 = -(m3^2*m4) + m4^3, r153 = 11 - 2*d, r154 = -(d*m3^2*m4^2) + m4^4*r153 + m3^4*r5, r155 = m4^2 + m3^2*r5, r156 = r142*r32*r33 + m5^2*r99, r157 = 11 - 3*d, r158 = -8 + 3*d, r159 = m5^2*r158 + m4^2*r21, r160 = -3*m3^4 + 2*m4^2*m5^2*r106 + m5^4*r157 + m3^2*r159 - m4^4*r18, r161 = -2*m2^6 + m5^2*r154 - 2*m5^4*r155 + m2^4*r156 + m2^2*r160 + r152^2*r4 + m5^6*r5, r162 = m4^2*r23 - 3*m3^2*r72, r163 = -4*m2^2 + m4^2*r18 + m3^2*r23, r164 = -m3^4 + m4^4, r165 = -(m2^4*r13) + m2^2*r162 + m1^2*r163 + r164*r4 + m1^4*r99, r166 = -19 + 4*d, r167 = m4^2 + m3^2*r72, r168 = m3^2 + m4^2*r69, r169 = -2*r168 + 4*m2^2*r4, r170 = -m3^4 + m2^4*r13 - m4^4*r166 + 2*m2^2*r167 + m1^2*r169 + 2*m3^2*m4^2*r72 + m1^4*r99, r171 = m1^2 - m2^2 + 4*m4^2, r172 = -(m5^2*r170) + r165*r32*r33 + m5^6*r72 - m5^4*r171*r72, r173 = m2^2 + m3^2, r174 = -(m4^2*r13) + r131*r173 + m1^2*r8, r175 = m5^2*r174 - 2*m5^4*r4 + r130*r32*r33*r4, r176 = 2*m1^6*m4^2 + m1^4*r144 + m1^2*r151 + m3^2*r161 + PP*r172 + PP^2*r175 - 2*m5^2*PP^3*r4, r177 = m3^2 + m4^2 - m5^2, r178 = -2*m1^2 + m3^2 - m4^2 + m5^2, r179 = -m3^2 + m4^2 + m5^2, r180 = m2^2*r177 + m4^2*r178 + PP*r179, r181 = -2*m2^2 - m3^2 + m4^2 + m5^2, r182 = m1^2*r177 + m3^2*r181 + PP*r77, r183 = -(m2^2*r13) - 2*m3^2*r5, r184 = m1^2*r183 - 2*m3^4*r4 + m2^4*r57 + m1^4*r72 - m2^2*m3^2*r99, r185 = 3*m2^2*r4 + m3^2*r72, r186 = m2^4*r106 + 2*m1^2*r185 + m1^4*r40 - 2*m2^2*m3^2*r6, r187 = r111*r13 - m3^2*r4, r188 = m2^2*r184 + m4^2*r186 - m4^4*r187 + m4^6*r4, r189 = 2*m1^2 + m3^2*r10 + 2*m2^2*r5, r190 = m2^2*r5 + m3^2*r72 + 2*m1^2*r99, r191 = m2^2*r189 - m4^2*r190 - m4^4*r5, r192 = -(m3^2*r5) - m4^2*r72, r193 = 2*m2^2*r4 + m4^2*r69 - m3^2*r72, r194 = m2^2*r192 + m1^2*r193 - 2*m2^4*r4 + 2*m4^2*r4*r9, r195 = m2^2 + m4^2 + m3^2*r72, r196 = -(m3^2*r6) - m4^2*r72, r197 = m2^4*r157 + 2*m1^2*r195 + 2*m2^2*r196 + 2*m4^2*r17*r4 + m1^4*r72, r198 = m4^2*r10 - 2*m2^2*r5 + 2*m1^2*r72 + m3^2*r72, r199 = r107*r108*r194 + m5^2*r197 - m5^4*r198 + m5^6*r72, r200 = m1^2 - m2^2 - m3^2 + m4^2, r201 = m1^2 + m2^2 + m3^2 + 5*m4^2, r202 = 2*m5^4 - r107*r108*r200 - m5^2*r201, r203 = r107*r108*r110 - m5^2*r188 - m5^4*r191 + PP*r199 + 2*m5^2*PP^3*r4 + PP^2*r202*r4 + m5^6*r5*r89*r90, r204 = m4^2 + m5^2, r205 = -2*m5^2*r5 + m4^2*r99, r206 = 18 - 5*d, r207 = m4^2*r206 + m5^2*r8 - 2*m3^2*r99, r208 = m2^2*r207 + 2*m2^4*r4 - m3^4*r5 - m3^2*r204*r5 + r205*r94*r95, r209 = 2*m3^2*m4^2 + m4^4*r142 + 2*m3^4*r5, r210 = -(m4^2*r18) + m3^2*r5, r211 = 3 - 2*d, r212 = m5^2 + m4^2*r157 + m3^2*r211, r213 = m4^2*r106 + m3^2*r4, r214 = -(d*m3^4) + 10*m3^2*m4^2 - 2*d*m3^2*m4^2 - 2*m4^4 + d*m4^4 + 2*m5^2*r213 - 2*m5^4*r4, r215 = d*m3^2*m4^4 - 2*m4^6 - m5^2*r209 + m5^4*r210 + m2^4*r212 + m2^2*r214 + m2^6*r4 + m5^6*r5 - m3^4*m4^2*r99, r216 = m4^2*r13 + m3^2*r99, r217 = m3^2*r5 - m4^2*r72, r218 = 13 - 4*d, r219 = 3*m3^2 + m5^2*r218 + m4^2*r23, r220 = m4^2*r142 + m5^2*r61, r221 = 2*m3^4 + 2*m4^2*m5^2 - m4^4*r13 + m3^2*r220 + 2*m5^4*r6, r222 = m4^2*m5^2*r216 + m5^4*r217 + m2^4*r219 + m2^2*r221 - m5^6*r5 + m2^6*r99, r223 = -(m3^2*r10) + m4^2*r5, r224 = 4*m3^2*m4^2 + m1^2*r122 + m4^4*r13 + m2^2*r223 + m1^4*r4 - m2^4*r4 - m3^4*r99, r225 = -m3^2 + m2^2*r72 - m4^2*r72, r226 = -2*m4^2*r106 + 2*m3^2*r69, r227 = m1^4*r106 + m2^4*r106 - m4^4*r13 - 2*m1^2*r225 + m2^2*r226 - 4*m3^2*m4^2*r4 - m3^4*r99, r228 = m3^2 + 3*m4^2, r229 = r107*r108*r224 - m5^2*r227 + m5^6*r72 - m5^4*r228*r72, r230 = m4^2*r131 + m1^2*r4 + m2^2*r4 + m3^2*r8, r231 = 2*m5^4*r106 - m5^2*r230 - r107*r108*r200*r4, r232 = m1^4*r208 - m1^2*r215 - m3^2*r222 + PP*r229 + PP^2*r231 + 2*m5^2*PP^3*r4 + m1^6*r7, r233 = -2*m3^2 + m4^2, r234 = -m2^2 + m4^2 - 2*m5^2, r235 = -m1^2 + m2^2 + m5^2, r236 = m1^4 + m5^4 + m2^2*r233 + m1^2*r234 + PP*r235 - m5^2*r46, r237 = -m2^2 + m5^2, r238 = m2^2 + m3^2 - 2*m4^2 + m5^2, r239 = -m1^2 + m2^2 - m5^2, r240 = m1^4 + m3^2*r237 - m1^2*r238 + PP*r239, r241 = m3^2 + 3*m4^2 - m5^2, r242 = -3*m3^2 - m4^2 + m5^2, r243 = m5^4 - m5^2*r228 + m1^2*r241 + m2^2*r242 + 2*PP*r32*r33 + 2*m4^2*r9, r244 = 2*m1^2 + m2^2 + m4^2, r245 = -2*m1^2 - m3^2 - m4^2 + 3*m5^2, r246 = m1^4 - 3*m2^2*m3^2 + m5^4 + PP^2 + m4^2*r173 - m5^2*r244 + PP*r245, r247 = -2*m3^2 + m4^2 + m5^2, r248 = -m2^4 - m4^2*m5^2 + PP*r235 + m2^2*r247 + m1^2*r46, r249 = m2^2*r153 + m1^2*r5, r250 = 2*m1^2 + m2^2*r4, r251 = m2^2*r13 + m1^2*r139, r252 = r107*r108*r250 + m3^2*r251 - m3^4*r4, r253 = m1^2*r140 + 2*m3^2*r4 + m2^2*r72, r254 = m3^4*r249 + m4^2*r252 + m4^4*r253 - m4^6*r4 + m2^2*m3^2*r100*r99, r255 = 2*m3^2 + m4^2*r13, r256 = -2*m3^2*r5 + m2^2*r99 - m4^2*r99, r257 = -11 + 2*d, r258 = -(m4^4*r106) + 2*m3^2*m4^2*r23 - m3^4*r257, r259 = 4*m4^2 + m3^2*r13, r260 = -2*m2^4 + 6*m3^2*m4^2 + 2*m2^2*r259 + m4^4*r37 + m3^4*r5, r261 = -5*m3^4*m4^2 + m2^4*r255 + m1^4*r256 + m2^2*r258 + m1^2*r260 - m2^6*r4 + m3^6*r5 + m4^6*r6 - 3*m3^2*m4^4*r72, r262 = m3^4 + m3^2*m4^2 + m4^4, r263 = m1^4 + m2^4 - 2*r262 + m1^2*r81 + m2^2*r81, r264 = m1^2 + m2^2 - m3^2 - m4^2, r265 = -(r13*r32*r33) + m2^2*r99, r266 = -2*m1^2*r265 - r32^2*r33^2*r4 + 2*m2^2*r13*r9 + m1^4*r99 + m2^4*r99, r267 = m3^2*r13 + m4^2*r4, r268 = -16 + 3*d, r269 = m3^2*r13 - m4^2*r268 + m2^2*r4, r270 = 2*m2^2*r267 + 2*m1^2*r269 + r13*r228*r32*r33 + m2^4*r61 + m1^4*r99, r271 = 2*m2^2 + m4^2*r23 - m3^2*r72, r272 = -(m5^2*r270) - 2*m5^4*r271 + r266*r32*r33, r273 = 2*m3^2 - 2*m4^2 - m5^2, r274 = m1^2*r5 - m2^2*r5 + r273*r72, r275 = r200*r254 + m5^2*r261 + PP*r272 + 2*m5^2*PP^2*r274 + m5^4*r263*r5 - m5^6*r264*r5, r276 = -2*m2^2*m3^2 - 2*m3^4 + 3*m3^2*m4^2 - m4^4 + 3*m3^2*m5^2 + 2*m4^2*m5^2 - m5^4 + m1^2*r177 + PP*r77, r277 = -(m4^2*r106) + m2^2*r4 - m3^2*r5, r278 = -2*m3^4 - m3^2*m4^2*r13 + m2^2*r196 + m2^4*r4 + m4^4*r4, r279 = m4^2*r131 + m3^2*r8, r280 = m2^2*r279 - 2*m2^4*r4 + m4^2*r32*r33*r99, r281 = m1^4*r277 + m2^2*r278 + m1^2*r280, r282 = 11*m3^2 - 3*d*m3^2 + 9*m4^2 - 2*d*m4^2, r283 = 15 - 4*d, r284 = m4^2*r106 + m2^2*r283 + m3^2*r5, r285 = m4^4*r13 + 4*m3^2*m4^2*r5 - m3^4*r99, r286 = -m4^2 + m3^2*r5, r287 = -(m4^2*r5) + m3^2*r6, r288 = 2*m2^2*r287 + m2^4*r72 - 2*r286*r81, r289 = -2*m3^2*m4^4 + m2^4*r282 + m1^4*r284 + m2^2*r285 + m1^2*r288 - m4^6*r4 + m1^6*r5 + m2^6*r6 + m3^4*m4^2*r99, r290 = 2*m2^2 - m3^2 - m4^2, r291 = 2*m1^4 + 2*m2^4 - m3^4 - m4^4 + m1^2*r290 - m2^2*r81, r292 = m2^2 - m3^2 + m4^2, r293 = m1^4*r4 + m2^4*r4 - 2*m1^2*r292*r4 + 2*m2^2*r4*r9 - r32^2*r33^2*r99, r294 = m3^2*r13 - m4^2*r131, r295 = m2^2*r13 - r4*r81, r296 = m1^4*r131 + 2*m2^2*r294 - 2*m1^2*r295 - 2*m3^2*m4^2*r4 + m4^4*r8 - m2^4*r99 - m3^4*r99, r297 = 2*m4^2 - m2^2*r5 + m1^2*r72, r298 = r107*r108*r293 - m5^2*r296 + 2*m5^4*r297, r299 = -2*m5^2*r32*r33*r5 + 2*m5^4*r72, r300 = r130*r281 - m5^2*r289 + PP*r298 + PP^2*r299 - m5^6*r264*r5 + m5^4*r291*r5, r301 = -2*m2^2*m3^2 - m3^2*m4^2 + m4^4 + m5^4 - m5^2*r17 + m1^2*r177 + PP*r77, r302 = m2^2 + 2*m3^2 - 3*m4^2, r303 = -m1^2 + m2^2 - 3*m5^2, r304 = m1^4 - m2^2*m4^2 - m5^4 + m5^2*r149 - m1^2*r302 + PP*r303, r305 = -((r45*TBI[d, PP, {{1, m4}, {1, m2}}]* TBI[d, PP, {{2, m1}, {1, m3}}])/(4*r3)) + (r76*TBI[d, PP, {{1, m3}, {1, m1}}]* TBI[d, PP, {{2, m2}, {1, m4}}])/(4*r3) 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r182*TVI[d, PP, {{1, m5}, {1, m2}, {3, m3}, {1, m4}}] + (r203*TVI[d, PP, {{1, m5}, {1, m3}, {2, m2}, {1, m1}}])/ (4*r3) + (r232* TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {1, m2}}])/ (4*r3) + (r236* TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {2, m2}}])/2 + r240*TVI[d, PP, {{1, m5}, {1, m4}, {3, m1}, {1, m2}}] + (r45*TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {1, m3}}])/ (4*r3) + (r86*r88* TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {2, m3}}])/2 + (r92*TVI[d, PP, {{1, m5}, {2, m1}, {2, m4}, {1, m3}}])/2 - (r76*TVI[d, PP, {{1, m5}, {2, m2}, {1, m3}, {1, m4}}])/ (4*r3) - (r243* TVI[d, PP, {{1, m5}, {2, m2}, {2, m3}, {1, m4}}])/2 + (r45*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {1, m1}}])/(4*r3) + (r86*r88*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {2, m1}}])/2 + (r246*TVI[d, PP, {{1, m5}, {2, m3}, {2, m2}, {1, m1}}])/2 - (r76*TVI[d, PP, {{1, m5}, {2, m4}, {1, m1}, {1, m2}}])/ (4*r3) + (r248* TVI[d, PP, {{1, m5}, {2, m4}, {2, m1}, {1, m2}}])/2 + r86*r88*TVI[d, PP, {{1, m5}, {3, m1}, {1, m4}, {1, m3}}] + 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n1 - n2)* (-2 - d + 2*n1 + 2*n2)* (3*d - 2*n1 - 2*n2 - 2*n3)* (-1 - d + n1 + n2 + n3)* TJI[d, m3^2, {{-1 + n1, 0}, {n2, 0}, {n3, m3}} ])/(2*m3^2*(d - 2*n1)* (-1 + n1)* (2*d - 2*n1 - 2*n2 - n3)* (1 + 2*d - 2*n1 - 2*n2 - n3)))) /; n1 > 1 && m3 =!= 0 && PP === m3^2]\ \>", "Input", Editable->False] }, Open ]], Cell[CellGroupData[{ Cell[" MakeFun (203)", "Subsection", CellTags->"T1.6.117.1"], Cell[BoxData[ \(Subscript[f, \ 203]\ = HoldForm[\n\t\t\ TJR[d_, \ 0, \ {{\((n1_)\)?PQ, \ 0}, \ {\((n2_)\)?PQ, \ m2_}, \ \n\ \ \ \ {\((n3_)\)?PQ, \ m2_}}]\ := \((\n\t\t\t\t\ TComment["\<(203)\>", \ \n\ \ \ \ \ \ \ \ \ TJIC[d, 0, \ {{n1, \ 0}, \ {n2, \ m2}, \ {n3, \ m2}}]]; \ \n\t\t\t\t\((\((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n2)\))\)*\n\ \ \ \ \ \((1\ + \ d\ - \ n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n3)\))\)*\n\ \ \ \ \ TJR[ d, \ 0, \ {{\(-1\)\ + \ n1, \ 0}, \ {n2, \ m2}, \ \n\ \ \ \ \ \ \ {n3, \ m2}}])\)/\n\ \ \ \((2* m2^2*\((d\ - \ 2*n1)\)*\n\ \ \ \ \ \((1\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((2\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\))\)\n\t\t\t\n\t\t\t)\)]\)], "Input", Editable->False] }, Open ]], Cell[CellGroupData[{ Cell[" MakeFun (204)", "Subsection", CellTags->"T1.6.118.1"], Cell[BoxData[ \(Subscript[f, \ 204]\ = HoldForm[\n\t\t\ TJR[d_, \ 0, \ {\ {\((n2_)\)?PQ, \ m2_}, \ {\((n1_)\)?PQ, \ 0}, \n\ \ \ \ {\((n3_)\)?PQ, \ m2_}}]\ := \((\n\t\ TComment["\<(204)\>", \ \n\ \ \ \ \ \ \ \ \ TJIC[d, 0, \ {\ {n2, \ m2}, \ {n1, \ 0}, {n3, \ m2}}]]; \ \n\t\((\((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n2)\))\)*\n\ \ \ \ \ \((1\ + \ d\ - \ n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n3)\))\)*\n\ \ \ \ \ TJR[ d, \ 0, \ {{\(-1\)\ + \ n1, \ 0}, \ {n2, \ m2}, \ \n\ \ \ \ \ \ \ {n3, \ m2}}])\)/\n\ \ \ \((2* m2^2*\((d\ - \ 2*n1)\)*\n\ \ \ \ \ \((1\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((2\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\))\)\n\t\t\t)\)]\)], "Input", Editable->False] }, Open ]], Cell[CellGroupData[{ Cell[" MakeFun (205)", "Subsection", CellTags->"T1.6.119.1"], Cell[BoxData[ \(Subscript[f, \ 205]\ = HoldForm[\n\t\t\ TJR[d_, \ 0, \ {\ {\((n2_)\)?PQ, \ m2_}, \n\ \ \ \ {\((n3_)\)?PQ, \ m2_}, \ {\((n1_)\)?PQ, \ 0}}]\ := \((\n\t\ TComment["\<(205)\>", \ \n\ \ \ \ \ \ \ \ \ TJIC[d, 0, \ {\ {n2, \ m2}, {n3, \ m2}, \ {n1, \ 0}}]]; \ \n\((\((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n2)\))\)*\n\ \ \ \ \ \((1\ + \ d\ - \ n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n3)\))\)*\n\ \ \ \ \ TJR[ d, \ 0, \ {{\(-1\)\ + \ n1, \ 0}, \ {n2, \ m2}, \ \n\ \ \ \ \ \ \ {n3, \ m2}}])\)/\n\ \ \ \((2* m2^2*\((d\ - \ 2*n1)\)*\n\ \ \ \ \ \((1\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((2\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\))\)\n\t\t\t)\)]\)], "Input", Editable->False] }, Open ]], Cell[CellGroupData[{ Cell["Input (1xxxx)", "Subsection", CellTags->"T1.6.120.1"], Cell["\<\ If[MatchQ[$RankLimit, {_Integer?NonNegative, _Integer?NonNegative}], $TarasovTdeltaplimit = $RankLimit[[1]]; ($TarasovTplimit = $RankLimit[[2]]; ), $TarasovTdeltaplimit = 2; $TarasovTplimit = 2]; \ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"tarti", "=", RowBox[{"Timing", "[", RowBox[{"Do", "[", RowBox[{ RowBox[{"If", "[", RowBox[{\(0 < a + b + r + es\), ",", RowBox[{\(WriteString["\", {a, b, r, es}]\), ";", RowBox[{"Set", "@@", RowBox[{"{", RowBox[{\(s\_\(10\^4 + 1000\ a + 100\ b + 10\ r + es\)\), ",", RowBox[{ RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "DP", ",", \({a, b}\), ",", \({0, 0, r, es, 0}\), ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", InterpretationBox[\(m\_1\), m1]}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", InterpretationBox[\(m\_2\), m2]}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", InterpretationBox[\(m\_3\), m3]}], "}"}], ",", RowBox[{"{", RowBox[{"n4", ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", RowBox[{"{", RowBox[{"n5", ",", InterpretationBox[\(m\_5\), m5]}], "}"}]}], "}"}]}], "]"}], "==", RowBox[{"ApplyTarasovT", "[", RowBox[{ RowBox[{"TarasovT", "[", RowBox[{ "a", ",", "b", ",", "r", ",", "es", ",", InterpretationBox[\(p\^2\), PP], ",", "DP"}], "]"}], ",", RowBox[{"STLI", "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", InterpretationBox[\(m\_1\), m1]}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", InterpretationBox[\(m\_2\), m2]}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", InterpretationBox[\(m\_3\), m3]}], "}"}], ",", RowBox[{"{", RowBox[{"n4", ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", RowBox[{"{", RowBox[{"n5", ",", InterpretationBox[\(m\_5\), m5]}], "}"}]}], "}"}]}], "]"}]}], "]"}]}], "/.", RowBox[{"STLI", "\[Rule]", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}]}]}], "}"}]}]}]}], "]"}], ",", \({a, 0, $TarasovTdeltaplimit}\), ",", \({b, 0, $TarasovTdeltaplimit - a}\), ",", \({r, 0, $TarasovTplimit}\), ",", \({es, 0, $TarasovTplimit - r}\)}], "]"}], "]"}]}]], "Input"], Cell["\<\ {0, 0, 0, 1}{0, 0, 0, 2}{0, 0, 0, 3}{0, 0, 0, 4}{0, 0, 0, 5}{0, 0, \ 0, 6}{0, 0, 1, 0}{0, 0, 1, 1}{0, 0, 1, 2}{0, 0, 1, 3}{0, 0, 1, 4}{0, 0, 1, \ 5}{0, 0, 2, 0}{0, 0, 2, 1}{0, 0, 2, 2}{0, 0, 2, 3}{0, 0, 2, 4}{0, 0, 3, 0}{0, \ 0, 3, 1}{0, 0, 3, 2}{0, 0, 3, 3}{0, 0, 4, 0}{0, 0, 4, 1}{0, 0, 4, 2}{0, 0, 5, \ 0}{0, 0, 5, 1}{0, 0, 6, 0}\ \>", "Print"] }, Open ]], Cell["Share[]", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(matarti = Timing[Do[ If[0 < ia + ib + ir + es, WriteString["\", {ia, ib, ir, es}]; Set[f\_\(10\^4 + 1000\ ia + 100\ ib + 10\ ir + es\), MakeFun[s\_\(10\^4 + 1000\ ia + 100\ ib + 10\ ir + es\), \ "\<(1\>" <> ToString[ia] <> ToString[ib] <> ToString[ir] <> ToString[es] <> "\<)\>"] /. PQ :> PNQ]], {ia, 0, \ $TarasovTdeltaplimit}, {ib, 0, $TarasovTdeltaplimit - ia}, {ir, 0, \ \ $TarasovTplimit}, {es, 0, $TarasovTplimit - ir}]]\)], "Input"], Cell["\<\ {0, 0, 0, 1}{0, 0, 0, 2}{0, 0, 0, 3}{0, 0, 0, 4}{0, 0, 0, 5}{0, 0, \ 0, 6}{0, 0, 1, 0}{0, 0, 1, 1}{0, 0, 1, 2}{0, 0, 1, 3}{0, 0, 1, 4}{0, 0, 1, \ 5}{0, 0, 2, 0}{0, 0, 2, 1}{0, 0, 2, 2}{0, 0, 2, 3}{0, 0, 2, 4}{0, 0, 3, 0}{0, \ 0, 3, 1}{0, 0, 3, 2}{0, 0, 3, 3}{0, 0, 4, 0}{0, 0, 4, 1}{0, 0, 4, 2}{0, 0, 5, \ 0}{0, 0, 5, 1}{0, 0, 6, 0}\ \>", "Print"] }, Open ]], Cell[BoxData[ \(Share[]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["symmetry", "Subsection", CellTags->"Tsymmetry"], Cell["Uncomment this ...", "Text"], Cell["\<\ TVR[d_, pp_, {a_, b_, c_, z_}] := TVR[d, pp, {c, b, a, z}] /; !OrderedQ[{a, c}]\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["special TVR reductions", "Subsection", CellTags->"specialTVR"], Cell["\<\ TVR[2 + d_Symbol, pp_, {{1, m1_}, {1, m1_}, {2, 0}, {1, m1_}}] := ((-6*m1^2 + 2*d*m1^2 + 3*pp)*TAI[d, 0, {{1, m1}}]^2)/ (12*(-3 + d)*(-1 + d)*m1^2*pp) + ((4*m1^2 - pp)*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ (4*(-3 + d)*(-1 + d)*m1^2) - ((6*m1^2 - 2*d*m1^2 - 7*pp + 2*d*pp)* TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(6*(-2 + d)*(-1 + d)*pp) + ((-4*m1^2 + pp)*(-6*m1^2 + 2*d*m1^2 + 3*pp)* TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ (6*(-3 + d)*(-2 + d)*(-1 + d)*pp) /; (m1=!=0)&&(pp=!=0);\ \>", "Input"], Cell["\<\ TVR[4 + d_Symbol, pp_, {{1, m1_}, {1, m1_}, {2, 0}, {1, m1_}}] := -((-96*d*m1^6 + 352*d^2*m1^6 - 384*d^3*m1^6 + 128*d^4*m1^6 - 192*m1^4*pp + 1008*d*m1^4*pp - 1632*d^2*m1^4*pp + 912*d^3*m1^4*pp - 144*d^4*m1^4*pp + 288*m1^2*pp^2 - 1536*d*m1^2*pp^2 + 2316*d^2*m1^2*pp^2 - 1086*d^3*m1^2*pp^2 + 66*d^4*m1^2*pp^2 + 72*d*pp^3 - 166*d^2*pp^3 + 81*d^3*pp^3 + 4*d^4*pp^3)*TAI[d, 0, {{1, m1}}]^2)/ (36*(-1 + d)^2*d^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) + ((4*m1^2 - pp)^2*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ (4*(-1 + d)^2*d*(1 + d)) - ((288*m1^8 - 1152*d*m1^8 + 1504*d^2*m1^8 - 768*d^3*m1^8 + 128*d^4*m1^8 - 816*m1^6*pp + 2480*d*m1^6*pp - 2224*d^2*m1^6*pp + 736*d^3*m1^6*pp - 80*d^4*m1^6*pp + 864*m1^4*pp^2 - 2196*d*m1^4*pp^2 + 1446*d^2*m1^4*pp^2 - 252*d^3*m1^4*pp^2 - 6*d^4*m1^4*pp^2 - 432*m1^2*pp^3 + 1086*d*m1^2*pp^3 - 895*d^2*m1^2*pp^3 + 315*d^3*m1^2*pp^3 - 44*d^4*m1^2*pp^3 + 4*d*pp^4 - 2*d^2*pp^4 - 4*d^3*pp^4 + 2*d^4*pp^4)*TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ (18*(-2 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) + (m1^2*(4*m1^2 - pp)*(-96*m1^6 + 352*d*m1^6 - 384*d^2*m1^6 + 128*d^3*m1^6 + 240*m1^4*pp - 624*d*m1^4*pp + 384*d^2*m1^4*pp - 48*d^3*m1^4*pp - 192*m1^2*pp^2 + 420*d*m1^2*pp^2 - 162*d^2*m1^2*pp^2 - 18*d^3*m1^2*pp^2 + 72*pp^3 - 154*d*pp^3 + 81*d^2*pp^3 - 8*d^3*pp^3)*TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ (18*(-2 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; \ (m1=!=0)&&(pp=!=0);\ \>", "Input"], Cell["\<\ TVR[4 + d_Symbol, pp_, {{1, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := ((-72*d^2*m1^6 + 144*d^3*m1^6 - 88*d^4*m1^6 + 16*d^5*m1^6 - 240*d*m1^4*pp + 572*d^2*m1^4*pp - 398*d^3*m1^4*pp + 84*d^4*m1^4*pp - 2*d^5*m1^4*pp - 96*m1^2*pp^2 + 480*d*m1^2*pp^2 - 744*d^2*m1^2*pp^2 + 390*d^3*m1^2*pp^2 - 50*d^4*m1^2*pp^2 + 4*d^5*m1^2*pp^2 - 24*d*pp^3 + 54*d^2*pp^3 - 27*d^3*pp^3)*TAI[d, 0, {{1, m1}}]^2)/ (24*(-3 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*m1^2*pp^2) + ((4*m1^2 - pp)^2*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ (8*(-3 + d)*(-1 + d)^2*(1 + d)*m1^2) + ((-72*d*m1^6 + 144*d^2*m1^6 - 88*d^3*m1^6 + 16*d^4*m1^6 - 96*m1^4*pp + 260*d*m1^4*pp - 166*d^2*m1^4*pp + 12*d^3*m1^4*pp + 6*d^4*m1^4*pp + 160*m1^2*pp^2 - 300*d*m1^2*pp^2 + 50*d^2*m1^2*pp^2 + 90*d^3*m1^2*pp^2 - 24*d^4*m1^2*pp^2 - 48*pp^3 + 114*d*pp^3 - 67*d^2*pp^3 + 4*d^3*pp^3 + 2*d^4*pp^3)*TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ (12*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) - ((-4*m1^2 + pp)*(72*d*m1^6 - 144*d^2*m1^6 + 88*d^3*m1^6 - 16*d^4*m1^6 + 96*m1^4*pp - 236*d*m1^4*pp + 122*d^2*m1^4*pp + 12*d^3*m1^4*pp - 10*d^4*m1^4*pp - 96*m1^2*pp^2 + 180*d*m1^2*pp^2 - 30*d^2*m1^2*pp^2 - 46*d^3*m1^2*pp^2 + 8*d^4*m1^2*pp^2 + 24*pp^3 - 54*d*pp^3 + 27*d^2*pp^3)* TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ (12*(-3 + d)*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; \ (m1=!=0)&&(pp=!=0);\ \>", "Input"], Cell["\<\ TVR[6 + d_Symbol, pp_, {{1, m1_}, {1, m1_}, {4, 0}, {1, m1_}}] := ((2304*d*m1^10 - 4608*d^2*m1^10 - 3520*d^3*m1^10 + 6976*d^4*m1^10 + 1472*d^5*m1^10 - 2624*d^6*m1^10 - 256*d^7*m1^10 + 256*d^8*m1^10 + 4608*m1^8*pp - 9600*d*m1^8*pp - 7680*d^2*m1^8*pp + 9312*d^3*m1^8*pp + 11680*d^4*m1^8*pp - 6560*d^5*m1^8*pp - 2880*d^6*m1^8*pp + 1088*d^7*m1^8*pp + 32*d^8*m1^8*pp + 6912*m1^6*pp^2 - 35712*d*m1^6*pp^2 + 1056*d^2*m1^6*pp^2 + 85296*d^3*m1^6*pp^2 - 37032*d^4*m1^6*pp^2 - 20484*d^5*m1^6*pp^2 + 8700*d^6*m1^6*pp^2 - 12*d^7*m1^6*pp^2 - 84*d^8*m1^6*pp^2 - 20736*m1^4*pp^3 + 58752*d*m1^4*pp^3 + 40560*d^2*m1^4*pp^3 - 150536*d^3*m1^4*pp^3 + 18980*d^4*m1^4*pp^3 + 48946*d^5*m1^4*pp^3 - 6748*d^6*m1^4*pp^3 - 146*d^7*m1^4*pp^3 + 128*d^8*m1^4*pp^3 + 3456*m1^2*pp^4 - 13824*d*m1^2*pp^4 - 4176*d^2*m1^2*pp^4 + 35784*d^3*m1^2*pp^4 - 8332*d^4*m1^2*pp^4 - 10162*d^5*m1^2*pp^4 + 1122*d^6*m1^2*pp^4 - 80*d^7*m1^2*pp^4 - 8*d^8*m1^2*pp^4 + 864*d*pp^5 - 216*d^2*pp^5 - 2268*d^3*pp^5 + 486*d^4*pp^5 + 729*d^5*pp^5)*TAI[d, 0, {{1, m1}}]^2)/ (432*(-3 + d)*(-1 + d)^2*d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)* (-2 + 3*d)*(2 + 3*d)*m1^2*pp^3) + ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ (16*(-3 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*m1^2) - ((-1152*m1^10 + 2880*d*m1^10 + 320*d^2*m1^10 - 3648*d^3*m1^10 + 1088*d^4*m1^10 + 768*d^5*m1^10 - 256*d^6*m1^10 - 192*m1^8*pp + 1312*d*m1^8*pp + 2080*d^2*m1^8*pp - 6880*d^3*m1^8*pp + 4032*d^4*m1^8*pp - 192*d^5*m1^8*pp - 160*d^6*m1^8*pp + 6336*m1^6*pp^2 - 6960*d*m1^6*pp^2 - 16960*d^2*m1^6*pp^2 + 17292*d^3*m1^6*pp^2 - 1828*d^4*m1^6*pp^2 - 828*d^5*m1^6*pp^2 + 68*d^6*m1^6*pp^2 - 9504*m1^4*pp^3 + 3624*d*m1^4*pp^3 + 26104*d^2*m1^4*pp^3 - 10938*d^3*m1^4*pp^3 - 4976*d^4*m1^4*pp^3 + 330*d^5*m1^4*pp^3 + 400*d^6*m1^4*pp^3 + 6336*m1^2*pp^4 - 3640*d*m1^2*pp^4 - 14584*d^2*m1^2*pp^4 + 9190*d^3*m1^2*pp^4 + 1374*d^4*m1^2*pp^4 - 600*d^5*m1^2*pp^4 - 56*d^6*m1^2*pp^4 - 864*pp^5 + 732*d*pp^5 + 1864*d^2*pp^5 - 1695*d^3*pp^5 + 148*d^4*pp^5 + 36*d^5*pp^5 + 4*d^6*pp^5)* TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ (216*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* (2 + 3*d)*pp^3) + ((-4*m1^2 + pp)* (1152*m1^10 - 2880*d*m1^10 - 320*d^2*m1^10 + 3648*d^3*m1^10 - 1088*d^4*m1^10 - 768*d^5*m1^10 + 256*d^6*m1^10 + 576*m1^8*pp - 2208*d*m1^8*pp - 2304*d^2*m1^8*pp + 8000*d^3*m1^8*pp - 4256*d^4*m1^8*pp - 32*d^5*m1^8*pp + 224*d^6*m1^8*pp - 6336*m1^6*pp^2 + 6288*d*m1^6*pp^2 + 16320*d^2*m1^6*pp^2 - 14868*d^3*m1^6*pp^2 + 684*d^4*m1^6*pp^2 + 804*d^5*m1^6*pp^2 - 12*d^6*m1^6*pp^2 + 6912*m1^4*pp^3 - 3192*d*m1^4*pp^3 - 18160*d^2*m1^4*pp^3 + 7950*d^3*m1^4*pp^3 + 3128*d^4*m1^4*pp^3 - 78*d^5*m1^4*pp^3 - 160*d^6*m1^4*pp^3 - 3456*m1^2*pp^4 + 1800*d*m1^2*pp^4 + 8136*d^2*m1^2*pp^4 - 4322*d^3*m1^2*pp^4 - 1042*d^4*m1^2*pp^4 + 128*d^5*m1^2*pp^4 + 16*d^6*m1^2*pp^4 + 432*pp^5 - 324*d*pp^5 - 972*d^2*pp^5 + 729*d^3*pp^5)* TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ (216*(-3 + d)*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)* (-2 + 3*d)*(2 + 3*d)*pp^3) /; (m1=!=0)&&(pp=!=0);\ \>", "Input"], Cell["\<\ TVR[6 + d_Symbol, pp_, {{2, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := -((-1536*d*m1^10 + 2560*d^2*m1^10 + 3200*d^3*m1^10 - 3584*d^4*m1^10 - 2176*d^5*m1^10 + 1024*d^6*m1^10 + 512*d^7*m1^10 - 3072*m1^8*pp + 6528*d*m1^8*pp + 5376*d^2*m1^8*pp - 7520*d^3*m1^8*pp - 5568*d^4*m1^8*pp + 3232*d^5*m1^8*pp + 1344*d^6*m1^8*pp - 320*d^7*m1^8*pp - 2304*m1^6*pp^2 + 13824*d*m1^6*pp^2 + 192*d^2*m1^6*pp^2 - 31584*d^3*m1^6*pp^2 + 11232*d^4*m1^6*pp^2 + 8088*d^5*m1^6*pp^2 - 2304*d^6*m1^6*pp^2 - 24*d^7*m1^6*pp^2 + 6912*m1^4*pp^3 - 19584*d*m1^4*pp^3 - 12688*d^2*m1^4*pp^3 + 50584*d^3*m1^4*pp^3 - 7516*d^4*m1^4*pp^3 - 16982*d^5*m1^4*pp^3 + 2564*d^6*m1^4*pp^3 + 310*d^7*m1^4*pp^3 - 1152*m1^2*pp^4 + 4608*d*m1^2*pp^4 + 1392*d^2*m1^2*pp^4 - 11896*d^3*m1^2*pp^4 + 2820*d^4*m1^2*pp^4 + 3374*d^5*m1^2*pp^4 - 414*d^6*m1^2*pp^4 + 8*d^7*m1^2*pp^4 - 288*d*pp^5 + 72*d^2*pp^5 + 756*d^3*pp^5 - 162*d^4*pp^5 - 243*d^5*pp^5)*TAI[d, 0, {{1, m1}}]^2)/ (144*(-1 + d)^2*d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* (2 + 3*d)*m1^2*pp^3) + ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ (16*(-1 + d)^2*d*(1 + d)*(3 + d)*m1^2) - ((2304*m1^10 - 5760*d*m1^10 - 640*d^2*m1^10 + 7296*d^3*m1^10 - 2176*d^4*m1^10 - 1536*d^5*m1^10 + 512*d^6*m1^10 - 1344*m1^8*pp + 1120*d*m1^8*pp - 1376*d^2*m1^8*pp + 5280*d^3*m1^8*pp - 4896*d^4*m1^8*pp + 1280*d^5*m1^8*pp - 64*d^6*m1^8*pp - 5184*m1^6*pp^2 + 7584*d*m1^6*pp^2 + 14800*d^2*m1^6*pp^2 - 21496*d^3*m1^6*pp^2 + 6120*d^4*m1^6*pp^2 + 280*d^5*m1^6*pp^2 - 184*d^6*m1^6*pp^2 + 9504*m1^4*pp^3 - 3720*d*m1^4*pp^3 - 27296*d^2*m1^4*pp^3 + 15378*d^3*m1^4*pp^3 + 4114*d^4*m1^4*pp^3 - 666*d^5*m1^4*pp^3 - 674*d^6*m1^4*pp^3 - 6336*m1^2*pp^4 + 5720*d*m1^2*pp^4 + 13712*d^2*m1^2*pp^4 - 13926*d^3*m1^2*pp^4 + 1284*d^4*m1^2*pp^4 + 946*d^5*m1^2*pp^4 - 80*d^6*m1^2*pp^4 + 864*pp^5 - 1020*d*pp^5 - 1636*d^2*pp^5 + 2311*d^3*pp^5 - 693*d^4*pp^5 + 20*d^5*pp^5 + 4*d^6*pp^5)* TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ (72*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* (2 + 3*d)*pp^3) + ((4*m1^2 - pp)* (-768*m1^10 + 1664*d*m1^10 + 768*d^2*m1^10 - 2176*d^3*m1^10 + 512*d^5*m1^10 + 192*m1^8*pp + 288*d*m1^8*pp + 704*d^2*m1^8*pp - 2272*d^3*m1^8*pp + 1024*d^4*m1^8*pp + 64*d^5*m1^8*pp + 1920*m1^6*pp^2 - 1824*d*m1^6*pp^2 - 5472*d^2*m1^6*pp^2 + 4584*d^3*m1^6*pp^2 - 168*d^5*m1^6*pp^2 - 2304*m1^4*pp^3 + 616*d*m1^4*pp^3 + 6192*d^2*m1^4*pp^3 - 1946*d^3*m1^4*pp^3 - 1128*d^4*m1^4*pp^3 - 230*d^5*m1^4*pp^3 + 1152*m1^2*pp^4 - 600*d*m1^2*pp^4 - 2744*d^2*m1^2*pp^4 + 1414*d^3*m1^2*pp^4 + 374*d^4*m1^2*pp^4 - 16*d^5*m1^2*pp^4 - 144*pp^5 + 108*d*pp^5 + 324*d^2*pp^5 - 243*d^3*pp^5)* TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ (72*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* (2 + 3*d)*pp^3) /; (m1=!=0)&&(pp=!=0);\ \>", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["five -> four", "Subsection", CellTags->"T1.6.121.1"], Cell[BoxData[ \(TFI[d_, \ PP_ /; Head[PP] =!= List, {\ {0, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n3_, \ m3_}, \ {n4_, \ m4_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n5_, \ m5_}\ }]\ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TFI[ d_, \ \ PP_ /; Head[PP] =!= List, {\ {\((n2_)\), \ m2_}, {0, \ m1_}, \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n4_)\), \ m4_}, \ {\((n3_)\), \ m3_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n5_)\), \ m5_}\ }]\ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TFI[ d_, \ \ \ PP_ /; Head[PP] =!= List, {\ {\((n3_)\), \ m3_}, \ {\((n4_)\), \ m4_}, \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {0, \ m1_}, \ {\((n2_)\), \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n5_)\), \ m5_}\ }]\ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TFI[ d_, \ \ \ PP_ /; Head[PP] =!= List, {\ {\((n4_)\), \ m4_}, {\((n3_)\), \ m3_}, \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n2_)\), \ m2_}, \ {0, \ m1_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n5_)\), \ m5_}\ }]\ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell["\<\ TFI[d_, PP_/;Head[PP]=!=List,{{(n1_), m1_}, {(n2_), m2_}, {(n3_), m3_}, {(n4_), m4_}, {0, m5_}}] := TBI[d, PP, {{n1, m1}, {n3, m3}}]* TBI[d, PP, {{n2, m2}, {n4, m4}}] \ \>", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["four -> three", "Subsection", CellTags->"T1.6.122.1"], Cell[BoxData[ \(TVI[d_, \ PP_, {\ {0, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n3_, \ m3_}, \ {n4_, \ m4_}\ }]\ := \ \n TAI[d, 0, {{n3, m3}}]\ TBI[d, PP, {{n2, m2}, {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TVI[d_, \ PP_, {\ {n1_, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {0, \ m3_}, \ {n4_, \ m4_}\ }]\ := \ \n TAI[d, 0, {{n1, m1}}]\ TBI[d, PP, {{n2, m2}, {n4, m4}}]\)], "Input"], Cell["\<\ TVI[d_, PP_, {{n1_, m1_}, {0, m2_}, {n3_, m3_}, {n4_, m4_}}] := TJI[d, 0, {{n1, m1}, {n3, m3}, {n4, m4}}]\ \>", "Input"], Cell[BoxData[ \(TVI[d_, \ PP_, {\ {n1_, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n3_, \ m3_}, \ {0, \ m4_}\ }]\ := \ \n TJI[d, PP, \ {{n2, m2}, {n1, m1}, {n3, m3}\ }]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["three -> two", "Subsection", CellTags->"T1.6.123.1"], Cell[BoxData[ \(TJI[d_, \ PP_, {\ {0, \ m1_}, \ {\((n2_)\), \ m2_}, \ {\((n3_)\), \ m3_}\ }]\ := \ \n TAI[d, 0, {{n2, m2}}]\ \ TAI[d, 0, {{n3, m3}}]\)], "Input"], Cell[BoxData[ \(TJI[d_, \ PP_, {\ {\((n1_)\), \ m1_}, \ {0, \ m2_}, \ {\((n3_)\), \ m3_}\ }]\ := \ \n TAI[d, 0, {{n1, m1}}]\ \ TAI[d, 0, {{n3, m3}}]\)], "Input"], Cell[BoxData[ \(TJI[d_, \ PP_, {\ {\((n1_)\), \ m1_}, \ {\((n2_)\), \ m2_}, \ {0, \ m3_}\ }]\ := \ \n TAI[d, 0, {{n1, m1}}]\ \ TAI[d, 0, {{n2, m2}}]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["two -> one", "Subsection", CellTags->"T1.6.124.1"], Cell[BoxData[ \(\(\(\(TBI[d_, \ PP_, {\ {0, \ m1_}, \ {\((n2_)\), \ m2_}\ }]\)\(\ \)\)\(:=\)\(\ \)\(\n\)\(TAI[d, 0, {{n2, m2}}]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(\(\(\(TBI[d_, \ PP_, {\ {\((n1_)\), \ m1_}, \ {0, \ m2_}\ }]\)\(\ \)\)\(:=\)\(\ \)\(\n\)\(TAI[d, 0, {{n1, m1}}]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(TAI[d_, {{n_Integer, m_}}] := TAI[d, 0, {{n, m}}]; \)], "Input"], Cell[BoxData[ \(TAI[d_, {n_Integer, m_}] := TAI[d, 0, {{n, m}}]; \)], "Input"], Cell[BoxData[ \(TAI[d_, 0, {n_Integer, m_}] := TAI[d, 0, {{n, m}}]; \)], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["TarcerRecurse and TFIRecurse", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.7.1"], Cell[CellGroupData[{ Cell["TFIRecurse & TFISimplify", "Subsection", CellTags->"T1.7.1.1"], Cell["This cancels scalar products.", "Text"], Cell[BoxData[ \($TLRComment = False; \)], "Input"], Cell[BoxData[ \(TLRComment[s_String] := WriteString["\", s, "\< \>"] /; $TLRComment === True; \)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(applytlrules[y_, fun_]\), " ", ":=", RowBox[{"fun", "[", RowBox[{ RowBox[{ RowBox[{"y", " ", "/.", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "->", "TLR"}]}], "/.", "TLRules"}], "/.", RowBox[{"TLR", "->", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}]}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ \(TFIRecurse[z_, f_ : Identity]\ := \ FixedPoint[\ applytlrules[#, f] &, z, 1000]; \)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(applytlrules2[y_, fun_]\), " ", ":=", RowBox[{"fun", "[", RowBox[{ RowBox[{ RowBox[{"y", " ", "/.", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "->", "TLR"}]}], "/.", "TLRules2"}], "/.", RowBox[{"TLR", "->", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}]}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ \(TFISimplify[z_, f_ : Identity]\ := \ FixedPoint[\ applytlrules2[#, f] &, z, 1000]; \)], "Input"], Cell["\<\ TFIRecurse[z_]:=z/.TFI\[Rule]TLR//.TLRules/.TLR\[Rule]TFI;\ \>", \ "Text"], Cell[BoxData[ \(ExpandMaybe = Identity; \)], "Input"], Cell[BoxData[ \(fN[li_List] := \(fN[li] = li /. {0, _} \[RuleDelayed] {0, 0}\); \)], "Input"], Cell["\<\ RM: new Feb. 1999 need TLR[ ...]:= rule; (copy from TFI definition) (in order to get e.g. TarcerRecurse[TFI[D,pp,{1,1,1,1,1},{{1,0},{1,M},{0,0},{1,m},{1,M}}]] to work)\ \>", "Text", CellTags->"TLRdef"], Cell[BoxData[ \(TLR[depp__, {a___, b_Integer, c___}] := TLR[depp, {a, {b, 0}, c}]; \)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(tlrule[1]\), "=", RowBox[{\(TLR[d_, pp_, {0, 0, 0, 0, 0}, pr_]\), "\[RuleDelayed]", RowBox[{"(", RowBox[{\(NoTLRComment["\"]\), ";", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", \(d, pp, pr /. {0, _} \[RuleDelayed] {0, 0}\), "]"}]}], ")"}]}]}], ";"}]], "Input"], Cell["(* q1^2 *)", "Text"], Cell[BoxData[ \(tlrule[2] = TLR[dpp__, {v_?PQ, w_, x_, y_, z_}, {{n1_?PQ, m1_}, nm2_, nm3_, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ If[v \[LessEqual] n1, If[m1 === 0, TLR[dpp, {0, w, x, y, z}, {{n1 - v, 0}, nm2, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%v Binomial[v, i]\ TLR[ dpp, \ {0, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]\ \((m1\^2)\)\^\(v - i\)], If[m1 === 0, TLR[dpp, {v - n1, w, x, y, z}, {{0, 0}, nm2, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%n1 Binomial[n1, i]\ TLR[ dpp, {v - n1, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]\ \((m1\^2)\)\^\(n1 - i\)]]])\); \)], \ "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`q\_2\%2\)]]], "Text"], Cell[BoxData[ \(tlrule[3] = TLR[dpp__, {v_, w_?PQ, x_, y_, z_}, {nm1_, {n2_?PQ, m2_}, nm3_, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ If[w \[LessEqual] n2, If[m2 === 0, TLR[dpp, {v, 0, x, y, z}, {nm1, {n2 - w, 0}, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%w Binomial[w, i]\ TLR[ dpp, {v, 0, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]\ \((m2\^2)\)\^\(w - i\)], If[m2 === 0, TLR[dpp, {v, w - n2, x, y, z}, {nm1, {0, 0}, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%n2 Binomial[n2, i]\ TLR[ dpp, {v, w - n2, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]\ \((m2\^2)\)\^\(n2 - i\)]]])\); \)], \ "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`p\[CenterDot]q\_1\)]]], "Text"], Cell[BoxData[ \(tlrule[4] = TLR[dpp__, {v_, w_, x_?PQ, y_, z_}, {{n1_?PQ, m1_}, nm2_, {n3_?PQ, m3_}, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ 1\/2\ TLR[ dpp, {v + 1, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}] - 1\/2\ TLR[ dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + 1\/2\ \(({dpp}\[LeftDoubleBracket]2\[RightDoubleBracket] - m3\^2)\)\ TLR[ dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}]])\); \)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`p\[CenterDot]q\_2\)]]], "Text"], Cell[BoxData[ \(tlrule[5] = TLR[dpp__, {v_, w_, x_, y_?PQ, z_}, {{n1_, m1_}, {n2_?PQ, m2_}, nm3_, {n4_?PQ, m4_}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ 1\/2\ TLR[ dpp, {v, w + 1, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}] - 1\/2\ TLR[ dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, fN[{n4 - 1, m4}], nm5}] + 1\/2\ \(({dpp}\[LeftDoubleBracket]2\[RightDoubleBracket] - m4\^2)\)\ TLR[ dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}]])\); \)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`q\_1\[CenterDot]q\_2\)]]], "Text"], Cell[BoxData[ \(tlrule[6] = TLR[dpp__, {v_, w_, x_, y_, z_?PQ}, {{n1_, m1_}, {n2_, m2_}, nm3_, nm4_, {n5_?PQ, m5_}}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ 1\/2\ TLR[ dpp, {v + 1, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - 1\/2\ TLR[ dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, fN[{n5 - 1, m5}]}] + 1\/2\ TLR[ dpp, {v, w + 1, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - 1\/2\ m5\^2\ TLR[ dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}]])\); \)], "Input"], Cell["(* q1.q1 --> q1.p *)", "Text"], Cell[BoxData[ \(tlrule[7] = TLR[d_, pp_, dp___, {v_?PQ, w_, x_, y_, z_}, {{0, _}, nm2_, {n3_?PQ, m3_}, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + 2\ TLR[d, pp, dp, {v - 1, w, x + 1, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}] - \((pp - m3\^2)\)\ TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}]])\); \)], "Input"], Cell["(* q2.q2 --> q2.p *)", "Text"], Cell[BoxData[ \(tlrule[8] = TLR[d_, pp_, dp___, {v_, w_?PQ, x_, y_, z_}, {nm1_, {0, _}, nm3_, {n4_?PQ, m4_}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, fN[{n4 - 1, m4}], nm5}] + 2\ TLR[d, pp, dp, {v, w - 1, x, y + 1, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}] - \((pp - m4\^2)\)\ TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}]])\); \)], "Input"], Cell["(* eq. (3) - (5) *)", "Text"], Cell[BoxData[ \(tlrule[9] = TLR[d_, pp_, {v_, w_, x_, y_, z_?PQ}, {nm1_, nm2_, nm3_, nm4_, {0, _}}] \[RuleDelayed] \((TLRComment["\"]; FunctionExpand[ ExpandMaybe[\[Sum]\+\(k = 0\)\%\(Floor[z\/2]\)\(\[Sum]\+\(i = 0\)\ \%k\(\[Sum]\+\(j = 0\)\%k\((Gamma[k + 1\/2]\ Gamma[d\/2 - 1\/2]\ Binomial[z, 2\ k]\ Binomial[k, i]\ Binomial[k, j]\ \((\(-1\))\)\^\(i + j\)\ pp\^\(i + j - z\)\ \ TLR[d, pp, {v + i, w + j, x + z - 2\ i, y + z - 2\ j, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])\)/\((Gamma[1\/2]\ Gamma[ k + d\/2 - 1\/2])\)\)\)]])\); \)], "Input"], Cell[" OLD trule[10]:", "Text"], Cell["\<\ tlrule[10] = (* (9) and (10) *) TLR[d_, pp_, {v_,w_,x_?PQ,y_?PQ,z_}, {{n1_?PQ,m1_},{n2_?PQ,m2_}, {0,_},{0,_},nm5_}] :> ( TLRComment[\"tlrule10\"]; 0 /; OddQ[x+y] );\ \>", "Text"], Cell["New tlrule[10]:", "Text"], Cell["\<\ tlrule[10] = TLR[d_, pp_, {v_, w_, (x_)?PNQ, (y_)?PNQ, z_}, {{(n1_)?PQ, m1_}, {(n2_)?PQ, m2_}, {0, _}, {0, _}, nm5_}] :> \ (TLRComment[\"tlrule10\"]; 0 /; OddQ[x + y]); \ \>", "Input"], Cell["\<\ Bug in tlrule[11] and tlrule[12] fixed on Feb. 26th 1998 by \ R.Scharf with thanks to York Schroeder for locating the bug.\ \>", "Text"], Cell["\<\ tlrule[11] = TLR[d_, pp_, {v_,w_,x_?PQ,y_?PQ,z_}, {nm1_,nm2_,{0,_},{0,_},{(n5_)?PQ, m5_}}] \ :> ( TLRComment[\"tlrule11\"]; ExpandMaybe[ pp/(d+x+y-2)( (x-1) TLR[d, pp, {v+1,w,x-2,y,z}, {{n1,m1},{n2,m2},{0,0},{0,0},{n5,m5}}] + y TLR[d, pp, {v,w,x-1,y-1,z+1}, {nm1,nm2,{0,0},{0,0},{n5,m5}}] ) ] /; EvenQ[x+y] && x > 1 );\ \>", "Input"], Cell["\<\ tlrule[12] = TLR[d_, pp_, {v_,w_,x_?PQ,y_?PQ,z_}, {nm1_,nm2_,{0,_},{0,_},{(n5_)?PQ, m5_}}] \ :> ( TLRComment[\"tlrule12\"]; ExpandMaybe[ pp/(d+x+y-2)( (y-1) TLR[d, pp, {v,w+1,x,y-2,z}, {{n1,m1},{n2,m2},{0,0},{0,0},{n5,m5}}] + x TLR[d, pp, {v,w,x-1,y-1,z+1}, {nm1,nm2,{0,0},{0,0},{n5,m5}}] ) ] /; EvenQ[x+y] && y > 1 );\ \>", "Input"], Cell["(*symm. 1 <-> 3 && 2 <-> 4 *)", "Text"], Cell[BoxData[ \(tlrule[13] = TLR[d_, pp_, {0, 0, 0, y_?PQ, 0}, {nm1_, {0, 0}, nm3_, {n4_?PQ, m4_}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i \ = 0\)\%y Binomial[y, i]\ pp\^\(y - i\)\ \((\(-1\))\)\^i\ TLR[d, pp, {0, 0, 0, i, 0}, {nm3, {n4, m4}, nm1, {0, 0}, nm5}])\); \)], "Input"], Cell["(*symm. 1 <-> 3 && 2 <-> 4 *)", "Text"], Cell[BoxData[ \(tlrule[14] = TLR[d_, pp_, {0, 0, x_?PQ, 0, 0}, {{0, 0}, nm2_, {n3_?PQ, m3_}, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i \ = 0\)\%x Binomial[x, i]\ pp\^\(x - i\)\ \((\(-1\))\)\^i\ TLR[d, pp, {0, 0, i, 0, 0}, {{n3, m3}, nm4, {0, 0}, nm2, nm5}])\); \)], "Input"], Cell["(* 0's *)", "Text"], Cell[BoxData[ \(tlrule[15] = HoldPattern[ TLR[d_, pp_, {v_, w_, x_, y_, z_}, {{n1_, 0}, {n2_, 0}, {0, _}, {0, _}, {0, _}}]] \[RuleDelayed] \ \((TLRComment["\"]; 0)\); \)], "Input"], Cell[BoxData[ \(tlrule[16] = TLR[d_, pp_, {0, 0, x_?PQ, y_?PQ, 0}, {{n1_, _}, {n2_, _}, {0, _}, {0, _}, {0, _}}] \[RuleDelayed] \ \((TLRComment["\"]; 0 /; OddQ[x] || OddQ[y])\); \)], "Input"], Cell["bug in tlrule[17] fixedApril 23rd 1999", "Text", CellTags->"tlrule17"], Cell[BoxData[ \(tlrule[17] = TLR[d_, pp_, {a_?PQ, b_, 0, de_, 0}, {{0, _}, {n2_, m2_}, {0, _}, {n4_, m4_}, {n5_, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \ \[Sum]\+\(i = 0\)\%a\(\[Sum]\+\(j = 0\)\%i Binomial[a, i]\ Binomial[i, j]\ \((1 + \((\(-1\))\)\^j)\)\ 2\^\(j - 1\)\ TLR[d, pp, {a - i, b + i - j, 0, de, j}, {{n5, m5}, {n2, m2}, {0, 0}, {n4, m4}, {0, 0}}]\))\); \)], "Input"], Cell[BoxData[ \(tlrule[18] = TLR[d_, pp_, dp_, {a_?PNQ, b_?PNQ}, {1, 0, 0, 0, 0}, {{0, 0}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \ \[Sum]\+\(i = 0\)\%a\(\[Sum]\+\(j = 0\)\%b Binomial[a, i]\ Binomial[b, j]\ \((\((pp + m3\^2)\)\ TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] + TLR[d, pp, dp, {i, j}, {{n3 - 1, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] - 2\ TLR[d, pp, dp, {i, j}, {0, 0, 1, 0, 0}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}])\)\ \((\(-1\))\)\^\(i + j\)\ dp\^\(a + b - \ i - j\)\))\); \)], "Input"], Cell[BoxData[ \(tlrule[19] = TLR[d_, pp_, dp_, {a_?PNQ, b_?PNQ}, {0, 1, 0, 0, 0}, {{n1_, m1_}, {0, 0}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \ \[Sum]\+\(i = 0\)\%a\(\[Sum]\+\(j = 0\)\%b Binomial[a, i]\ Binomial[b, j]\ \((\((pp + m4\^2)\)\ TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}] + TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4 - 1, m4}, {n1, m1}, {0, 0}, {n5, m5}}] - 2\ TLR[d, pp, dp, {i, j}, {0, 0, 0, 1, 0}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}])\)\ \((\(-1\))\)\^\(i + j\)\ dp\^\(a + b - \ i - j\)\))\); \)], "Input"], Cell["(* q1.q1 --> q1.p *)", "Text"], Cell[BoxData[ \(tlrule[20] = TLR[d_, pp_, {v_?PQ, w_, x_, y_, 0}, {{0, _}, nm2_, {0, _}, nm4_, {n5_?PQ, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \ \[Sum]\+\(j = 0\)\%x\(\[Sum]\+\(i = 0\)\%v\(\[Sum]\+\(r = 0\)\%i Binomial[i, r]\ Binomial[v, i]\ Binomial[x, j]\ 2\^r\ TLR[d, pp, {v - i, \(-r\) + i + w, j, x - j + y, r}, {{n5, m5}, nm2, 0, nm4, 0}]\)\))\); \)], "Input"], Cell[BoxData[ \(tlrule[21] = TLR[d_, pp_, {v_, w_?PQ, x_, y_, 0}, {nm1_, {0, _}, nm3_, {0, _}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; TLR[d, pp, {w, v, y, x, 0}, {{0, 0}, nm1, {0, 0}, nm3, nm5}])\); \)], "Input"], Cell[BoxData[ \(tlrule[22] = TLR[d_, pp_, dp_, {0, b_?PNQ}, {0, w_?PNQ, 0, y_?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] \[RuleDelayed] \((TLRComment["\"]; \(1\/pp\) \ \((TLR[d, pp, dp, {0, b}, {0, w, 1, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])\))\); \)], "Input"], Cell[TextData[{ "Using FeynCalc : \n\n", Cell[BoxData[ \(TIDL[{{k1, \[Mu]}, {k1, \[Nu]}}, {p}]\)], "Input"], "\n", Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["k1", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"], "-", RowBox[{ SuperscriptBox[ FormBox["k1", "TraditionalForm"], "2"], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]}], ")"}]}], RowBox[{\((1 - D)\), " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]], "-", FractionBox[ RowBox[{ SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{"D", " ", SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["k1", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"]}], "-", RowBox[{ SuperscriptBox[ FormBox["k1", "TraditionalForm"], "2"], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]}], ")"}]}], RowBox[{\((1 - D)\), " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "4"]}]]}], TraditionalForm]], "Output"], "\n", Cell[BoxData[ \(Collect2[Calc[\ FVD[OPEDelta, \[Mu]] FVD[k2, \[Nu]] %], {k1, k2}]\)], "Input"], "\n", Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{ FormBox["k2", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"]}], " ", SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["k1", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"]}], RowBox[{\((1 - D)\), " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]], "-", FractionBox[ RowBox[{"D", " ", RowBox[{ FormBox["k2", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], " ", SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["k1", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"]}], RowBox[{\((1 - D)\), " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "4"]}]], "-", FractionBox[ RowBox[{ SuperscriptBox[ FormBox["k1", "TraditionalForm"], "2"], " ", RowBox[{ FormBox["k2", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"]}]}], \(1 - D\)], "+", FractionBox[ RowBox[{ SuperscriptBox[ FormBox["k1", "TraditionalForm"], "2"], " ", RowBox[{ FormBox["k2", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], RowBox[{\((1 - D)\), " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]]}], TraditionalForm]], "Output"], "\n" }], "Text"], Cell[BoxData[ \(tlrule[23] = TLR[d_, pp_, dp_, {1, b_?PNQ}, {0, w_?PNQ, 0, y_?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] \[RuleDelayed] \((TLRComment["\"]; \(1\/\(\((1 \ - d)\) pp\)\) \((TLR[d, pp, dp, {0, b + 1}, {0, w, 2, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])\) - \(\(d\ \ dp\)\/\(\((1 - d)\) pp\^2\)\) \((TLR[d, pp, dp, {0, b}, {0, w, 2, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])\) - \(1\/\(1 - d\)\) TLR[d, pp, dp, {0, b + 1}, {1, w, 0, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + \(dp\/\(\((1 - d)\) pp\)\) TLR[d, pp, dp, {0, b}, {1, w, 0, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])\); \)], "Input"], Cell[TextData[{ Cell[BoxData[ \(TIDL[{{k1, \[Mu]}, {k1, \[Nu]}, {k1, \[Rho]}}, {p}]\)], "Input"], "\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{ SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["k1", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], " ", RowBox[{"(", RowBox[{ RowBox[{\((D + 2)\), " ", SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["k1", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"]}], "-", RowBox[{"3", " ", SuperscriptBox[ FormBox["k1", "TraditionalForm"], "2"], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]}], ")"}]}], RowBox[{\((1 - 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