FunKit.m

(* ::Package:: *)

(************************************************************************)\012(* This file was generated automatically by the Mathematica front end.  *)\012(* It contains Initialization cells from a Notebook file, which         *)\012(* typically will have the same name as this file except ending in      *)\012(* ".nb" instead of ".m".                                               *)\012(*                                                                      *)\012(* This file is intended to be loaded into the Mathematica kernel using *)\012(* the package loading commands Get or Needs.  Doing so is equivalent   *)\012(* to using the Evaluate Initialization Cells menu command in the front *)\012(* end.                                                                 *)\012(*                                                                      *)\012(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)\012(* automatically each time the parent Notebook file is saved in the     *)\012(* Mathematica front end.  Any changes you make to this file will be    *)\012(* overwritten.                                                         *)\012(************************************************************************)\012\012

(* ::Input::Initialization:: *)
If[($AllowInternet&&$NetworkConnected)&&$FrontEnd=!=Null&&
(* at most once a day, tracked by a per-user stamp file *)
Module[{stampFile=FileNameJoin[{$TemporaryDirectory,"FunKit-update-check-"<>$UserName}],due},due=!FileExistsQ[stampFile]||AbsoluteTime[]-AbsoluteTime[FileDate[stampFile,"Modification"]]>24 3600;If[due,Quiet[Close[OpenWrite[stampFile]]]];due],
Module[{FCurPacletAddr,FCurPaclet,FCurVersion,FCurVersionList,
FInstalledPaclet,FInstalledVersion,FInstalledVersionList},

FCurPacletAddr="https://github.com/satfra/FunKit/raw/refs/heads/main/PacletInfo.m";
FCurPaclet=CheckAbort[TimeConstrained[Import[FCurPacletAddr],2,$Failed],$Failed];

If[FCurPaclet=!=$Failed,
FCurPaclet=(List@@FCurPaclet)[[1]];
FCurVersion=FCurPaclet["Version"];
FCurVersionList=ToExpression/@StringSplit[FCurVersion,"."];

FInstalledPaclet=(List@@Import[FileNameJoin[{$UserBaseDirectory,"Applications","FunKit","PacletInfo.m"}]])[[1]];
FInstalledVersion=FInstalledPaclet["Version"];
FInstalledVersionList=ToExpression/@StringSplit[FInstalledVersion,"."];

If[!OrderedQ[{FCurVersionList,FInstalledVersionList}],
If[ChoiceDialog[
TemplateApply["There is a newer FunKit version on the internet. 
The installed version is `a`, whereas `b` is available. Do you want to install it?",<|"a"->FInstalledVersion,"b"->FCurVersion|>]
,WindowTitle->"Update FunKit",WindowSize->{Medium,All}],
Import["https://raw.githubusercontent.com/satfra/FunKit/main/FunKitInstaller.m"];
Echo["Please restart your Kernel."];Exit[],
Print["Consider updating the FunKit package for bugfixes and new features!"];
];
];
];
];
];


(* ::Input::Initialization:: *)
Unprotect[$FUNKITDIR]
$FUNKITDIR=SelectFirst[
Join[
{
FileNameJoin[{$UserBaseDirectory,"Applications","FunKit"}],
FileNameJoin[{$BaseDirectory,"Applications","FunKit"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Applications","FunKit"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Packages","FunKit"}],
FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","FunKit"}]
},
Select[$Path,StringContainsQ[#,"FunKit"]&]
],
DirectoryQ[#]&
]<>"/";
Protect[$FUNKITDIR]


(* ::Input::Initialization:: *)
(*Hide styling if we are in a CLI context.*)
If[$FrontEnd===Null||$Notebooks===False,
Unprotect[Style];
Unprotect[StyleBox];
Unprotect[Print];
Style[expr_,opts___]:=expr;
StyleBox[expr_,opts___]:=expr;
Print[expr__]:=Write[$Output,StringJoin[ToString[#,OutputForm]&/@{expr}]];
Protect[Print];
Protect[StyleBox];
Protect[Style];
];


(* ::Input::Initialization:: *)
PrintTemporary["\!\(\*
StyleBox[\"Loading\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"external\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"dependencies\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];

TensorBasesInstalled[]:=Module[{TensorBasesDirectory},
TensorBasesDirectory=SelectFirst[
Join[
{
FileNameJoin[{$UserBaseDirectory,"Applications","TensorBases"}],
FileNameJoin[{$BaseDirectory,"Applications","TensorBases"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Applications","TensorBases"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Packages","TensorBases"}],
FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","TensorBases"}]
},
Select[$Path,StringContainsQ[#,"TensorBases"]&]
],
DirectoryQ[#]&
]<>"/"//Quiet;
If[Head[TensorBasesDirectory]=!=String,Return[False]];
Return[True];
];

If[Not@TensorBasesInstalled[],
If[ChoiceDialog["TensorBases does not seem to be installed. Do you want to install it?",WindowTitle->"Install TensorBases",WindowSize->{Medium,All}],
Import["https://raw.githubusercontent.com/satfra/TensorBases/main/TensorBasesInstaller.m"],
Print["\!\(\*
StyleBox[\"FunKit\",\nFontWeight->\"Bold\"]\) requires \!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\) to run."];Abort[];
];
];

FunKitLoad::tensorBasesVersion="FunKit requires TensorBases `1` or newer, but version `2` is installed in `3`. From `1` on, TBMakePropagator expands the inverse propagator with all momenta incoming; with an older TensorBases every momentum-odd propagator dressing -- for instance the pslash dressing of the quark propagator -- is returned with the wrong sign relative to the momentum-even ones, and silently so. Re-run dependencies/install.sh or update TensorBases.";
Module[{tbDir,tbPaclet,tbVersion,tbVerList,requiredVersion="1.3.0",requiredList},requiredList=PadRight[ToExpression/@StringSplit[requiredVersion,"."],3,0];tbDir=SelectFirst[Join[{FileNameJoin[{$UserBaseDirectory,"Applications","TensorBases"}],FileNameJoin[{$BaseDirectory,"Applications","TensorBases"}],FileNameJoin[{$InstallationDirectory,"AddOns","Applications","TensorBases"}],FileNameJoin[{$InstallationDirectory,"AddOns","Packages","TensorBases"}],FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","TensorBases"}]},Select[$Path,StringContainsQ[#1,"TensorBases"]&]],DirectoryQ[#1]&];
tbPaclet=Quiet[Check[(List@@Import[FileNameJoin[{tbDir,"PacletInfo.m"}]])[[1]],$Failed]];
tbVersion=If[AssociationQ[tbPaclet]&&KeyExistsQ[tbPaclet,"Version"],tbPaclet["Version"],"0.0.0"];
tbVerList=PadRight[ToExpression/@StringSplit[tbVersion,"."],3,0];
If[!OrderedQ[{requiredList,tbVerList}],
If[$FrontEnd===Null||$Notebooks===False,Message[FunKitLoad::tensorBasesVersion,requiredVersion,tbVersion,tbDir];Abort[];];
If[ChoiceDialog[TemplateApply["FunKit requires TensorBases version `r` or newer. The installed TensorBases is version `i`. Do you want to update now?",Association["r"->requiredVersion,"i"->tbVersion]],WindowTitle->"Update TensorBases",WindowSize->{Medium,All}],
Import["https://raw.githubusercontent.com/satfra/TensorBases/main/TensorBasesInstaller.m"],
Print["\!\(\*StyleBox[\"FunKit\",FontWeight->\"Bold\"]\) requires \!\(\*StyleBox[\"TensorBases\",FontWeight->\"Bold\"]\) version "<>requiredVersion<>" or newer."];Abort[];];
];
];

Print[""]
Block[{(*Print*)},Get["TensorBases`"]];
Print[""]
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"TensorBases\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];


(* ::Input::Initialization:: *)
If[Length@PacletFind["MaTeX"]===0,
If[$AllowInternet&&$NetworkConnected&&$VersionNumber>=12.0,
ResourceFunction["MaTeXInstall"][],
PacletInstall[$FUNKITDIR<>"/dependencies/MaTeX-1.7.10.paclet"]
];
];
Get["MaTeX`"]
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"MaTeX\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];


(* ::Input::Initialization:: *)
Get[$FUNKITDIR<>"/utils/MathematicaTeXUtilities.m"]


(* ::Input::Initialization:: *)
BeginPackage["FunKit`"];
Unprotect["FunKit`*"];
Unprotect["FunKit`Private`*"];
ClearAll["FunKit`*"];
ClearAll["FunKit`Private`*"];


(* ::Input::Initialization:: *)
$FunKitDirectory=SelectFirst[
Join[
{
FileNameJoin[{$UserBaseDirectory,"Applications","FunKit"}],
FileNameJoin[{$BaseDirectory,"Applications","FunKit"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Applications","FunKit"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Packages","FunKit"}],
FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","FunKit"}]
},
Select[$Path,StringContainsQ[#,"FunKit"]&]
],
DirectoryQ[#]&
]<>"/";


(* ::Input::Initialization:: *)
Begin["`Private`"]
Get[$FunKitDirectory<>"modules/common/util.m"];
End[]


(* ::Input::Initialization:: *)
$FunKitVersion=(List@@Import[FileNameJoin[{$UserBaseDirectory,"Applications","FunKit","PacletInfo.m"}]])[[1]]["Version"];


(* ::Input::Initialization:: *)
ModuleLoaded[FunKit]=True;


(* ::Input::Initialization:: *)
If[Head[$DistributedContexts]=!=List,$DistributedContexts={}];
$DistributedContexts=$DistributedContexts\[Union]{$Context,"FunKit`Private`","FormTracer`","FormTracer`Private`"}


(* ::Input::Initialization:: *)
Begin["`Private`"]
If[Head[$DistributedContexts]=!=List,$DistributedContexts={}];
$DistributedContexts=$DistributedContexts\[Union]{$Context,"FunKit`Private`","FormTracer`","FormTracer`Private`"}
End[]


(* ::Input::Initialization:: *)
$FunKitDebugLevel=0;
FSetDebugLevel[newLevel_Integer]:=Module[{},
Unprotect@$FunKitDebugLevel;
Set[$FunKitDebugLevel,newLevel];
Protect@$FunKitDebugLevel;

Unprotect@FunKitDebug;
If[$FunKitDebugLevel<=0,ClearAll[FunKitDebug];SetAttributes[FunKitDebug,HoldAll];];
If[$FunKitDebugLevel>0,ClearAll[FunKitDebug];
FunKitDebug[level_Integer,$a___]:=If[level<=$FunKitDebugLevel,Echo[Row[{$a}],"FunKit "<>ToString[level]<>StringRepeat["    ", level]]];
];
Protect@FunKitDebug;
];
(*
0: no info
1: basic information what is happening
2: in-depth what steps are being processed
3: the guts of the program
4: nested guts of the program
*)


(* ::Input::Initialization:: *)
FunKit::invalidArguments="Invalid arguments given for function `1`, for correct usage, see `1`::usage."
FunKit::warning="Warning: `1`"
FunKit::noGlobalSetup="No global setup has been set. Either pass a setup as first argument, or set one via FSetGlobalSetup[setup]."


(* ::Input::Initialization:: *)
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"Loading\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"modules\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
Get[$FunKitDirectory<>"modules/FEDeriK.m"];
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"FEDeriK\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
Get[$FunKitDirectory<>"modules/AnSEL.m"];
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"AnSEL\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
Get[$FunKitDirectory<>"modules/DiANE.m"];
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"DiANE\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
Get[$FunKitDirectory<>"modules/DiRK.m"];
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"DiRK\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
Get[$FunKitDirectory<>"modules/TRACY.m"];
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"TRACY\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
Get[$FunKitDirectory<>"modules/COEN.m"];
$FrontEnd===Null||PrintTemporary["\!\(\*
StyleBox[\"...\",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"COEN\",\nFontSize->10,\nFontWeight->\"Bold\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSize->10,\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"loaded\",\nFontSize->10,\nFontWeight->\"Plain\",\nFontSlant->\"Italic\"]\)"];
If[$FrontEnd=!=Null,
Print["Welcome to  \!\(\*
StyleBox[\"\:2588\:2580\",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\" \",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\"\:2590\:2584\:2588\",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\" \",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\"\:2588\:259a\:258c\",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\" \",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\"\:2590\[FilledLeftTriangle]\",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\" \",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\"\:2588\",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\" \",\nFontColor->GrayLevel[0]]\)\!\(\*
StyleBox[\"\:2580\:2588\:2580\",\nFontColor->GrayLevel[0]]\)
\!\(\*
StyleBox[\"Author\",\nFontWeight->\"Bold\"]\): Franz Richard Sattler
\!\(\*
StyleBox[\"Version\",\nFontWeight->\"Bold\"]\): ",$FunKitVersion,"
\!\(\*
StyleBox[\"Year\",\nFontWeight->\"Bold\"]\): 2025
For more information and a brief introduction to the package, call \!\(\*
StyleBox[\"FInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[].
To run the testing suite, you can call  \!\(\*
StyleBox[\"FTest\",\nFontColor->RGBColor[1, 0.5, 0]]\)[].
"],
Print["Welcome to \!\(\*
StyleBox[\"FunKit\",\nFontWeight->\"Bold\"]\)"];
Print["\!\(\*
StyleBox[\"Author\",\nFontWeight->\"Bold\"]\): Franz Richard Sattler"];
Print["\!\(\*
StyleBox[\"Version\",\nFontWeight->\"Bold\"]\): ",$FunKitVersion];
Print["\!\(\*
StyleBox[\"Year\",\nFontWeight->\"Bold\"]\): 2026"];
];


(* ::Input::Initialization:: *)
Get[$FunKitDirectory<>"modules/CoBra.m"];


(* ::Input::Initialization:: *)
FInfo[]:=Module[{},
Print["To see an overview and some examples for the syntax of \!\(\*
StyleBox[\"FEDeriK\",\nFontWeight->\"Bold\"]\), which forms the basis for all of \!\(\*
StyleBox[\"FunKit\",\nFontWeight->\"Bold\"]\), call \!\(\*
StyleBox[\"FInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"FEDeriK\"]."]
];


(* ::Input::Initialization:: *)
$framedPrint[fpr_]:=Internal`InheritedBlock[{Print},
Unprotect@Print;
Print=Echo[Framed[#]]&;
Protect@Print;
ReleaseHold[fpr]
];
SetAttributes[$framedPrint,HoldAll];


(* ::Input::Initialization:: *)
FInfo[str_String]/;(str=!="federik"&&ToLowerCase[str]==="federik"):=FInfo["federik"];
FInfo["federik"]:=Module[{},
Print["\!\(\*
StyleBox[\"General\",\nFontSize->18,\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontSize->18,\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\"syntax\",\nFontSize->18,\nFontWeight->\"Bold\"]\)

The overall syntax used throughout \!\(\*
StyleBox[\"FunKit\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)is given by its core module\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\"FEDeriK\",\nFontWeight->\"Bold\"]\).
Any equation is comprised of terms that contain (possibly non-commuting) factors.
These terms are written out using the \!\(\*
StyleBox[\"FTerm\",\nFontColor->RGBColor[1, 0.5, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0.5, 0]]\)tag, e.g. the Wetterich equation ",MaTeX`MaTeX["\\partial_t \\Gamma = \\frac{1}{2}\\,G_{ab}\\partial_t R^{ab}"]," is given by
    \!\(\*
StyleBox[\"FTerm\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\!\(\*FractionBox[\(1\), \(2\)]\), \!\(\*
StyleBox[\"Propagator\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{a,b}], \!\(\*
StyleBox[\"Rdot\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{-a,-b}]]
Similar to the \!\(\*
StyleBox[\"xAct\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)Mathematica package, we use negative indices (-a, -b) to indicate lower indices and positive indices (a, b) to indicate upper ones.
Furthermore, we have utilised syntax for \!\(\*
StyleBox[\"indexed\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"objects\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSlant->\"Italic\"]\)in the above. Both \!\(\*
StyleBox[\"Propagator\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)and \!\(\*
StyleBox[\"Rdot\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)are such indexed objects. 
Any indexed object must be comprised of two lists: the first one gives the field content, and the second list the corresponding super-indices or explicit indices.
To see a list of all indexed objects known to \!\(\*
StyleBox[\"FEDeriK\",\nFontWeight->\"Bold\"]\), one can call \!\(\*
StyleBox[\"ShowIndexedObjects\",\nFontColor->RGBColor[1, 0.5, 0]]\)[], which outputs "];
$framedPrint@ShowIndexedObjects[];
Print["in the current case. One can register custom indexed objects with \!\(\*
StyleBox[\"FEDeriK\",\nFontWeight->\"Bold\"]\) by using \!\(\*
StyleBox[\"AddIndexedObject\",\nFontColor->RGBColor[1, 0.5, 0]]\)[_Symbol]. 
A subset of the indexed objects are correlation functions, and \!\(\*
StyleBox[\"ShowCorrelationFunctions\",\nFontColor->RGBColor[1, 0.5, 0]]\)[] outputs "];
$framedPrint@ShowCorrelationFunctions[];
Print["These are special indexed objects, which are always hit by functional derivatives. 
As an example, take the generalised flow equation ",MaTeX`MaTeX["\\partial_t \\Gamma = -\\dot\\Phi^a\\Gamma_a + \\frac{1}{2}G^{ac}\\Bigg(\\gamma_c^{\\phantom{c}b}\\partial_t  + 2 \\frac{\\delta\\dot{\\Phi}^b}{\\delta\\Phi^c}\\Bigg){R}_{ab}"],
"First, we add a new correlation function using \!\(\*
StyleBox[\"FAddCorrelationFunction\",\nFontColor->RGBColor[1, 0.5, 0]]\)[Phidot] and mark its last index to be never re-ordered using \!\(\*
StyleBox[\"FSetUnorderedIndices\",\nFontColor->RGBColor[1, 0.5, 0]]\)[Phidot,1]"];
FAddCorrelationFunction[Phidot];
FSetUnorderedIndices[Phidot,1];
Print["Then, the flow equation can be written out as 

    \!\(\*
StyleBox[\"FEx\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\!\(\*
StyleBox[\"FTerm\",\nFontColor->RGBColor[1, 0.5, 0]]\)[-1, \!\(\*
StyleBox[\"Phidot\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{a}], \!\(\*
StyleBox[\"GammaN\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{-a}]],\[IndentingNewLine]    \!\(\*
StyleBox[\"FTerm\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\!\(\*FractionBox[\(1\), \(2\)]\), \!\(\*
StyleBox[\"Propagator\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{a,b}], \!\(\*
StyleBox[\"Rdot\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{-a,-b}]],\[IndentingNewLine]    \!\(\*
StyleBox[\"FTerm\",\nFontColor->RGBColor[1, 0.5, 0]]\)[ \!\(\*
StyleBox[\"Propagator\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{a,c}], \!\(\*
StyleBox[\"Phidot\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{-c,b}], \!\(\*
StyleBox[\"R\",\nFontWeight->\"Bold\"]\)[{\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\),\!\(\*
StyleBox[\"AnyField\",\nFontWeight->\"Bold\"]\)},{-a,-b}]]]

In fact, Phidot has been already defined like this in \!\(\*
StyleBox[\"FEDeriK\",\nFontWeight->\"Bold\"]\). Some of the pre-defined equations, which you can examine in \!\(\*
StyleBox[\"FEDeriK\",\nFontWeight->\"Bold\"]\), are the two examples given above, which you can use under the names

	\!\(\*
StyleBox[\"WetterichEquation\",\nFontColor->RGBColor[1, 0.5, 0]]\)
	\!\(\*
StyleBox[\"GeneralizedFlowEquation\",\nFontColor->RGBColor[1, 0.5, 0]]\)
"];
];


(* ::Input::Initialization:: *)
FTest[]:=Module[{},
Get[$FunKitDirectory<>"tests/Test.m"]
]


(* ::Input::Initialization:: *)
Protect["FunKit`*"];
EndPackage[];


(* ::Input::Initialization:: *)
(* Note that we do NOT just call
DistributeDefinitions["FunKit`"]
DistributeDefinitions["FunKit`Private`"]
As this takes a LOT of time - in the following we only distribute precisely the things that are actually used (bringing down the distribution time by a factor of 10)
*)


(* ::Input::Initialization:: *)
DistributeDefinitions[
"FunKit`FTerm",
"FunKit`FFormSimplify",
"FunKit`FunKitDebug",
"FunKit`Private`SafeReplaceTrace",
"FunKit`Private`GetAllCustomSymbols",
"FunKit`Private`ImportAndSimplifyFORM",
"FunKit`Private`scallDef",
"FunKit`Private`$AlwaysExpandLorentzTensors",
"FunKit`Private`makeTemporaryFileName",
"FunKit`Private`$DefaultTimeConstraint",
"FunKit`Private`$StandardQuickSimplify",
"FunKit`Private`makeHashFile",
"FunKit`Private`NormalizeIndices",
"FunKit`Private`$TraceCacheDir",
"FunKit`Private`$standardFORMmomentumRules",
"FunKit`Private`GetAllMomenta"
];