From d930e297d1b0401c43e5bead322dfa41a19f5642 Mon Sep 17 00:00:00 2001 From: "Franz R. Sattler" Date: Wed, 18 Dec 2024 12:48:59 +0100 Subject: [PATCH] doc: update documentation of CodeTools package --- Mathematica/DiFfRG/CodeTools.m | 80 ++- Mathematica/DiFfRG/CodeTools.nb | 317 ++++++---- .../Documentation/English/Guides/DiFfRG.nb | 51 +- .../English/Guides/DiFfRGCodeTools.nb | 292 ++++++--- .../Symbols/AddCodeOptimizeFunctions.nb | 514 ++++++++++++++++ .../Symbols/ClearCodeOptimizeFunctions.nb | 502 ++++++++++++++++ .../ReferencePages/Symbols/CodeForm.nb | 503 ++++++++++++++++ .../Symbols/DeclareAnglesP34Dpqr.nb | 518 ++++++++++++++++ .../Symbols/DeclareSymmetricPoints2DP3.nb | 514 ++++++++++++++++ .../Symbols/DeclareSymmetricPoints2DP4.nb | 514 ++++++++++++++++ .../Symbols/DeclareSymmetricPoints3DP3.nb | 512 ++++++++++++++++ .../Symbols/DeclareSymmetricPoints3DP4.nb | 515 ++++++++++++++++ .../Symbols/DeclareSymmetricPoints4DP3.nb | 512 ++++++++++++++++ .../Symbols/DeclareSymmetricPoints4DP4.nb | 514 ++++++++++++++++ .../ReferencePages/Symbols/MakeFlowClass.nb | 531 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Mathematica/DiFfRG/doc_built/html/ref/Files/ShowTypes.en/i_1.txt create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/Files/UseKernelOptimizations.en/I_1.png create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/Files/UseKernelOptimizations.en/i_1.txt create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/MakeFlowClass.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/MakeFlowClassFiniteT.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/MakeKernel.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/SafeFiniteTFunctions.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/SetCppNames.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/SetFlowDirectory.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/SetKernelDefinitions.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/ShowCodeOptimizeFunctions.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/ShowFlowDirectory.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/ShowKernelDefinitions.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/ShowTypes.html create mode 100644 Mathematica/DiFfRG/doc_built/html/ref/UseKernelOptimizations.html diff --git a/Mathematica/DiFfRG/CodeTools.m b/Mathematica/DiFfRG/CodeTools.m index 3772834..678589e 100644 --- a/Mathematica/DiFfRG/CodeTools.m +++ b/Mathematica/DiFfRG/CodeTools.m @@ -36,7 +36,7 @@ Obtain properly formatted and processed C++ code from an expression."; SetCppNames::usage = "SetCppNames[rules___] -Set additional replacement rules used when invoking CodeForm[expr_]. +Set additional replacement rules used when invoking CodeForm[expr]. Example Call: SetCppNames[\"k\"->\"k_bosonic\", \"Arccos(\"->\"std::arccos(\"]"; @@ -53,7 +53,7 @@ add_executable(QCD QCD.cc ${flow_sources})"; -SetFlowDirectory::usage="SetFlowDirectory[dir_String] +SetFlowDirectory::usage="SetFlowDirectory[dir] Set the current flow directory, i.e. where all generated files are saved. Default is ./flows/"; ShowFlowDirectory::usage="ShowFlowDirectory[] Show the current flow directory, i.e. where all generated files are saved. Default is ./flows/"; @@ -71,25 +71,73 @@ This Function creates an integrator that evaluates (constantFlow + \[Integral]integrandFlow). One can prepend additional c++ definitions to the flow equation by using the integrandDefinitions and constantDefinitions parameters. These are prepended to the respective methods of the integration kernel, allowing one to e.g. define specific angles one needs for the flow code."; -DeclareSymmetricPoints4DP4::usage=""; -DeclareSymmetricPoints4DP3::usage=""; -DeclareSymmetricPoints3DP4::usage=""; -DeclareSymmetricPoints3DP3::usage=""; -DeclareSymmetricPoints2DP4::usage=""; -DeclareSymmetricPoints2DP3::usage=""; - -DeclareAnglesP34Dpqr::usage=""; +DeclareSymmetricPoints4DP4::usage="DeclareSymmetricPoints4DP4[] +Obtain C++ code declaring angles for a four-point symmetric configuration in 4D. +The angles will have the names cosp1q, cosp2q, cosp3q and cosp4q. +DeclareSymmetricPoints4DP4[computeType] +Set the type of the declared C++ variables (should be double or float)."; + +DeclareSymmetricPoints4DP3::usage="DeclareSymmetricPoints4DP3[] +Obtain C++ code declaring angles for a four-point symmetric configuration in 4D. +The angles will have the names cosp1q, cosp2q, cosp3q and cosp4q. +DeclareSymmetricPoints4DP3[computeType] +Set the type of the declared C++ variables (should be double or float)."; + +DeclareSymmetricPoints3DP4::usage="DeclareSymmetricPoints3DP4[] +Obtain C++ code declaring angles for a four-point symmetric configuration in 3D. +The angles will have the names cosp1q, cosp2q, cosp3q and cosp4q. +DeclareSymmetricPoints3DP4[computeType] +Set the type of the declared C++ variables (should be double or float)."; + +DeclareSymmetricPoints3DP3::usage="DeclareSymmetricPoints3DP3[] +Obtain C++ code declaring angles for a three-point symmetric configuration in 3D. +The angles will have the names cosp1q, cosp2q and cosp3q. +DeclareSymmetricPoints3DP3[computeType] +Set the type of the declared C++ variables (should be double or float)."; + +DeclareSymmetricPoints2DP4::usage="DeclareSymmetricPoints2DP4[] +Obtain C++ code declaring angles for a four-point symmetric configuration in 2D. +The angles will have the names cosp1q, cosp2q, cosp3q and cosp4q. +DeclareSymmetricPoints2DP4[computeType] +Set the type of the declared C++ variables (should be double or float)."; + +DeclareSymmetricPoints2DP3::usage="DeclareSymmetricPoints2DP3[] +Obtain C++ code declaring angles for a three-point symmetric configuration in 2D. +The angles will have the names cosp1q, cosp2q and cosp3q. +DeclareSymmetricPoints2DP3[computeType] +Set the type of the declared C++ variables (should be double or float)."; + +DeclareAnglesP34Dpqr::usage="DeclareAnglesP34Dpqr[q,p,r] +Obtain C++ code declaring angles for the angles in a full three-point function in 4D. +The angles will have the names cospq and cosqr, where q,p,r are replaced by the given Symbol names and ordered alphabetically. +DeclareAnglesP34Dpqr[q,p,r,computeType] +Set the type of the declared C++ variables (should be double or float)."; SafeFiniteTFunctions::usage=""; -ShowTypes::usage=""; -AddCodeOptimizeFunctions::usage=""; -ShowCodeOptimizeFunctions::usage=""; -ClearCodeOptimizeFunctions::usage=""; -UseKernelOptimizations::usage=""; + +ShowTypes::usage="ShowTypes[] +Show a list of all types available for use in a parameter list to make a kernel."; + +AddCodeOptimizeFunctions::usage="AddCodeOptimizeFunctions[func1[__], func2[__],...] +Add the functions func1, func2, ... to the functions to be optimized out, i.e. calculated only once in auto-generated kernel code."; + +ShowCodeOptimizeFunctions::usage="ShowCodeOptimizeFunctions[] +Show a list of all functions which DiFfRG will try to optimize out when generating C++ code."; + +ClearCodeOptimizeFunctions::usage="ClearCodeOptimizeFunctions[] +Remove all optimization functions from the internal list"; + +UseKernelOptimizations::usage="UseKernelOptimizations[True] +Turn on code optimizations in auto-generation of C++ code. +UseKernelOptimizations[False] +Turn off code optimizations in auto-generation of C++ code. +"; SetKernelDefinitions::usage="SetKernelDefinitions[definitionCode_String] sets the kernel definitions to definitionCode. SetKernelDefinitions[] resets the kernel definitions to the standard."; -ShowKernelDefinitions::usage="ShowKernelDefinitions[]"; + +ShowKernelDefinitions::usage="ShowKernelDefinitions[] +Show the currently specified kernel definitions code."; Begin["`Private`"]; diff --git a/Mathematica/DiFfRG/CodeTools.nb b/Mathematica/DiFfRG/CodeTools.nb index fa8b348..fcbb076 100644 --- a/Mathematica/DiFfRG/CodeTools.nb +++ b/Mathematica/DiFfRG/CodeTools.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 325316, 7367] -NotebookOptionsPosition[ 313870, 7156] -NotebookOutlinePosition[ 314660, 7182] -CellTagsIndexPosition[ 314617, 7179] +NotebookDataLength[ 328800, 7422] +NotebookOptionsPosition[ 317347, 7211] +NotebookOutlinePosition[ 318140, 7237] +CellTagsIndexPosition[ 318097, 7234] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -82,7 +82,7 @@ from an expression.\>\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{"SetCppNames", "::", "usage"}], " ", "=", " ", "\"\\\\"k_bosonic\\\", \\\"Arccos(\\\"->\\\"std::arccos(\\\ \"]\>\""}], ";"}], "\n"}], "\n", RowBox[{ @@ -113,9 +113,8 @@ ${flow_sources})\>\""}], ";"}], "\n", "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{"SetFlowDirectory", "::", "usage"}], "=", - "\"\\""}], ";"}], "\n", - + "\"\\""}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{ @@ -157,68 +156,119 @@ integration kernel, allowing one to e.g. define specific angles one needs for \ the flow code.\>\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ - RowBox[{"DeclareSymmetricPoints4DP4", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n", + RowBox[{ + RowBox[{"DeclareSymmetricPoints4DP4", "::", "usage"}], "=", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ - RowBox[{"DeclareSymmetricPoints4DP3", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n", + RowBox[{ + RowBox[{"DeclareSymmetricPoints4DP3", "::", "usage"}], "=", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ - RowBox[{"DeclareSymmetricPoints3DP4", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n", + RowBox[{ + RowBox[{"DeclareSymmetricPoints3DP4", "::", "usage"}], "=", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ - RowBox[{"DeclareSymmetricPoints3DP3", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n", + RowBox[{ + RowBox[{"DeclareSymmetricPoints3DP3", "::", "usage"}], "=", + "\"\\""}], ";"}], + "\n"}], "\n", RowBox[{ RowBox[{ - RowBox[{"DeclareSymmetricPoints2DP4", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n", + RowBox[{ + RowBox[{"DeclareSymmetricPoints2DP4", "::", "usage"}], "=", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"DeclareSymmetricPoints2DP3", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n"}], "\n", + RowBox[{"DeclareSymmetricPoints2DP3", "::", "usage"}], "=", + "\"\\""}], ";"}], + "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"DeclareAnglesP34Dpqr", "::", "usage"}], "=", "\"\<\>\""}], ";"}], + RowBox[{"DeclareAnglesP34Dpqr", "::", 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RowBox[{"ClearCodeOptimizeFunctions", "::", "usage"}], "=", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"UseKernelOptimizations", "::", "usage"}], "=", "\"\<\>\""}], - ";"}], "\n"}], "\n", + RowBox[{"UseKernelOptimizations", "::", "usage"}], "=", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ - RowBox[{"SetKernelDefinitions", "::", "usage"}], "=", - "\"\\""}], ";"}], "\n", +definitions to the standard.\>\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{"ShowKernelDefinitions", "::", "usage"}], "=", - "\"\\""}], ";"}]}], "Code", + "\"\\""}], ";"}]}], "Code", CellChangeTimes->{{3.916637829669835*^9, 3.91663783796828*^9}, { 3.916638110622831*^9, 3.916638118237995*^9}, {3.9167289728094*^9, 3.916728976539971*^9}, {3.916730910644607*^9, 3.916730924497292*^9}, { @@ -247,15 +297,20 @@ definitions to the standard.\>\""}], ";"}], "\n", 3.943356212474441*^9}, {3.943356244052917*^9, 3.943356507237863*^9}, { 3.9434347923639927`*^9, 3.943434867234779*^9}, 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CellID->1130176294] +}, Closed]] +}, Open ]] +} +] +*) + diff --git a/Mathematica/DiFfRG/doc_built/html/guide/DiFfRG.html b/Mathematica/DiFfRG/doc_built/html/guide/DiFfRG.html index 08bd569..2c6edcd 100644 --- a/Mathematica/DiFfRG/doc_built/html/guide/DiFfRG.html +++ b/Mathematica/DiFfRG/doc_built/html/guide/DiFfRG.html @@ -98,7 +98,39 @@ -

DiFfRG

The Mathematica package of the DiFfRG (Discretization framework for functional Renormalization Group flows). See also the Code generation documentation.

Utility functions

AutoExport — Turn on automatic export of the current notebook to a  ▪  m file .

AutoSaveRestore — Export expression to a file, or load it from an existing file.

ClearTraceCache — Remove the entire trace cache, or parts of it.

GetDirectory — Return the directory in which either the package file or notebook is located .

QuickSimplify — Simplify with a small time constraint.

Tracing functionality

ExtendedFormTrace — Runs PreTrace and then FormTrace.

TraceDiagrams — Trace a list of diagrams, saving them to temporary files.

SumDiagrams — Process and sum the result of TraceDiagrams to a result.

MakeSPFormRule — Project momenta to the symmetric point.

MakeSPFiniteTFormRule — Project momenta to the symmetric point in the spatial domain.

FormMomentumExpansion — Make a PostTraceRule which tries to simplify momenta.

FiniteTFormMomentumExpansion — Make a PostTraceRule to expand all momenta into spatial and temporal components.

MakeP0FormRule — Make a PostTraceRule to replace (imaginary)-time components of momenta.

GetFTSynonym — Get the internal FormTracer name of a symbol.

UseSU3GellMannTrace — Trace the FormTracer group called color using explicit Gell-Mann matrices.

PreTrace — Resolve charge conjugation and explicit color tracing.

SetDisentangle — Set whether TraceDiagrams uses DisentangleLorentzStructures.

Momentum handling

MatsubaraSum — Perform a (bosonic) Matsubara sum.

SeparateScalarProductsFiniteT — Separate all scalar products into spatial and temporal parts.

ExpandScalarProductsFiniteT — Separate all scalar products into spatial and temporal parts and write them in an angular representation.

ExpandScalarProducts — Write all scalar products an angular representation.

SimplifyAllMomenta — Replace all composite objects to single symbols. Necessary for code output.

ProjectToSymmetricPoint — Project an expression to the symmetric point.

ProjectToSymmetricPointFiniteT — Project an expression to the spatial symmetric point.

+
  • + Related Guides + +
    • +
  • + Tech Notes + +
    • +

    DiFfRG

    The Mathematica package of the DiFfRG (Discretization framework for functional Renormalization Group flows). See also the Code generation documentation.

    Utility functions

    AutoExport — Turn on automatic export of the current notebook to a  ▪  m file .

    AutoSaveRestore — Export expression to a file, or load it from an existing file.

    ClearTraceCache — Remove the entire trace cache, or parts of it.

    GetDirectory — Return the directory in which either the package file or notebook is located .

    QuickSimplify — Simplify with a small time constraint.

    Tracing functionality

    ExtendedFormTrace — Runs PreTrace and then FormTrace.

    TraceDiagrams — Trace a list of diagrams, saving them to temporary files.

    SumDiagrams — Process and sum the result of TraceDiagrams to a result.

    MakeSPFormRule — Project momenta to the symmetric point.

    MakeSPFiniteTFormRule — Project momenta to the symmetric point in the spatial domain.

    FormMomentumExpansion — Make a PostTraceRule which tries to simplify momenta.

    FiniteTFormMomentumExpansion — Make a PostTraceRule to expand all momenta into spatial and temporal components.

    MakeP0FormRule — Make a PostTraceRule to replace (imaginary)-time components of momenta.

    GetFTSynonym — Get the internal FormTracer name of a symbol.

    UseSU3GellMannTrace — Trace the FormTracer group called color using explicit Gell-Mann matrices.

    PreTrace — Resolve charge conjugation and explicit color tracing.

    SetDisentangle — Set whether TraceDiagrams uses DisentangleLorentzStructures.

    Momentum handling

    MatsubaraSum — Perform a (bosonic) Matsubara sum.

    SeparateScalarProductsFiniteT — Separate all scalar products into spatial and temporal parts.

    ExpandScalarProductsFiniteT — Separate all scalar products into spatial and temporal parts and write them in an angular representation.

    ExpandScalarProducts — Write all scalar products an angular representation.

    SimplifyAllMomenta — Replace all composite objects to single symbols. Necessary for code output.

    ProjectToSymmetricPoint — Project an expression to the symmetric point.

    ProjectToSymmetricPointFiniteT — Project an expression to the spatial symmetric point.

    diff --git a/Mathematica/DiFfRG/doc_built/html/guide/DiFfRGCodeTools.html b/Mathematica/DiFfRG/doc_built/html/guide/DiFfRGCodeTools.html index d616df0..22087ea 100644 --- a/Mathematica/DiFfRG/doc_built/html/guide/DiFfRGCodeTools.html +++ b/Mathematica/DiFfRG/doc_built/html/guide/DiFfRGCodeTools.html @@ -20,24 +20,128 @@
    -

    DiFfRG`CodeTools`

    The code-generation sub-package of DiFfRG

    Auto-Generating C++ Code

    MakeFlowClass — Create a base class that holds all integration kernel objects and generate CMake information.

    MakeFlowClassFiniteT — Create a base class that holds all integration kernel objects and generate CMake information.

    MakeKernel — Generate code for an integration kernel.

    CodeForm — Convert an expression to a C++ string.

    SafeFiniteTFunctions — Replace mathematical functions by alternatives with built-in safety.

    Declaring angular configurations

    DeclareSymmetricPoints4DP4 — Declare angles for a four-point symmetric point in 4D

    DeclareSymmetricPoints4DP3 — Declare angles for a three-point symmetric point in 4D

    DeclareSymmetricPoints3DP4 — Declare angles for a four-point symmetric point in 3D

    DeclareSymmetricPoints3DP3 — Declare angles for a three-point symmetric point in 3D

    DeclareSymmetricPoints2DP4 — Declare angles for a four-point symmetric point in 2D

    DeclareSymmetricPoints2DP3 — Declare angles for a three-point symmetric point in 2D

    DeclareAnglesP34Dpqr — Declare angles for a full three-point vertex in 4D

    Setting the global output directory

    +

    DiFfRG`CodeTools`

    The code-generation sub-package of DiFfRG

    Auto-Generating C++ Code

    MakeFlowClass — Create a base class that holds all integration kernel objects and generate CMake information.

    MakeFlowClassFiniteT — Create a base class that holds all integration kernel objects and generate CMake information.

    MakeKernel — Generate code for an integration kernel.

    CodeForm — Convert an expression to a C++ string.

    SafeFiniteTFunctions — Replace mathematical functions by alternatives with built-in safety.

    Declaring angular configurations

    DeclareSymmetricPoints4DP4 — Declare angles for a four-point symmetric point in 4D

    DeclareSymmetricPoints4DP3 — Declare angles for a three-point symmetric point in 4D

    DeclareSymmetricPoints3DP4 — Declare angles for a four-point symmetric point in 3D

    DeclareSymmetricPoints3DP3 — Declare angles for a three-point symmetric point in 3D

    DeclareSymmetricPoints2DP4 — Declare angles for a four-point symmetric point in 2D

    DeclareSymmetricPoints2DP3 — Declare angles for a three-point symmetric point in 2D

    DeclareAnglesP34Dpqr — Declare angles for a full three-point vertex in 4D

    Setting the global output directory

    - SetFlowDirectory + SetFlowDirectory  ▪  - ShowFlowDirectory -

    ShowTypes — Information about the usable types.

    Configure code optimizations

    + ShowFlowDirectory +

    ShowTypes — Information about the usable types.

    Configure code optimizations

    - AddCodeOptimizeFunctions + AddCodeOptimizeFunctions  ▪  - ShowCodeOptimizeFunctions + ShowCodeOptimizeFunctions  ▪  - ClearCodeOptimizeFunctions -

    UseKernelOptimizations — Toggle kernel optimizations.

    Configure C++ and kernel export

    + ClearCodeOptimizeFunctions +

    UseKernelOptimizations — Toggle kernel optimizations.

    Configure C++ and kernel export

    - SetKernelDefinitions + SetKernelDefinitions  ▪  - ShowKernelDefinitions -

    SetCppNames — Set additional replacements for C++ generation.

    + ShowKernelDefinitions +

    SetCppNames — Set additional replacements for C++ generation.

    diff --git a/Mathematica/DiFfRG/doc_built/html/ref/AddCodeOptimizeFunctions.html b/Mathematica/DiFfRG/doc_built/html/ref/AddCodeOptimizeFunctions.html new file mode 100644 index 0000000..d23ea29 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/AddCodeOptimizeFunctions.html @@ -0,0 +1,69 @@ + + + + + + + + + + +AddCodeOptimizeFunctions—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    AddCodeOptimizeFunctions

    +
    +

    + AddCodeOptimizeFunctions[func1[__],func2[__],...] +

    +

    Add the functions func1, func2, ... to the functions to be optimized out, i.e. calculated only once in auto-generated kernel code.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/AutoExport.html b/Mathematica/DiFfRG/doc_built/html/ref/AutoExport.html index 20ce0cb..4170572 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/AutoExport.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/AutoExport.html @@ -36,7 +36,7 @@

    Turns on automatic export of the current notebook to a .m file.

    -

    Examples

    +

    Examples

    Evaluates expr if the file fileName does not yet exist and saves it to fileName as a .m file. If the fileName exists, it does not evaluate expr, but simply loads the contents.

    -

    Examples

    +

    Examples

    + + + + + + + + +ClearCodeOptimizeFunctions—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    ClearCodeOptimizeFunctions

    +
    +

    + ClearCodeOptimizeFunctions[] +

    +

    Remove all optimization functions from the internal list

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/ClearTraceCache.html b/Mathematica/DiFfRG/doc_built/html/ref/ClearTraceCache.html index ff89fc9..19f7fb9 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/ClearTraceCache.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/ClearTraceCache.html @@ -42,7 +42,7 @@

    Removes the folder TraceBuffer/name/

    -

    Examples

    +

    Examples

    + + + + + + + + +CodeForm—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    CodeForm

    +
    +

    + CodeForm[expr] +

    +

    Obtain properly formatted and processed C++ code from an expression.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareAnglesP34Dpqr.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareAnglesP34Dpqr.html new file mode 100644 index 0000000..bc376e2 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareAnglesP34Dpqr.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareAnglesP34Dpqr—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareAnglesP34Dpqr

    +
    +

    + DeclareAnglesP34Dpqr[q,p,r] +

    +

    Obtain C++ code declaring angles for the angles in a full three-point function in 4D. The angles will have the names cospq and cosqr,where q,p,r are replaced by the given Symbol names and ordered alphabetically.

    +
    +
    +

    + DeclareAnglesP34Dpqr[q,p,r,computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints2DP3.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints2DP3.html new file mode 100644 index 0000000..61686ed --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints2DP3.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareSymmetricPoints2DP3—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareSymmetricPoints2DP3

    +
    +

    + DeclareSymmetricPoints2DP3[] +

    +

    Obtain C++ code declaring angles for a three-point symmetric configuration in 2D. The angles will have the names cosp1q,cosp2q and cosp3q.

    +
    +
    +

    + DeclareSymmetricPoints2DP3[computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints2DP4.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints2DP4.html new file mode 100644 index 0000000..8215dd6 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints2DP4.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareSymmetricPoints2DP4—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareSymmetricPoints2DP4

    +
    +

    + DeclareSymmetricPoints2DP4[] +

    +

    Obtain C++ code declaring angles for a four-point symmetric configuration in 2D. The angles will have the names cosp1q,cosp2q,cosp3q and cosp4q.

    +
    +
    +

    + DeclareSymmetricPoints2DP4[computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints3DP3.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints3DP3.html new file mode 100644 index 0000000..0d90d44 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints3DP3.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareSymmetricPoints3DP3—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareSymmetricPoints3DP3

    +
    +

    + DeclareSymmetricPoints3DP3[] +

    +

    Obtain C++ code declaring angles for a three-point symmetric configuration in 3D. The angles will have the names cosp1q,cosp2q and cosp3q.

    +
    +
    +

    + DeclareSymmetricPoints3DP3[computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints3DP4.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints3DP4.html new file mode 100644 index 0000000..c3f71f8 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints3DP4.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareSymmetricPoints3DP4—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareSymmetricPoints3DP4

    +
    +

    + DeclareSymmetricPoints3DP4[] +

    +

    Obtain C++ code declaring angles for a four-point symmetric configuration in 3D. The angles will have the names cosp1q,cosp2q,cosp3q and cosp4q.

    +
    +
    +

    + DeclareSymmetricPoints3DP4[computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints4DP3.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints4DP3.html new file mode 100644 index 0000000..ed666dd --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints4DP3.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareSymmetricPoints4DP3—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareSymmetricPoints4DP3

    +
    +

    + DeclareSymmetricPoints4DP3[] +

    +

    Obtain C++ code declaring angles for a four-point symmetric configuration in 4D. The angles will have the names cosp1q,cosp2q,cosp3q and cosp4q.

    +
    +
    +

    + DeclareSymmetricPoints4DP3[computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints4DP4.html b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints4DP4.html new file mode 100644 index 0000000..f1a1114 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/DeclareSymmetricPoints4DP4.html @@ -0,0 +1,75 @@ + + + + + + + + + + +DeclareSymmetricPoints4DP4—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    DeclareSymmetricPoints4DP4

    +
    +

    + DeclareSymmetricPoints4DP4[] +

    +

    Obtain C++ code declaring angles for a four-point symmetric configuration in 4D. The angles will have the names cosp1q,cosp2q,cosp3q and cosp4q.

    +
    +
    +

    + DeclareSymmetricPoints4DP4[computeType] +

    +

    Set the type of the declared C++ variables (should be double or float).

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/ExpandScalarProducts.html b/Mathematica/DiFfRG/doc_built/html/ref/ExpandScalarProducts.html index 02e8035..6f4a167 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/ExpandScalarProducts.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/ExpandScalarProducts.html @@ -36,7 +36,7 @@

    Write all scalar products in expr into their angular form, i.e. sp[a,b] is replaced by a b cos[a,b]

    -

    Examples

    +

    Examples

    First, expand all scalar products into spatial and temporal parts. Then write all scalar products in expr into their angular form, i.e. sps[a,b] is replaced by a b cos[a,b]

    -

    Examples

    +

    Examples

    Trace an expression with DiFfRG extensions to FormTrace. Specify additional FORM rules

    -

    Examples

    +

    Examples

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    Create a Form rule to try and simplify all scalar products involving p1, p2, ... This method also expands scalar products into spatial and temporal parts.

    -

    Examples

    +

    Examples

    Create a Form rule to try and simplify all scalar products involving p1, p2, ...

    -

    Examples

    +

    Examples

    Returns the directory in which either the package file or notebook is located.

    -

    Examples

    +

    Examples

    Obtain the FormTracer-internal symbol name for the given symbol, for use with custom FORM rules.

    -

    Examples

    +

    Examples

    + + + + + + + + +MakeFlowClass—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    MakeFlowClass

    +
    +

    + MakeFlowClass[name,kernels] +

    +

    This creates a file flows.hh inside the flow directory, containing a class with the specified name, as well as several other files. All defined kernels have a corresponding integrator object in this class. Also automatically calls MakeCMakeFile with the passed list of kernels.

    +
    +
    +

    Details and Options

    +
    +
      +
    • The following options can be given:
      • +
    • + + + + + + + + +
      "Regulator""PolynomialExpRegulator", A regulator in the DiFfRG namespace
      "RegulatorOptionCode"{, }A list of two strings: the name of the options struct and the C++ code to define the struct.
      +
      • +
    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/MakeFlowClassFiniteT.html b/Mathematica/DiFfRG/doc_built/html/ref/MakeFlowClassFiniteT.html new file mode 100644 index 0000000..1aa10b0 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/MakeFlowClassFiniteT.html @@ -0,0 +1,87 @@ + + + + + + + + + + +MakeFlowClassFiniteT—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    MakeFlowClassFiniteT

    +
    +

    + MakeFlowClassFiniteT[name_String,kernels_List] +

    +

    This creates a file flows.hh inside the flow directory, containing a class with the specified name, as well as several other files. Alldefined kernels have a corresponding integrator object in this class. Automatically calls MakeCMakeFile with the passed list of kernels.

    +
    +
    +

    Details and Options

    +
    +
      +
    • The following options can be given:
      • +
    • + + + + + + + + +
      "Regulator""PolynomialExpRegulator", A regulator in the DiFfRG namespace
      "RegulatorOptionCode"{, }A list of two strings: the name of the options struct and the C++ code to define the struct.
      +
      • +
    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/MakeKernel.html b/Mathematica/DiFfRG/doc_built/html/ref/MakeKernel.html new file mode 100644 index 0000000..52e5f7c --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/MakeKernel.html @@ -0,0 +1,90 @@ + + + + + + + + + + +MakeKernel—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    MakeKernel

    +
    +

    + MakeKernel[kernel,parameterList,integrandFlow] +

    +

    Make a kernel from a given flow equation, parameter list and kernel.

    +
    +
    +

    + MakeKernel[kernel,parameterList,integrandFlow,constantFlow] +

    +

    Add a constant to be added to the flow. Default is a value of 0 for constantFlow.

    +
    +
    +

    + MakeKernel[kernel,parameterList,integrandFlow,constantFlow,integrandDefinitions,constantDefinitions] +

    +

    Add C++ code to be inserted into the beginning of the flow and constant methods.

    +
    +
    +

    Details and Options

    +
    +
      +
    • This Function creates an integrator that evaluates (constantFlow + ∫integrandFlow).
      • +
    • The kernel must be a valid specification of an integration kernel, see also How to use DiFfRG.
      • +
    • One can prepend additional c++ definitions to the flow equation by using the integrandDefinitions and constantDefinitions parameters. These are prepended to the respective methods of the integration kernel, allowing one to e.g. define specific angles one needs for the flow code.
      • +
    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/MakeP0FormRule.html b/Mathematica/DiFfRG/doc_built/html/ref/MakeP0FormRule.html index 49338de..3319e80 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/MakeP0FormRule.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/MakeP0FormRule.html @@ -36,7 +36,7 @@

    Make a FORM rule for use with FormTrace or ExtendedFormTrace, which projects the zeroth components of the given momenta p1,p2,... onto specified expressions proj1,proj2,....

    -

    Examples

    +

    Examples

    Make a FORM rule for use with FormTrace or ExtendedFormTrace, which projects the given momenta onto a spatial symmetric-point rule associated with them.

    -

    Examples

    +

    Examples

    Make a FORM rule for use with FormTrace or ExtendedFormTrace, which projects the given momenta onto a symmetric-point rule associated with them.

    -

    Examples

    +

    Examples

    Sums the expression expr over p0, with p0=2π T n, where n∈

    -

    Examples

    +

    Examples

    Resolve charge conjugation and perform possibly the explicit color trace.

    -

    Examples

    +

    Examples

    Project expr to a symmetric point involving the given momenta. p is the resulting average momentum and q is the loop momentum.

    -

    Examples

    +

    Examples

    Project expr to a spatial symmetric point involving the given momenta. p is the resulting average momentum and q is the loop momentum.

    -

    Examples

    +

    Examples

    Simplify the expression with a small time constraint.

    -

    Examples

    +

    Examples

    + + + + + + + + +SafeFiniteTFunctions—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    SafeFiniteTFunctions

    +
    +

    + SafeFiniteTFunctions[expression] +

    +

    Replace some hyperbolic functions with liftable singularities by safe alternatives.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/SeparateScalarProductsFiniteT.html b/Mathematica/DiFfRG/doc_built/html/ref/SeparateScalarProductsFiniteT.html index b1d2c2c..8b5c4c1 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/SeparateScalarProductsFiniteT.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/SeparateScalarProductsFiniteT.html @@ -29,7 +29,7 @@ -
    DiFfRG`
    DiFfRG`

    SeparateScalarProductsFiniteT

    Examples

    +
    DiFfRG`
    DiFfRG`

    SeparateScalarProductsFiniteT

    Examples

    + + + + + + + + +SetCppNames—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    SetCppNames

    +
    +

    + SetCppNames[rules___] +

    +

    Set additional replacement rules used when invoking CodeForm[expr].

    +
    +

    Examples

    +
    +
    +

    Basic Examples  (0)

    +
    +
    SetCppNames["k"->"k_bosonic","Arctan("->"std::arctan("]
    +
    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/SetDisentangle.html b/Mathematica/DiFfRG/doc_built/html/ref/SetDisentangle.html index 4b8eb00..c876d31 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/SetDisentangle.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/SetDisentangle.html @@ -36,7 +36,7 @@

    Set whether TraceDiagrams uses DisentangleLorentzStructures from FormTracer or not.

    -

    Examples

    +

    Examples

    + + + + + + + + +SetFlowDirectory—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    SetFlowDirectory

    +
    +

    + SetFlowDirectory[dir] +

    +

    Set the current flow directory, i.e. where all generated files are saved. Default is ./flows/

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/SetKernelDefinitions.html b/Mathematica/DiFfRG/doc_built/html/ref/SetKernelDefinitions.html new file mode 100644 index 0000000..efc3ab5 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/SetKernelDefinitions.html @@ -0,0 +1,75 @@ + + + + + + + + + + +SetKernelDefinitions—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    SetKernelDefinitions

    +
    +

    + SetKernelDefinitions[definitionCode] +

    +

    sets the kernel definitions to definitionCode.

    +
    +
    +

    + SetKernelDefinitions[] +

    +

    resets the kernel definitions to the standard.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/ShowCodeOptimizeFunctions.html b/Mathematica/DiFfRG/doc_built/html/ref/ShowCodeOptimizeFunctions.html new file mode 100644 index 0000000..8170e66 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/ShowCodeOptimizeFunctions.html @@ -0,0 +1,69 @@ + + + + + + + + + + +ShowCodeOptimizeFunctions—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    ShowCodeOptimizeFunctions

    +
    +

    + ShowCodeOptimizeFunctions[] +

    +

    Show a list of all functions which DiFfRG will try to optimize out when generating C++ code.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/ShowFlowDirectory.html b/Mathematica/DiFfRG/doc_built/html/ref/ShowFlowDirectory.html new file mode 100644 index 0000000..bf81b86 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/ShowFlowDirectory.html @@ -0,0 +1,69 @@ + + + + + + + + + + +ShowFlowDirectory—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    ShowFlowDirectory

    +
    +

    + ShowFlowDirectory[] +

    +

    Show the current flow directory, i.e. where all generated files are saved. Default is ./flows/

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/ShowKernelDefinitions.html b/Mathematica/DiFfRG/doc_built/html/ref/ShowKernelDefinitions.html new file mode 100644 index 0000000..6c161bf --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/ShowKernelDefinitions.html @@ -0,0 +1,69 @@ + + + + + + + + + + +ShowKernelDefinitions—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    ShowKernelDefinitions

    +
    +

    + ShowKernelDefinitions[] +

    +

    Show the currently specified kernel definitions code.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/ShowTypes.html b/Mathematica/DiFfRG/doc_built/html/ref/ShowTypes.html new file mode 100644 index 0000000..cd46894 --- /dev/null +++ b/Mathematica/DiFfRG/doc_built/html/ref/ShowTypes.html @@ -0,0 +1,69 @@ + + + + + + + + + + +ShowTypes—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    ShowTypes

    +
    +

    + ShowTypes[] +

    +

    Show a list of all types available for use in a parameter list to make a kernel.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/SimplifyAllMomenta.html b/Mathematica/DiFfRG/doc_built/html/ref/SimplifyAllMomenta.html index d4b8b2d..1d34128 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/SimplifyAllMomenta.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/SimplifyAllMomenta.html @@ -36,7 +36,7 @@

    Replace all angles between momenta cos[p1,p2] by auto-generated symbols. This step is necessary for code export.

    -

    Examples

    +

    Examples

    Save the diagram to outputName instead of the standard "sum.m".

    -

    Examples

    +

    Examples

    Use the function func on the result from FormTracer instead of the $StandardSimplify used otherwise.

    -

    Examples

    +

    Examples

    + + + + + + + + +UseKernelOptimizations—Wolfram Language Documentation + + + + + + + + + + +
    +
    DiFfRG`
    DiFfRG`

    UseKernelOptimizations

    +
    +

    + UseKernelOptimizations[True] +

    +

    Turn on code optimizations in auto-generation of C++ code.

    +
    +
    +

    + UseKernelOptimizations[False] +

    +

    Turn off code optimizations in auto-generation of C++ code.

    +
    +

    Examples

    +
    +
    +
    + + + +
    +
    +
    + + + \ No newline at end of file diff --git a/Mathematica/DiFfRG/doc_built/html/ref/UseSU3GellMannTrace.html b/Mathematica/DiFfRG/doc_built/html/ref/UseSU3GellMannTrace.html index 7ab16a3..dbc5fa3 100644 --- a/Mathematica/DiFfRG/doc_built/html/ref/UseSU3GellMannTrace.html +++ b/Mathematica/DiFfRG/doc_built/html/ref/UseSU3GellMannTrace.html @@ -36,7 +36,7 @@

    Toggle the use of the explicit tracing for the color group.

    -

    Examples

    +

    Examples

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