├── .gitattributes ├── tests ├── PrintSystemVersion.mt ├── TestSuite.mt ├── xAct.mt ├── xCoba.mt ├── xCore.mt ├── Invar.mt └── xPert.mt ├── .gitignore ├── xTras ├── Kernel │ └── init.m └── Documentation │ └── English │ └── ReferencePages │ └── Symbols │ ├── Coefficients.nb │ ├── ConstantPrefix.nb │ ├── SortMethod.nb │ ├── OrderParameter.nb │ ├── CollectMethod.nb │ ├── SymmetrizeMethod.nb │ ├── AuxiliaryTensor.nb │ ├── FreeMetrics.nb │ ├── Description.nb │ ├── UncontractedIndices.nb │ ├── SimplifyMethod.nb │ ├── $SymCovDCache.nb │ ├── IncludeDuals.nb │ ├── ExtraRules.nb │ ├── BackgroundSolution.nb │ ├── BasicDDITableaux.nb │ ├── ConstantExprQ.nb │ ├── BasicDDIRelations.nb │ ├── ManifestSymmetry.nb │ ├── TermsOf.nb │ ├── MetricOfKillingVector.nb │ ├── DivFreeQ.nb │ └── YoungTableauQ.nb ├── .MathematicaResources ├── .project ├── PacletInfo.m ├── xAct └── xTras │ ├── xCoba.m │ ├── xCore.m │ └── Kernel │ └── init.m └── README.md /.gitattributes: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /tests/PrintSystemVersion.mt: -------------------------------------------------------------------------------- 1 | Print[System`$Version]; 2 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /dist 2 | /log.txt 3 | /CHANGELOG 4 | /deploy.xml 5 | /build 6 | /docbuild 7 | -------------------------------------------------------------------------------- /xTras/Kernel/init.m: -------------------------------------------------------------------------------- 1 | (* Mathematica Init File *) 2 | 3 | xAct`xTras`Private`$xTrasContext = "xTras`"; 4 | Get["xAct`xTras`"]; -------------------------------------------------------------------------------- /tests/TestSuite.mt: -------------------------------------------------------------------------------- 1 | TestSuite[{ 2 | "PrintSystemVersion.mt", 3 | "xCore.mt", 4 | "xTensor.mt", 5 | "xPert.mt", 6 | "Invar.mt", 7 | "xCoba.mt", 8 | "Algebra.mt", 9 | "Combinatorics.mt", 10 | "xAct.mt", 11 | "PrintSystemVersion.mt" 12 | }] -------------------------------------------------------------------------------- /.MathematicaResources: -------------------------------------------------------------------------------- 1 | Resources[ 2 | Version[1], 3 | Sources[ 4 | Directory["~"] 5 | ], 6 | ExecutionBuildCommand["< 2 | 3 | xact-xtras 4 | 5 | 6 | 7 | 8 | 9 | com.wolfram.eclipse.MEET.MathematicaProjectBuilder 10 | 11 | 12 | 13 | 14 | 15 | com.wolfram.eclipse.MEET.SimpleMathematicaNature 16 | 17 | 18 | -------------------------------------------------------------------------------- /PacletInfo.m: -------------------------------------------------------------------------------- 1 | (* Paclet Info File *) 2 | 3 | (* created 2014/08/22*) 4 | 5 | Paclet[ 6 | Name -> "xTras", 7 | Version -> "1.4.2", 8 | MathematicaVersion -> "6+", 9 | Description -> "Field theory inspired additions to xAct", 10 | Creator -> "Teake Nutma", 11 | Extensions -> 12 | { 13 | {"Kernel", Context -> 14 | {"xTras`"} 15 | }, 16 | {"Documentation", Resources -> 17 | {"Guides/xTras"} 18 | , Language -> "English", LinkBase -> "xTras", MainPage -> "Guides/xTras"} 19 | } 20 | ] 21 | 22 | 23 | -------------------------------------------------------------------------------- /tests/xAct.mt: -------------------------------------------------------------------------------- 1 | (* Mathematica Test File *) 2 | 3 | (* This file contains tests for the core xAct packages, not for xTras. *) 4 | 5 | 6 | (* ToCanonical 1.1.0 issue reported here: https://groups.google.com/d/msg/xAct/t0vAM34PYYU/yv3xLPvXRywJ *) 7 | 8 | DefTensor[S6[a,b,c,d,e,f],M,Symmetric@Range@6]; 9 | 10 | Test[ 11 | Block[{$IterationLimit = 500}, 12 | ToCanonical @ Symmetrize @ S6[a,b,c,d,e,f] 13 | ] 14 | , 15 | S6[a,b,c,d,e,f] 16 | , 17 | TestID->"xAct-20140224-C9X8J2" 18 | ] 19 | 20 | 21 | 22 | (* xTensor perfomance issue reported here: https://groups.google.com/d/msg/xAct/ol7hmHXMJxk/wYHXwLefJ7oJ *) 23 | 24 | dim = 4; 25 | xAct`xTras`Private`DefBasicDDI[CD]; 26 | 27 | Test[ 28 | TimeConstrained[ 29 | ToCanonical[ 30 | BasicDDICD4[-a, -b, -c, -d, -e, -f, -g, -h, -i, -j] S2[k, l] CD[i, j]@RiemannCD[e, f, g, h] CD[b, c, d]@S3[a, -k, -l] 31 | ], 32 | 1 33 | ] 34 | , 35 | 0 36 | , 37 | TestID->"xAct-20140224-U4J3L4" 38 | ] 39 | 40 | dim =. ; 41 | 42 | (* ToCanonical on PD reported by Guillaume. *) 43 | 44 | DefManifold[E3, 3, {aa, bb, ii, jj}] 45 | DefMetric[1, Metricdelta[-ii,-jj], PD, {",", "\[PartialD]"},FlatMetric -> True] 46 | DefTensor[v[ii], E3] 47 | 48 | Test[ 49 | ToCanonical[ 50 | v[aa] v[bb] PD[-ii][v[-bb]] PD[ii][v[-aa]] - 51 | v[aa] v[-bb] PD[-ii][v[-aa]] PD[ii][v[bb]] 52 | ] 53 | , 54 | 0 55 | , 56 | TestID->"xAct-20140302-Z5O4J5" 57 | ] -------------------------------------------------------------------------------- /tests/xCoba.mt: -------------------------------------------------------------------------------- 1 | dim=4; 2 | DefChart[B1,M,{0,1,2,3},{t[],r[],\[Theta][],\[Phi][]},BasisColor->RGBColor[0,0.7,0]]; 3 | DefChart[B2,M,{0,1,2,3},{\[Tau][],\[Rho][],\[Theta][],\[Phi][]},BasisColor->RGBColor[1,0,0]]; 4 | 5 | \[Rho]/:InChart[\[Rho][],B1]=Function[{t,r,\[Theta],\[Phi]},ArcSinh[r/L]]; 6 | \[Tau]/:InChart[\[Tau][],B1]=Function[{t,r,\[Theta],\[Phi]},t/L]; 7 | r/:InChart[r[],B2]=Function[{\[Tau],\[Rho],\[Theta],\[Phi]},L Sinh[\[Rho]]]; 8 | t/:InChart[t[],B2]=Function[{\[Tau],\[Rho],\[Theta],\[Phi]},L \[Tau]]; 9 | 10 | ComputeBasisValues[B1, B2]; 11 | 12 | Test[ 13 | Basis[{-a,-B1},{b,B2}]//ComponentArray//ToValues 14 | , 15 | {{L^(-1), 0, 0, 0}, {0, 1/(L*Sqrt[1 + r[]^2/L^2]), 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}} 16 | , 17 | TestID->"xCoba-20130102-Q9K3F5" 18 | ] 19 | 20 | Test[ 21 | Basis[{-a,-B2},{b,B1}]//ComponentArray//ToValues 22 | , 23 | {{L, 0, 0, 0}, {0, L*Cosh[\[Rho][]], 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}} 24 | , 25 | TestID->"xCoba-20130102-N7D4T5" 26 | ] 27 | 28 | DefTensor[vector[-a],M]; 29 | 30 | ImplodedTensorValues[CD, vector, B1]; 31 | 32 | Test[ 33 | CD[-a]@vector[-b] // Implode // ToBasis[B1] // ComponentArray // First // First // ToValues 34 | , 35 | -(ChristoffelCDPDB1[{0, B1}, {0, -B1}, {0, -B1}]*vector[{0, -B1}]) - 36 | ChristoffelCDPDB1[{1, B1}, {0, -B1}, {0, -B1}]*vector[{1, -B1}] - 37 | ChristoffelCDPDB1[{2, B1}, {0, -B1}, {0, -B1}]*vector[{2, -B1}] - 38 | ChristoffelCDPDB1[{3, B1}, {0, -B1}, {0, -B1}]*vector[{3, -B1}] + PDB1[{0, -B1}][vector[{0, -B1}]] 39 | , 40 | TestID->"xCoba-20130102-M4H4Y9" 41 | ] 42 | 43 | Unset[dim]; -------------------------------------------------------------------------------- /tests/xCore.mt: -------------------------------------------------------------------------------- 1 | Test[ 2 | LevelSpecQ[RandomInteger[{0,1000}]] 3 | , 4 | True 5 | , 6 | TestID->"xCore-20130101-L6P6S7" 7 | ] 8 | 9 | Test[ 10 | LevelSpecQ[-RandomInteger[{0,1000}]] 11 | , 12 | False 13 | , 14 | TestID->"xCore-20130101-J1P6A0" 15 | ] 16 | 17 | Test[ 18 | LevelSpecQ[{2,3}] 19 | , 20 | True 21 | , 22 | TestID->"xCore-20130101-L4R7Z0" 23 | ] 24 | 25 | Test[ 26 | LevelSpecQ[{3,2}] 27 | , 28 | False 29 | , 30 | TestID->"xCore-20130101-L1Y5R4" 31 | ] 32 | 33 | data = Table[RandomInteger[{1000, 2000}], {50}] 34 | 35 | Test[ 36 | MapTimed[Identity, data] 37 | , 38 | data 39 | , 40 | {FrontEndObject::notavail} 41 | , 42 | TestID->"xCore-20130101-C7F2A8" 43 | ] 44 | 45 | Test[ 46 | MapTimed[PartitionsQ, data] 47 | , 48 | Map[PartitionsQ, data] 49 | , 50 | {FrontEndObject::notavail} 51 | , 52 | TestID->"xCore-20130101-S2Y1A0" 53 | ] 54 | 55 | Test[ 56 | MapTimed[nonExistingFunction, data] 57 | , 58 | Map[nonExistingFunction, data] 59 | , 60 | {FrontEndObject::notavail} 61 | , 62 | TestID->"xCore-20130101-Q9R1S7" 63 | ] 64 | 65 | Test[ 66 | MapTimed[Identity, data, Parallelization->True] 67 | , 68 | data 69 | , 70 | {FrontEndObject::notavail} 71 | , 72 | TestID->"xCore-20130101-C7F2A8" 73 | ] 74 | 75 | Test[ 76 | MapTimed[PartitionsQ, data, Parallelization->True] 77 | , 78 | Map[PartitionsQ, data] 79 | , 80 | {FrontEndObject::notavail} 81 | , 82 | TestID->"xCore-20130101-S2Y1A0" 83 | ] 84 | 85 | Test[ 86 | MapTimed[nonExistingFunction, data, Parallelization->True] 87 | , 88 | Map[nonExistingFunction, data] 89 | , 90 | {FrontEndObject::notavail} 91 | , 92 | TestID->"xCore-20130101-Q9R1S7" 93 | ] 94 | 95 | 96 | 97 | data = Array[RandomInteger[{0,100}], {3,4,5,7}] 98 | 99 | Test[ 100 | MapTimed[PartitionsQ, data, {4}] 101 | , 102 | Map[PartitionsQ, data, {4}] 103 | , 104 | {FrontEndObject::notavail} 105 | , 106 | TestID->"xCore-20130101-E1P8E5" 107 | ] 108 | 109 | Test[ 110 | MapTimed[PartitionsQ, data, {4}, Parallelization->True] 111 | , 112 | Map[PartitionsQ, data, {4}] 113 | , 114 | {FrontEndObject::notavail} 115 | , 116 | TestID->"xCore-20130101-E1P8E5" 117 | ] -------------------------------------------------------------------------------- /xAct/xTras/xCoba.m: -------------------------------------------------------------------------------- 1 | ComputeBasisValues::usage = 2 | "ComputeBasisValues[chart1,chart2] computes and stores the values of the \ 3 | basis elements relating chart1 to chart2 and vice versa. Thus it computes \ 4 | Basis[-chart1,chart2] and Basis[-chart2,chart1]. \ 5 | \n\nNote that ComputeBasisValues internally uses InChart, so it is preferable \ 6 | to define the transformations of the coordinates from chart1 to chart2 and vice versa \ 7 | with InChart before using ComputeBasisValues."; 8 | 9 | ImplodedTensorValues::usage = 10 | "ImplodedTensorValues[CD, T, basis] computes the values \ 11 | of the covariant derivative CD of the tensor T in the given basis, and stores the values \ 12 | in the imploded tensor CDT. Both CD and T do not take indices." 13 | 14 | 15 | Begin["`Private`"] 16 | 17 | (********************) 18 | (* xCoba extensions *) 19 | (********************) 20 | 21 | ComputeBasisValues[B1_?ChartQ,B2_?ChartQ] := ComputeBasisValues1@@#& /@ {{B1,B2},{B2,B1}}; 22 | 23 | ComputeBasisValues1[B1_?ChartQ,B2_?ChartQ] := Module[ 24 | { 25 | C1,C2,basisArray,values 26 | }, 27 | values = Outer[ 28 | Simplify@D[#1,#2]&, 29 | InChart[B2]@ScalarsOfChart@B1, 30 | ScalarsOfChart@B2 31 | ]; 32 | {C1,C2} = CNumbersOf[#,VBundleOfBasis@#]&/@{B1,B2}; 33 | basisArray = Outer[Basis[{#1,B1},{#2,-B2}]&,C1,C2]; 34 | ComponentValue[basisArray,values] 35 | ]; 36 | 37 | 38 | ImplodedTensorValues[cd_?CovDQ, T_?xTensorQ, B_?BasisQ, f_:Identity] := Module[ 39 | { 40 | cdT,valueArray,implodedArray 41 | }, 42 | (* Construct the expression with derivative and indices. *) 43 | cdT = cd[DownIndex@DummyIn@First@VBundlesOfCovD@cd]@Apply[T,DummyIn/@SlotsOfTensor[T]]; 44 | (* Implode cdT, go to the basis, and give a component list. *) 45 | implodedArray = cdT//Implode//ToBasis[B]//ComponentArray; 46 | valueArray = f@ToValues[ 47 | (* Construct the component array of the unimploded cdT. *) 48 | (* Note that we once use FreeToBasis for the free indices and once 49 | DummyToBasis for the contraction with the Christoffels. *) 50 | (* Doing the ChangeCovD is not strictly necessary, but it is 'more correct' to change to the PD of the basis. *) 51 | cdT // FreeToBasis[B] // DummyToBasis[B] // ChangeCovD[#, cd, PDOfBasis@B]& // TraceBasisDummy // ComponentArray, 52 | (* Get a list of all the tensors in the problem, which are just the tensor T and the relevant Christoffel *) 53 | {T, GiveSymbol[Christoffel,cd,PDOfBasis@B]} 54 | ]; 55 | (* Assign values and return. *) 56 | (* Note that this is the main bottleneck for large tensors, because ComponentValue 57 | first checks for dependencies and modifies the TensorValues list for each component. 58 | It would be much faster to replace the TensorValues list in one go. *) 59 | ComponentValue[implodedArray, valueArray] 60 | ]; 61 | 62 | (* 63 | ToBasis[basis_][expr_] /; Apply[And, AIndexQ /@ IndicesOf[][expr]] := 64 | ChangeCovD[ 65 | expr, 66 | $CovDs, 67 | PDOfBasis[basis] 68 | ] /. i_?AbstractIndexQ :> {i, basis} 69 | *) 70 | 71 | End[] -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | xTras 2 | ===== 3 | 4 | [*xTras*](http://www.xact.es/xtras/) is a field-theory inspired add-on package for [*xAct*](http://www.xact.es/), 5 | the state-of-the-art tensor calculus package for Mathematica. 6 | 7 | Some of the extra functionality it brings is: 8 | 9 | * Generating a list of all contractions of a given tensorial expression. 10 | * Generating lists of dimensional dependent identities (e.g. the vanishing of the Weyl tensor in D=3). 11 | * Making any tensorial expression traceless. 12 | * Symmetrizing covariant derivatives. 13 | * Computing equations of motion of monomials of Riemann tensors. 14 | * Perturbations around AdS spaces. 15 | * Killing vectors. 16 | * Easy access to the database of the Invar package. 17 | * Young symmetrizers and projectors. 18 | * Solving linear systems of tensorial equations, both for constant variables (SolveConstants) 19 | and for tensors (SolveTensors). 20 | 21 | For more information, have a look at the [associated publication](http://arxiv.org/abs/1308.3493) 22 | or at the [online documentation](http://www.xact.es/xtras/documentation). 23 | 24 | 25 | Installation 26 | ------------ 27 | 28 | #### Installing the package in Mathematica 29 | 30 | If you just want to run the *xTras* package as a end user, download the compiled zip file from 31 | http://www.xact.es/xtras, unzip, and follow the instructions. 32 | 33 | #### Configuring the project in Wolfram Workbench 34 | 35 | If you want to set up *xTras* in Workbench to edit the code, you'll have to take a few extra steps. 36 | This assumes you already have a Workbench environment up and running. 37 | 38 | 1. Download and install the complete [*xAct*](http://www.xact.es/) bundle where Mathematica can find it, 39 | but remove or rename the `xAct/xTras/` subdirectory. 40 | 2. Checkout or download the *xTras* source, and import it in Workbench. 41 | 3. Edit the file `buildfiles/main.xml` such that properties in the section `Machine-specific config variables` 42 | match your setup. 43 | 44 | Running notebooks for testing code is the same as usual, but deploying and building the documentation is not, 45 | due to *xTras*' unusual structure (it's a sub-package for *xAct*, which isn't supported out-of-the-box in Workbench). 46 | Deploying can be done by running the `deploy` target in the `buildfiles/main.xml` file, and building the 47 | documentation by running the `documentation` target. The complete project can by build by running the 48 | `all` target. Be sure to set the `Runtime JRE` to `Separate JRE` in the `JRE` tab of the Eclipse external 49 | tools configuration of the Ant targets. 50 | 51 | The unit tests can be run by running the `tests/TestSuite.mt` as a Mathematica Test. 52 | 53 | 54 | What's what 55 | ----------- 56 | 57 | The Workbench project is structured into the following directories: 58 | 59 | buildfiles/ Ant files for building the docs, changelog, and the distributable zip. 60 | notebooks/ Mathematica *.nb files to run and / or test code. 61 | tests/ Unit test files. 62 | xAct/ The actual code of the package. 63 | xTras/ Documentation source. 64 | -------------------------------------------------------------------------------- /tests/Invar.mt: -------------------------------------------------------------------------------- 1 | (*******************) 2 | (* *) 3 | (* Euler density *) 4 | (* *) 5 | (*******************) 6 | 7 | 8 | Test[ 9 | ToCanonical[ 10 | NoScalar@EulerDensity[CD,4] 11 | - (4*RicciCD[-a, -b]*RicciCD[a, b] - RicciScalarCD[]^2 - 12 | RiemannCD[-a, -b, -c, -d]*RiemannCD[a, b, c, d] ) 13 | ] 14 | , 15 | 0 16 | , 17 | TestID->"Invar-20130102-C9X8J2" 18 | ] 19 | 20 | Test[ 21 | EulerDensity[CD,2] 22 | , 23 | -RicciScalarCD[] 24 | , 25 | TestID->"Invar-20141001-Z1G1N1" 26 | ] 27 | 28 | Test[ 29 | EulerDensity[CD,6] 30 | , 31 | -RicciScalarCD[]^3 + 12*RicciScalarCD[]*Scalar[RicciCD[-a, -b]*RicciCD[a, b]] 32 | -16*Scalar[RicciCD[-a, c]*RicciCD[a, b]*RicciCD[-b, -c]] 33 | -24*Scalar[RicciCD[a, b]*RicciCD[c, d]*RiemannCD[-a, -c, -b, -d]] 34 | -3*RicciScalarCD[]*Scalar[RiemannCD[-a, -b, -c, -d]*RiemannCD[a, b, c, d]] 35 | +24*Scalar[RicciCD[a, b]*RiemannCD[-a, c, d, e]*RiemannCD[-b, -c, -d, -e]] 36 | +8*Scalar[RiemannCD[-a, e, -c, f]*RiemannCD[a, b, c, d]*RiemannCD[-b, -f, -d, -e]] 37 | -2*Scalar[RiemannCD[-a, -b, e, f]*RiemannCD[a, b, c, d]*RiemannCD[-c, -d, -e, -f]] 38 | , 39 | TestID->"Invar-20141001-F7S9D3" 40 | ] 41 | 42 | (*******************************************) 43 | (* *) 44 | (* InvarWrapper & RiemannSimplification *) 45 | (* *) 46 | (*******************************************) 47 | 48 | (* Using RiemannSimplify without the InvarWrapper returns Cycles[] for this case. *) 49 | Test[ 50 | InvarWrapper[RiemannSimplify[#2, 4, True, #1] &, metric][ CD[a]@CD[-a]@RicciScalarCD[] ] 51 | , 52 | Scalar[ CD[-a]@CD[a]@RicciScalarCD[] ] 53 | , 54 | TestID->"Invar-20130102-Y7B5N2" 55 | ] 56 | 57 | Test[ 58 | InvarWrapper[RiemannSimplify[#2, 4, True, #1] &, metric][ CD[a]@CD[b]@RicciCD[-a, -b] ] 59 | , 60 | 1/2 Scalar[ CD[-a]@CD[a]@RicciScalarCD[] ] 61 | , 62 | TestID->"Invar-20130102-S3V7F7" 63 | ] 64 | 65 | Test[ 66 | ScreenDollarIndices@RiemannSimplification[][ CD[a]@CD[-a]@RicciScalarCD[] ] 67 | , 68 | CD[-a]@CD[a]@RicciScalarCD[] 69 | , 70 | TestID->"Invar-20130102-M1G8F3" 71 | ] 72 | 73 | Test[ 74 | ToCanonical@RiemannSimplification[][ 75 | 2 76 | + RiemannCD[a,b,c,d] RiemannCD[-a,-c,-b,-d] 77 | - RiemannCD[a,b,c,d] RiemannCD[-a,-b,-c,-d]/2 78 | ] 79 | , 80 | 2 81 | , 82 | TestID->"Invar-20130102-P6X6I8" 83 | ] 84 | 85 | Test[ 86 | ScreenDollarIndices@RiemannSimplification[][metric[e,f]RiemannCD[a,b,c,d] RiemannCD[-a,-c,-b,-d]+2RicciCD[e,f]] 87 | , 88 | 2 RicciCD[e, f] + 1/2 metric[e, f]*RiemannCD[-a, -b, -c, -d]*RiemannCD[a, b, c, d] 89 | , 90 | TestID->"Invar-20130102-G6C0O4" 91 | ] 92 | 93 | (*******************************************) 94 | (* *) 95 | (* FullSimplification *) 96 | (* *) 97 | (*******************************************) 98 | 99 | Test[ 100 | ScreenDollarIndices@FullSimplification[][CD[-a]@CD[-b]@RicciCD[-c,-d]] 101 | , 102 | RicciCD[-d, e]*RiemannCD[-a, -b, -c, -e] + 103 | RicciCD[-c, e]*RiemannCD[-a, -b, -d, -e] + 104 | CD[-b][CD[-a][RicciCD[-c, -d]]] 105 | , 106 | TestID->"Invar-20130102-T0T6F9" 107 | ] 108 | 109 | Test[ 110 | ScreenDollarIndices@FullSimplification[metric][CD[a]@CD[-c]@RicciCD[-a,-b]] 111 | , 112 | RicciCD[-b, a]*RicciCD[-c, -a] - RicciCD[a, d]*RiemannCD[-b, -a, -c, -d] + CD[-c][CD[-b][RicciScalarCD[]]]/2 113 | , 114 | TestID->"Invar-20130126-F0L3J9" 115 | ] 116 | 117 | (*******************************************) 118 | (* *) 119 | (* Invar database access *) 120 | (* *) 121 | (*******************************************) 122 | 123 | 124 | Test[ 125 | SingleInvariants[metric, {0}] 126 | , 127 | {1} 128 | , 129 | TestID->"Invar-20130102-G1C2W7" 130 | ] 131 | 132 | Test[ 133 | SingleInvariants[metric, {2}] 134 | , 135 | {RicciScalarCD[]} 136 | , 137 | TestID->"Invar-20130102-S9H9Y5" 138 | ] 139 | 140 | Test[ 141 | Sort[ScreenDollarIndices@ContractMetric@NoScalar[#] & /@ SingleInvariants[metric, {4}]] 142 | , 143 | { 144 | RicciCD[-a, -b]*RicciCD[a, b], 145 | RiemannCD[-a, -b, -c, -d]*RiemannCD[a, b, c, d], 146 | CD[-a][CD[a][RicciScalarCD[]]] 147 | } 148 | , 149 | TestID->"Invar-20130102-D0S4J9" 150 | ] 151 | 152 | Test[ 153 | Sort[ScreenDollarIndices@ContractMetric@NoScalar[#] & /@ ProductInvariants[metric, {4}]] 154 | , 155 | { 156 | RicciCD[-a, -b]*RicciCD[a, b], 157 | RicciScalarCD[]^2, 158 | RiemannCD[-a, -b, -c, -d]*RiemannCD[a, b, c, d], 159 | CD[-a][CD[a][RicciScalarCD[]]] 160 | } 161 | , 162 | TestID->"Invar-20130102-U2K6U3" 163 | ] 164 | 165 | Test[ 166 | Length@ProductInvariants[metric, {6}] 167 | , 168 | 17 169 | , 170 | TestID->"Invar-20130102-J6E2P1" 171 | ] 172 | 173 | Test[ 174 | Length@ProductInvariants[metric, {8}] 175 | , 176 | 92 177 | , 178 | TestID->"Invar-20130102-O5H4M8" 179 | ] -------------------------------------------------------------------------------- /tests/xPert.mt: -------------------------------------------------------------------------------- 1 | (****************) 2 | (* *) 3 | (* Setup *) 4 | (* *) 5 | (****************) 6 | 7 | DefConstantSymbol[L]; 8 | SetOptions[ToBackground, BackgroundSolution -> SymmetricSpaceRules[CD,K] ]; 9 | 10 | 11 | (*******************) 12 | (* *) 13 | (* VarL et.al. *) 14 | (* *) 15 | (*******************) 16 | 17 | Test[ 18 | ToCanonical[ 19 | ExpandPerturbation@Perturbation[Detmetric[]] 20 | - Detmetric[]*Perturbationmetric[LI[1], a, -a] 21 | ] 22 | , 23 | 0 24 | , 25 | TestID->"xPert-20130102-I4S7W1" 26 | ] 27 | 28 | Test[ 29 | Perturbation[ metric[-a,-b] ] 30 | , 31 | Perturbationmetric[LI[1],-a,-b] 32 | , 33 | TestID->"xPert-20130102-L4S5X5" 34 | ] 35 | 36 | Test[ 37 | Detmetric[] // Perturbation // ExpandPerturbation // ContractMetric // ToCanonical // ScreenDollarIndices 38 | , 39 | Detmetric[] * Perturbationmetric[LI[1], a, -a] 40 | , 41 | TestID->"xPert-20140923-T3L2W7" 42 | ] 43 | 44 | DetMetricDiff[n_]:= 45 | ToCanonical @ ContractMetric[ 46 | + ExpandPerturbation @ Perturbation[#, n] & @ Detmetric[] 47 | - Nest[ExpandPerturbation@Perturbation[#]&, Detmetric[], n] 48 | ] 49 | 50 | Test[ 51 | DetMetricDiff[1] 52 | , 53 | 0 54 | , 55 | TestID->"xPert-20140924-F7E5E6" 56 | ] 57 | 58 | Test[ 59 | DetMetricDiff[2] 60 | , 61 | 0 62 | , 63 | TestID->"xPert-20140923-C1M6D2" 64 | ] 65 | 66 | Test[ 67 | DetMetricDiff[3] 68 | , 69 | 0 70 | , 71 | TestID->"xPert-20140923-N2I5K4" 72 | ] 73 | 74 | Test[ 75 | DetMetricDiff[4] 76 | , 77 | 0 78 | , 79 | TestID->"xPert-20140923-F5O8U7" 80 | ] 81 | 82 | Test[ 83 | DetMetricDiff[5] 84 | , 85 | 0 86 | , 87 | TestID->"xPert-20140923-Y5T2W0" 88 | ] 89 | 90 | Test[ 91 | ToCanonical@VarL[metric[a, b], CD][RicciScalarCD[]] 92 | , 93 | RicciCD[-a, -b] - metric[-a, -b]/2 RicciScalarCD[] 94 | , 95 | TestID->"xPert-20130102-F7R9V5" 96 | ] 97 | 98 | Test[ 99 | ToCanonical[ 100 | ContractMetric@VarL[metric[a, b], CD][RicciCD[a,b]RicciCD[-a,-b]] 101 | - ( 2 RicciCD[-a, c] RicciCD[-b, -c] - 1/2 metric[-a, -b] RicciCD[-c, -d] RicciCD[c, d] 102 | - CD[-c]@CD[-a]@RicciCD[-b, c] - CD[-c]@CD[-b]@RicciCD[-a, c] 103 | + CD[-c]@CD[c]@RicciCD[-a, -b] + metric[-a, -b] CD[-d]@CD[-c]@RicciCD[c, d] ) 104 | ] 105 | , 106 | 0 107 | , 108 | TestID->"xPert-20130102-R9V2O6" 109 | ] 110 | 111 | (******************************) 112 | (* *) 113 | (* Background perturbations *) 114 | (* *) 115 | (******************************) 116 | 117 | Test[ 118 | ToCanonical@ToBackground[ RiemannCD[a,b,c,d] ] 119 | , 120 | K metric[a, c] metric[b, d] - K metric[a, d] metric[b, c] 121 | , 122 | TestID->"xPert-20130102-O9G7K5" 123 | ] 124 | 125 | Test[ 126 | Simplification@ContractMetric@ToBackground[ 127 | RiemannCD[-a,-b,-c,-d] RiemannCD[a,b,c,d] - KretschmannCD[] 128 | ] 129 | , 130 | 0 131 | , 132 | TestID->"xPert-20130106-O1E5Y3" 133 | ] 134 | 135 | Test[ 136 | Simplification@ContractMetric[ 137 | ToBackground@RicciCD[a,b] 138 | - metric[-c,-d] ToBackground@RiemannCD[a,c,b,d] 139 | ] 140 | , 141 | 0 142 | , 143 | TestID->"xPert-20130102-U8I2G8" 144 | ] 145 | 146 | Test[ 147 | Simplification@ContractMetric[ 148 | ToBackground@RicciScalarCD[] 149 | - metric[-a,-b] ToBackground@RicciCD[a,b] 150 | ] 151 | , 152 | 0 153 | , 154 | TestID->"xPert-20130102-F6A2P6" 155 | ] 156 | 157 | Test[ 158 | Simplification@ToBackground[ TFRicciCD[a,b] - TFRicciToRicci@TFRicciCD[a,b] ] 159 | , 160 | 0 161 | , 162 | TestID->"xPert-20130102-A5Q9E4" 163 | ] 164 | 165 | 166 | Test[ 167 | Simplification@ToBackground[ WeylCD[a,b,c,d] - WeylToRiemann@WeylCD[a,b,c,d] ] 168 | , 169 | 0 170 | , 171 | TestID->"xPert-20130102-C0F5U9" 172 | ] 173 | 174 | Test[ 175 | Simplification@ToBackground[ SchoutenCD[a,b] - SchoutenToRicci@SchoutenCD[a,b] ] 176 | , 177 | 0 178 | , 179 | TestID->"xPert-20130102-K6Q0V2" 180 | ] 181 | 182 | Test[ 183 | Simplification@ToBackground[ EinsteinCD[a,b] - EinsteinToRicci@EinsteinCD[a,b] ] 184 | , 185 | 0 186 | , 187 | TestID->"xPert-20130102-L4I9O6" 188 | ] 189 | 190 | Test[ 191 | Simplification@ToBackground[ SchoutenCCCD[LI[L],a,b] - SchoutenCCToRicci@SchoutenCCCD[LI[L],a,b] ] 192 | , 193 | 0 194 | , 195 | TestID->"xPert-20130102-F6H0U7" 196 | ] 197 | 198 | Test[ 199 | Simplification@ToBackground[ EinsteinCCCD[LI[L],a,b] - EinsteinToRicci@EinsteinCCCD[LI[L],a,b] ] 200 | , 201 | 0 202 | , 203 | TestID->"xPert-20130102-F3J1M8" 204 | ] 205 | 206 | Test[ 207 | Simplification@PerturbBackground[RicciScalarCD[]^2] 208 | , 209 | 2*(dim-1)*dim*K*Perturbation[RicciScalarCD[]] 210 | , 211 | TestID->"xPert-20130102-V6E5P0" 212 | ] 213 | 214 | Test[ 215 | Simplification@ContractMetric[ 216 | ExpandBackground[RicciScalarCD[]] 217 | - ((K - dim*K)*Perturbationmetric[LI[1], a, -a] + 218 | CD[-b][CD[-a][Perturbationmetric[LI[1], a, b]]] - 219 | CD[-b][CD[b][Perturbationmetric[LI[1], a, -a]]]) 220 | ] 221 | , 222 | 0 223 | , 224 | TestID->"xPert-20130102-U8R5L9" 225 | ] 226 | 227 | Test[ 228 | PD[-e]@metric[-f,-d] /. FlatRules[CD] 229 | , 230 | 0 231 | , 232 | TestID->"xPert-20130124-M1S8X7" 233 | ] 234 | -------------------------------------------------------------------------------- /xAct/xTras/xCore.m: -------------------------------------------------------------------------------- 1 | (*********************) 2 | (* *) 3 | (* Public messages *) 4 | (* *) 5 | (*********************) 6 | 7 | xTrasHelp::usage = "xTrasHelp[] opens the \!\(\*StyleBox[\"xTras\",\"IT\"]\) documentation."; 8 | 9 | LevelSpecQ::usage = 10 | "LevelSpecQ[levelspec] yields True if levelspec is a standard levelspec, and False otherwise."; 11 | 12 | ToLevelSpec::usage = 13 | "ToLevelSpec[levelspec] converts levelspec into the {min,max} format."; 14 | ToLevelSpec::error = "`1` is not a a valid level spec."; 15 | 16 | TimeString::usage = 17 | "TimeString[seconds] nicely formats the amount of seconds as a string."; 18 | 19 | Description::usage = "Description is an option for MapTimed."; 20 | 21 | MapTimed::usage = "\ 22 | MapTimed[f, expr] maps f over expr while monitoring the progress and the estimated time remaining.\n\ 23 | MapTimed[f, expr, Description->\"text\"] gives a description to the monitor.\n\ 24 | MapTimed[f, expr, Parallelization->True] performs a ParallelMap instead of a Map."; 25 | 26 | MapTimedIfPlus::usage = 27 | "MapTimedIfPlus[f, expr] maps f on the elements of expr while displaying a timer \ 28 | if expr has head Plus, or returns f[expr] otherwise."; 29 | 30 | If[System`$VersionNumber < 8., 31 | Parallelization::usage = "Parallelization is an option for MapTimed." 32 | ]; 33 | 34 | 35 | Begin["`Private`"] 36 | 37 | xTrasHelp[] := 38 | (* SystemOpen is MMA 7 and newer, but somehow it doesn't work in MMA 7. *) 39 | If[ System`$VersionNumber < 8., 40 | Documentation`HelpLookupPacletURI["paclet:xTras/guide/xTras"], 41 | SystemOpen["paclet:xTras/guide/xTras"] 42 | ]; 43 | 44 | 45 | TimeString[seconds_Integer]/;seconds >= 31536000:=TimeString1[seconds,31536000,2628000," year"," month"]; 46 | TimeString[seconds_Integer]/;seconds >= 2628000:=TimeString1[seconds,2628000,86400," month"," day"]; 47 | TimeString[seconds_Integer]/;seconds >= 86400:=TimeString1[seconds,86400,3600," day"," hour"]; 48 | TimeString[seconds_Integer]/;seconds >= 3600:=TimeString1[seconds,3600,60," hour"," minute"]; 49 | TimeString[seconds_Integer]/;seconds >= 60:=TimeString1[seconds,60,1," minute"," second"]; 50 | TimeString[seconds_Integer]/;seconds > 1:=StringJoin[ToString[seconds], " seconds"]; 51 | TimeString[1] := "1 second"; 52 | TimeString[0] := "0 seconds"; 53 | 54 | TimeString1[n_,t1_,t2_,s1_,s2_]:=StringJoin[ 55 | TimeString2a[Quotient[n,t1],s1], 56 | TimeString2b[Quotient[Mod[n,t1],t2],s2] 57 | ]; 58 | 59 | TimeString2a[0,_] := Sequence[]; 60 | TimeString2a[1,s_] := Sequence["1",s] 61 | TimeString2a[x_,s_] := Sequence[ToString[x],s,"s"]; 62 | 63 | TimeString2b[0,_] := Sequence[]; 64 | TimeString2b[1,s_] := Sequence[", 1",s] 65 | TimeString2b[x_,s_] := Sequence[", ",ToString[x],s,"s"]; 66 | 67 | 68 | 69 | LevelSpecQ[{x_Integer, y_Integer}] /; x >= 0 && y >= x := True 70 | LevelSpecQ[x_Integer] /; x >= 0 := True 71 | LevelSpecQ[{x_Integer}] /; x >= 0 := True 72 | LevelSpecQ[Infinity] = True 73 | LevelSpecQ[{x_Integer, Infinity}] /; x >= 0 := True 74 | LevelSpecQ[{Infinity, Infinity}] = True 75 | LevelSpecQ[___] := False 76 | 77 | ToLevelSpec[x_Integer] /; x >= 0 := {0,x}; 78 | ToLevelSpec[{x_Integer}] /; x >= 0 := {x,x}; 79 | ToLevelSpec[Infinity] = {0,Infinity}; 80 | ToLevelSpec[{Infinity}] = {Infinity,Infinity}; 81 | ToLevelSpec[All] = {0,Infinity}; 82 | ToLevelSpec[None] = {0,0}; 83 | ToLevelSpec[x_?LevelSpecQ] := x; 84 | ToLevelSpec[x_] := Throw@Message[ToLevelSpec::error, x]; 85 | 86 | 87 | Options[MapTimed] ^= { 88 | Description -> None, 89 | Parallelization -> False 90 | }; 91 | 92 | MapTimed[func_,expr_,levelspec_: {1},options___?OptionQ]/;LevelSpecQ[levelspec] := Module[ 93 | { 94 | desc, parallel, timer, ETA, 95 | length = 0, 96 | position = 0 97 | }, 98 | 99 | (* Determine the options. *) 100 | {desc,parallel} = {Description,Parallelization} /. CheckOptions[options] /. Options[MapTimed]; 101 | If[desc === None, 102 | desc = "", 103 | desc = " " <> ToString@desc; 104 | If[StringTake[desc,-1]=!=".", 105 | desc = desc <> "."; 106 | ] 107 | ]; 108 | 109 | (* Do a test run to determine the length of the map. *) 110 | Map[(length++)&,expr,levelspec]; 111 | 112 | (* Set the helper functions ETA and timer. *) 113 | With[ 114 | { 115 | begintime = AbsoluteTime[], 116 | l = length, 117 | s1 = " **" <> desc <> " Parts ", 118 | s2 = "/" <> ToString[length] <> " done. " 119 | }, 120 | ETA[pos_] := Ceiling[(AbsoluteTime[]-begintime)*(l-pos)/pos]; 121 | timer[pos_] := s1 <> ToString@pos <> s2 <> TimeString@ETA@pos <> " remaining."; 122 | ]; 123 | timer[0] = " **" <> desc <> " " <> ToString[length] <> " parts."; 124 | timer[length] = " **" <> desc <> " Parts " <> ToString[length] <> "/" <> ToString[length] <> " done."; 125 | 126 | (* Do the mapping. *) 127 | If[TrueQ[parallel] && System`$VersionNumber >= 7., 128 | SetSharedVariable[position]; 129 | (UnsetShared[position];#)&@Monitor[ParallelMap[((position++;#)&@func[#])&,expr,levelspec],timer@position] 130 | , 131 | Monitor[Map[((position++;#)&@func[#])&,expr,levelspec],timer@position] 132 | ] 133 | ]; 134 | 135 | MapTimedIfPlus[f_, expr_Plus, rest___] := MapTimed[f, expr, rest]; 136 | MapTimedIfPlus[f_, expr_, rest___] := f[expr]; 137 | 138 | ParallelxPermConnect[] := 139 | If[ System`$VersionNumber >= 7 && Not[ And @@ ($xpermLink =!= # & /@ ParallelEvaluate[$xpermLink]) ], 140 | ParallelEvaluate @ Block[{Print}, 141 | Needs["xAct`xPerm`"]; 142 | $xpermQ = xAct`xPerm`Private`xpermConnect 143 | ] 144 | ]; 145 | 146 | End[] -------------------------------------------------------------------------------- /xAct/xTras/Kernel/init.m: -------------------------------------------------------------------------------- 1 | (*********************) 2 | (* *) 3 | (* To-do list *) 4 | (* *) 5 | (*********************) 6 | 7 | (* 8 | 9 | * Add SyntaxInformation and argx messages to each function. 10 | * Undef hooks. 11 | * Add conditionals for when to define extra curvature tensors (e.g. when there's torsion etc). 12 | * Switch Modules to With's where approriate. 13 | 14 | *) 15 | 16 | 17 | (*********************) 18 | (* *) 19 | (* Package setup *) 20 | (* *) 21 | (*********************) 22 | 23 | xAct`xTras`$Version = {"1.4.2", {2014, 10, 30}}; 24 | xAct`xTras`$xTensorVersionExpected = {"1.1.1", {2014, 9, 6}}; 25 | xAct`xTras`$SymManipulatorVersionExpected = {"0.8.5", {2013, 4, 13}}; 26 | xAct`xTras`$MathematicaVersionNeeded = 6.; 27 | 28 | If[Unevaluated[xAct`xCore`Private`$LastPackage] === xAct`xCore`Private`$LastPackage, 29 | xAct`xCore`Private`$LastPackage = "xAct`xTras`" 30 | ]; 31 | 32 | (* 33 | * This is a (possibly dangerous) hack in order to enable the documentation tools in Workbench, 34 | * which only works for top-level packages. Set this to "xTras" before loading the package, 35 | * and you can use the documentation tools. 36 | *) 37 | If[Unevaluated[xAct`xTras`Private`$xTrasContext] === xAct`xTras`Private`$xTrasContext, 38 | xAct`xTras`Private`$xTrasContext = "xAct`xTras`" 39 | ]; 40 | 41 | BeginPackage[xAct`xTras`Private`$xTrasContext, { 42 | "xAct`xCore`", 43 | "xAct`xPerm`", 44 | "xAct`xTensor`", 45 | "xAct`xPert`", 46 | "xAct`Invar`", 47 | "xAct`xCoba`", 48 | "xAct`SymManipulator`" 49 | }] 50 | 51 | (* Print info *) 52 | Print[xAct`xCore`Private`bars]; 53 | Print["Package xAct`xTras` version ", xAct`xTras`$Version[[1]],", ",xAct`xTras`$Version[[2]]]; 54 | Print["CopyRight (C) 2012-2014, Teake Nutma, under the General Public License."]; 55 | 56 | 57 | (* Check if we have the correct version of xAct. *) 58 | If[Not@OrderedQ@Map[Last, {xAct`xTras`$xTensorVersionExpected, xAct`xTensor`$Version}], 59 | Message[General::versions, "xTensor", xAct`xTensor`$Version, xAct`xTras`$xTensorVersionExpected]; 60 | Abort[] 61 | ]; 62 | 63 | (* Check if we have the correct version of SymManipulator. *) 64 | If[Not@OrderedQ@Map[Last, {xAct`xTras`$SymManipulatorVersionExpected, xAct`SymManipulator`$Version}], 65 | Message[General::versions, "SymManipulator", xAct`SymManipulator`$Version, xAct`xTras`$SymManipulatorVersionExpected]; 66 | Abort[] 67 | ]; 68 | 69 | (* Check for MMA versions. *) 70 | If[System`$VersionNumber < xAct`xTras`$MathematicaVersionNeeded, 71 | Message[General::versions, "Mathematica", System`$VersionNumber, xAct`xTras`$MathematicaVersionNeeded]; 72 | Abort[] 73 | ]; 74 | 75 | (* Reset some options. *) 76 | ReportSet[$CovDFormat, "Prefix"]; 77 | ReportSetOption[DefCovD, CurvatureRelations -> True]; 78 | 79 | 80 | 81 | (* Load the code. *) 82 | Get["xAct`xTras`xCore`"]; 83 | Get["xAct`xTras`xTensor`"]; 84 | Get["xAct`xTras`xPert`"]; 85 | Get["xAct`xTras`Invar`"]; 86 | Get["xAct`xTras`xCoba`"]; 87 | Get["xAct`xTras`Algebra`"]; 88 | Get["xAct`xTras`Combinatorics`"]; 89 | 90 | (* Load fancy usage messages. 91 | These need to be loaded last because they overwrite plain usage messages 92 | defined in the files loaded above. *) 93 | Get["xAct`xTras`Interface`"]; 94 | 95 | Begin["`Private`"] 96 | 97 | (* 98 | * Add the xAct directory to the path of the PacletManager. 99 | * This allows it to find the documentation in xAct/xTras/Documentation. 100 | * We could have used xAct`xCore`$xActDirectory, but this is a bit more general. 101 | *) 102 | 103 | If[ 104 | System`$VersionNumber < 7. 105 | , 106 | xActDir = StringTake[ 107 | First@Select[ 108 | (* Find files / directories with "xTras" in their name *) 109 | FileNames["xTras", {$UserBaseDirectory, $BaseDirectory, $InstallationDirectory}, Infinity], 110 | (* Select the xTras directory *) 111 | StringMatchQ[#, "*xAct/xTras"] & 112 | ], 113 | (* Strip the "/xTras" from it *) 114 | {1, -7} 115 | ] 116 | , 117 | xActDir = FileNameJoin@Drop[FileNameSplit@FindFile["xAct`xTras`"], -3] 118 | ]; 119 | 120 | (* MMA 9 needs a Kernel extension in the PacletInfo.m file, whereas this chokes MMA 6. So remove it for MMA 6. *) 121 | If[ 122 | System`$VersionNumber < 7. 123 | , 124 | pacletFile = ToFileName[{xActDir,"xTras"},"PacletInfo.m"]; 125 | paclet = Get[pacletFile]; 126 | pacletNew = paclet /. {"Kernel", ___} -> Sequence[]; 127 | Put[pacletNew, pacletFile]; 128 | ] 129 | 130 | PacletManager`PacletDirectoryAdd[xActDir]; 131 | (* Rebuild the PacletData. Necessary on MMA 6. *) 132 | PacletManager`RebuildPacletData[]; 133 | 134 | (* Restore the old paclet file. *) 135 | If[ 136 | System`$VersionNumber < 7. 137 | , 138 | Put[paclet, pacletFile]; 139 | ] 140 | 141 | 142 | (* 143 | * The following is a dirty hack to get URI links in the Information output of all usage messages. 144 | * For "top-level" packages (i.e. packages whose symbols are all in one top-level context, 145 | * like "myPackage`") this isn't necessary, as then everythings works out of the box 146 | * But because we had to hack our way around the documentation tools because xTras lives 147 | * in "xAct`xTras`", the links do not work by themselves. 148 | * Therefore, we set for each public symbol the paclet link manually. 149 | *) 150 | 151 | (* Only do this when MMA can find the documentation. (Otherwise it's pointless). *) 152 | If[ 153 | (* Search for the AllContractions documentation. If it's there, good chance the rest is too. *) 154 | Documentation`CreateMessageLink["xTras`", "AllContractions", "usage", "English"] == "paclet:xTras/ref/AllContractions" 155 | , 156 | (* First, unprotect Documentation`CreateMessageLink. *) 157 | Unprotect[Documentation`CreateMessageLink]; 158 | 159 | (* For each public symbol, overwrite its output. *) 160 | Map[ 161 | Function[ 162 | symbol, 163 | Documentation`CreateMessageLink[ 164 | xAct`xTras`Private`$xTrasContext, 165 | ToString@symbol, 166 | "usage", 167 | "English" 168 | ] = "paclet:xTras/ref/" <> ToString@symbol 169 | ], 170 | Names[xAct`xTras`Private`$xTrasContext <> "*"] 171 | ]; 172 | 173 | (* For xTrasHelp, set the link to the xTras guide. *) 174 | Documentation`CreateMessageLink[ 175 | xAct`xTras`Private`$xTrasContext, 176 | "xTrasHelp", 177 | "usage", 178 | "English" 179 | ] = "paclet:xTras/guide/xTras"; 180 | 181 | (* Finally, protect Documentation`CreateMessageLink again. *) 182 | Protect[Documentation`CreateMessageLink]; 183 | ]; 184 | 185 | End[] 186 | 187 | (* Print license *) 188 | If[xAct`xCore`Private`$LastPackage === "xAct`xTras`", 189 | Unset[xAct`xCore`Private`$LastPackage]; 190 | Print[xAct`xCore`Private`bars]; 191 | Print["These packages come with ABSOLUTELY NO WARRANTY; for details \ 192 | type Disclaimer[]. This is free software, and you are welcome to \ 193 | redistribute it under certain conditions. See the General Public \ 194 | License for details."]; 195 | Print[xAct`xCore`Private`bars] 196 | ]; 197 | 198 | 199 | EndPackage[] -------------------------------------------------------------------------------- /xTras/Documentation/English/ReferencePages/Symbols/Coefficients.nb: -------------------------------------------------------------------------------- 1 | Notebook[{ 2 | Cell[TextData[{ 3 | "New in: ", 4 | Cell["1.0.0", "HistoryData", 5 | CellTags->"New"], 6 | " | Modified in: ", 7 | Cell[" ", "HistoryData", 8 | CellTags->"Modified"], 9 | " | Obsolete in: ", 10 | Cell[" ", "HistoryData", 11 | CellTags->"Obsolete"], 12 | " | Excised in: ", 13 | Cell[" ", "HistoryData", 14 | CellTags->"Excised"] 15 | }], "History", 16 | CellChangeTimes->{{3.5807958131449614`*^9, 3.5807958154990273`*^9}}, 17 | CellID->1247902091], 18 | 19 | Cell[CellGroupData[{ 20 | 21 | Cell["Categorization", "CategorizationSection", 22 | CellID->1122911449], 23 | 24 | Cell["Symbol", "Categorization", 25 | CellLabel->"Entity Type", 26 | CellID->686433507], 27 | 28 | Cell["xTras Package", "Categorization", 29 | CellLabel->"Paclet Name", 30 | CellID->96139307], 31 | 32 | Cell["xTras`", "Categorization", 33 | CellLabel->"Context", 34 | CellID->905630205], 35 | 36 | Cell["xTras/ref/Coefficients", "Categorization", 37 | CellLabel->"URI", 38 | CellID->1710249146] 39 | }, Closed]], 40 | 41 | Cell[CellGroupData[{ 42 | 43 | Cell["Keywords", "KeywordsSection", 44 | CellID->477174294], 45 | 46 | Cell["XXXX", "Keywords", 47 | CellID->1164421360] 48 | }, Closed]], 49 | 50 | Cell[CellGroupData[{ 51 | 52 | Cell["Syntax Templates", "TemplatesSection", 53 | CellID->1872225408], 54 | 55 | Cell[BoxData[""], "Template", 56 | CellLabel->"Additional Function Template", 57 | CellID->1562036412], 58 | 59 | Cell[BoxData[""], "Template", 60 | CellLabel->"Arguments Pattern", 61 | CellID->158391909], 62 | 63 | Cell[BoxData[""], "Template", 64 | CellLabel->"Local Variables", 65 | CellID->1360575930], 66 | 67 | 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}, Closed]], 113 | 114 | Cell[CellGroupData[{ 115 | 116 | Cell["Coefficients", "ObjectName", 117 | CellID->1224892054], 118 | 119 | Cell[TextData[{ 120 | Cell[" ", "ModInfo"], 121 | Cell[BoxData["Coefficients"], "InlineFormula"], 122 | "\[LineSeparator]is an option for ", 123 | Cell[BoxData[ 124 | ButtonBox["InvarLagrangian", 125 | BaseStyle->"Link", 126 | ButtonData->"paclet:xTras/ref/InvarLagrangian"]], "InlineFormula"], 127 | " that specifies the coefficients in the Lagrangian." 128 | }], "Usage", 129 | CellChangeTimes->{3.5807958229871693`*^9}], 130 | 131 | Cell["XXXX", "Notes", 132 | CellID->1067943069] 133 | }, Open ]], 134 | 135 | Cell[CellGroupData[{ 136 | 137 | Cell["Tutorials", "TutorialsSection", 138 | CellID->250839057], 139 | 140 | Cell["XXXX", "Tutorials", 141 | CellID->341631938] 142 | }, Open ]], 143 | 144 | Cell[CellGroupData[{ 145 | 146 | Cell["Related Demonstrations", "RelatedDemonstrationsSection", 147 | CellID->1268215905], 148 | 149 | Cell["XXXX", 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