OGRe: An Object-Oriented General Relativity Package for Mathematica

v1.6 (2021-08-07) New modules: TCalcGeodesicFromChristoffel: Creates a new rank-1 tensor object containing the geodesic equations obtained for each of the coordinates using the Christoffel symbols of the given metric: ẍσ + Γσμνẋμẋν = 0. The Christoffel symbols will be calculated automatically using TCalcChristoffel if they have not already been calculated. TCalcGeodesicFromLagrangian: Creates a new rank-1 tensor object containing the geodesic equations obtained for each of the coordinates by applying the Euler-Lagrange equations to the curve Lagrangian. The Lagrangian will be calculated automatically using TCalcLagrangian (see below) if it has not already been calculated. This module leaves the derivatives with respect to the curve parameter in the Euler-Lagrange equation unevaluated (using Inactive), which can sometimes help solve the geodesic equations by inspection. Use Activate to evaluate the derivatives. (Recall that TList and TShow can apply a function to the tensor's components before displaying them, so you can write e.g. TList["ID", Activate].) Often the equations obtained in this way will be different from the ones obtained using TCalcGeodesicFromChristoffel, but they will always have the same solutions. Usually, one of TCalcGeodesicFromChristoffel or TCalcGeodesicFromLagrangian will generate simpler equations for a given metric and/or coordinate system. TCalcLagrangian: Calculates the curve Lagrangian of a metric, defined as the norm-squared of the tangent to the curve: gμνẋμẋν. Taking the square root of (the absolute value of) the Lagrangian yields the integrand of the curve length functional. Varying the Lagrangian using the Euler-Lagrange equations yields the geodesic equations (see TCalcGeodesicFromLagrangian above). TMessage: Not really a module, just a placeholder symbol to which messages not associated with any specific OGRe module are attached. In particular, when a private module (called only internally within the package) invokes Message, the message will now be displayed as TMessage:: instead of the awkward OGRe`Private` :: . Not all modules use TMessage yet; the transition will be performed gradually in the upcoming releases. TSetAllowOverwrite: Allows or disallows overwriting tensors. The default value is False, which means you cannot create a new tensor with the same ID as an existing tensor. Calling TSetAllowOverwrite[True] will allow overwriting tensors, which is more convenient, but can result in loss of data. You will be warned whenever a tensor is being overwritten, but this warning can be turned off (like any other Message) using Off[TMessage::WarningOverwrite]. This setting is persistent between sessions. TSetCurveParameter: Sets the curve parameter used by TCalcGeodesicFromChristoffel, TCalcGeodesicFromLagrangian, and TCalcLagrangian. These modules will produce results in terms of the coordinate symbols as functions of the curve parameter and their derivatives with respect to this parameter. The default value is λ. If the Lagrangian or geodesic equation vector is displayed using TList or TShow, the arguments of the coordinate functions are omitted (e.g. x instead of x[λ]) and derivatives with respect to the curve parameter are displayed in Newton (dot) notation (e.g. ẋ instead of x'[λ]) for improved readability. However, extracting the components using TGetComponents will produce the full expressions (e.g. to be used with DSolve). When the curve parameter is changed, the parameter of the coordinate functions in all of the tensors calculated so far will be changed accordingly. TSetReservedSymbols: Works similar to TInitializeSymbols, which has now been removed. However, TSetReservedSymbols also saves the reserved symbols so they can be exported and then imported in a later session. If the reserved symbol is a function of the coordinates, TList and TShow will not show the arguments of the function when displaying the components of a tensor, for improved readability. TVolumeElementSquared: Calculates the determinant of a given metric. The square root of the determinant (or its negative, for a pseudo-Riemannian metric) is the volume element. Changes to existing modules: All TCalc* modules now check if the metric exists first. TGetComponents: This module now gets the components of the tensor in the default index configuration and/or coordinate system if either or both are not specified. However, if the default value is used, a message will let you know which representation the components are given in, to avoid confusion. TInitializeSymbols has been removed and replaced with TSetReservedSymbols (see above). TList and TShow: Partial derivatives are now displayed in compact notation for improved readability. TList will no longer list the same element twice if it is non-zero but equal to minus itself (e.g. ComplexInfinity). See TSetCurveParameter and TSetReservedSymbols above for other changes. TNewMetric: If the new metric overrides a previous metric with the same ID, all of the curvature tensors calculated from the metric being overwritten will be automatically deleted, for consistency. TSetParallelization: Now uses $MaxLicenseSubprocesses instead of the deprecated (as of Mathematica 12.3) $ConfiguredKernels to determine how many kernels to launch when enabling parallelization. Disabling parallelization now also closes the kernels. Tensor simplifications will no longer invoke parallelization if the tensor only has one component, to avoid unnecessary overhead. Other changes: A button to open the GitHub repository directly in Visual Studio Code has been added to the badges in README.md. This release is dedicated to my grandfather Yona Shoshany, who taught me BASIC, my first programming language, in my early childhood. He passed away a day before this release was published.

Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.