Tag Archives: geometry

SageMath 8.9 is out

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SageMath 8.9 has just been released. It has new features regarding symbolic calculus on manifolds. In particular, some tutorials about vector calculus have been added and computations related to the extrinsic geometry of hypersurfaces have been improved. For more details, see
https://sagemanifolds.obspm.fr/changelog.html

SageMath is a Python-based free computer algebra system, with some differential geometry and tensor calculus capabilities implemented via the SageManifolds project (https://sagemanifolds.obspm.fr/). See https://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.

Geometric Foundations of Gravity in Tartu, Estonia

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Geometric Foundations of Gravity in Tartu

is a conference dedicated to the geometric foundations of gravity theories that will take place June 17-21, 2019 in Tartu, Estonia. This conference is a continuation of series of conferences Geomgrav 2017 and Telegrav 2018. The aim of this conference is to gather experts on various alternative and modified approaches to gravity.

The main topics include:
— Gauge theories of gravity (Poincare, teleparallel, …)
— Extended field content & related theories ((multi)scalar-vector-tensor theories, Horndeski, f(R) gravity, generalized Proca, massive gravity and bimetric theories, …)
— Beyond Lorentzian geometry (Finsler, modified dispersion relations,…)
— Dynamical systems in cosmology

The conference is organized by the Laboratory of Theoretical Physics, University of Tartu, Estonia.

An up to date list of invited speakers, the registration procedure, participants and all further details can be found on

http://hexagon.fi.tartu.ee/~geomgrav2019/

We are looking forward to meet you in Tartu in June, the organizing committee:

Sebastian Bahamonde
Manuel Hohmann
Laur Jarv
Tomi Koivisto
Martin Krssak
Christian Pfeifer
Margus Saal

SageManifolds 1.3 is out

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SageMath 8.3 has just been released and is shipped with version 1.3 of SageManifolds code. SageMath is a Python-based free computer algebra system, with some differential geometry and tensor calculus capabilities implemented via the SageManifolds project (https://sagemanifolds.obspm.fr/). See https://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.

The new features with respect to version 1.2 of SageManifolds are:

– submanifolds and their geometry (induced metric, extrinsic curvature, etc.)
– Euclidean spaces as Riemannian manifolds diffeomorphic to R^n and equipped with a flat metric, with predefined coordinate charts (Cartesian, spherical, cylindrical); this allows for elementary vector calculus in standard curvilinear coordinates, see https://sagemanifolds.obspm.fr/vector_calculus.html
– tensor fields along a submanifold

See https://sagemanifolds.obspm.fr/changelog.html for details and examples.

It suffices to upgrade to SageMath 8.3 to benefit from these features. Binaries for Linux, MacOS X and Windows are available at http://www.sagemath.org/download.html.
Another option is to run SageMath 8.3 remotely, by creating a free account in CoCalc (https://cocalc.com/): open a Jupyter notebook and select “SageMath 8.3” in the menu Kernel -> Change kernel.

Eric Gourgoulhon,
on behalf of SageManifolds team (https://sagemanifolds.obspm.fr/authors.html)

SageManifolds 1.2 is out

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SageMath 8.2 has just been released and is shipped with version 1.2 of SageManifolds code. SageMath is a Python-based free computer algebra system, with some differential geometry and tensor calculus capabilities implemented via the SageManifolds project (http://sagemanifolds.obspm.fr/). See http://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.

The new features with respect to version 1.1 of SageManifolds are:
– the possibility to use SymPy instead of SageMath default (Pynac+Maxima) as the symbolic engine for calculus on coordinate expressions
– manifolds equipped with a default metric (i.e. pseudo-Riemannian manifolds)
– operators for vector calculus on any pseudo-Riemannian manifold: gradient, divergence, curl, Laplacian, Dalembertian, dot product, cross product and norm
– more functionalities in the naming of bases and vector frames

See http://sagemanifolds.obspm.fr/changelog.html for details and examples.

It suffices to upgrade to SageMath 8.2 to benefit from these features. Binaries for Linux, MacOS X and Windows are available at http://www.sagemath.org/download.html.
Another option is to run SageMath 8.2 remotely, by creating a free account in CoCalc (https://cocalc.com/): open a Jupyter notebook and select “SageMath 8.2” in the menu Kernel –> Change kernel.

Eric Gourgoulhon,
on behalf of SageManifolds team (http://sagemanifolds.obspm.fr/authors.html)

Teleparallel Gravity Workshop, Tartu, Estonia

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Teleparallel Gravity Workshop in Tartu

is a continuation of the conference Geometric Foundations of Gravity in Tartu, 2017. The workshop will take place June 25-29, 2018 at the University of Tartu in Estonia. The aim of this workshop is to gather experts on teleparallel gravity and its modifications and discuss the recent advances and upcoming challenges within the field.

The participation at the conference is free for all participants, but we do not provide any financial assistance. The workshop is organized by the Laboratory of Theoretical Physics, University of Tartu.

Organising Committee:
– Laur Jaerv
– Manuel Hohmann
– Martin Krssak
– Christian Pfeifer

SageManifolds 1.1 is out

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SageMath 8.1 has just been released and is shipped with version 1.1 of SageManifolds code. SageMath is a Python-based free computer algebra system, with some differential geometry and tensor calculus capabilities implemented via the SageManifolds project (http://sagemanifolds.obspm.fr/). See http://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.

The new features with respect to version 1.0.2 of SageManifolds are:
– computation of geodesics (and more generally integrated curves)
– exterior powers of free modules of finite rank
– multivector fields and the Schouten-Nijenhuis bracket
– some performance improvements

See http://sagemanifolds.obspm.fr/changelog.html for details and examples.

It suffices to upgrade to SageMath 8.1 to benefit from these features. Binaries for Linux, MacOS X and Windows are available at http://www.sagemath.org/download.html.
Another option is to run SageMath 8.1 remotely, by creating a free account in CoCalc (https://cocalc.com/): open a Jupyter notebook and select “SageMath 8.1” in the menu Kernel -> Change kernel.

Eric Gourgoulhon,
on behalf of SageManifolds team (http://sagemanifolds.obspm.fr/authors.html)

Geometric Foundations of Gravity in Tartu, Estonia

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Geometric Foundations of Gravity in Tartu

is a conference dedicated to the geometric foundations of gravity theories that will take place August 28 – September 1, 2017 in Tartu, Estonia. The aim of this conference is to gather experts on various alternative and modified approaches to gravity, as well as observations.

The main topics include:

* Gauge theories of gravity (Poincare, teleparallel, …)
* Extended field content and related theories ((multi)scalar-vector-tensor theories, Horndeski, f(R) gravity, generalized Proca, massive gravity and bimetric theories)
* Beyond Lorentzian geometry (Finsler geometry, modified dispersion relations)
* Observational evidence for GR and beyond

The conference is organized by the Laboratory of Theoretical Physics, University of Tartu, Estonia.

Invited speakers are:

-Salvatore Capozziello (Napoli, Italy)
-Friedrich W. Hehl (Cologne, Germany)
-Lavinia Heisenberg (Zurich, Switzerland)
-Tomi S. Koivisto (Stockholm, Sweden)
-Claus Laemmerzahl (Bremen, Germany)
-Yuri N. Obukhov (Moscow, Russia)
-Sergei D. Odintsov (Barcelona, Spain)
-Jose G. Pereira (Sao Paulo, Brazil)
-Frederic Schuller (Erlangen, Germany)

The conference includes a social program including a presentation of the history of gravitational physics in Estonia, a public lecture and an excursion to Estonian natural heritage sites.

Registration is open and possible via the conference homepage

http://hexagon.fi.tartu.ee/~geomgrav2017

where all details on the meeting are available.

We are looking forward to meet you in Tartu in August, the organizing committee:
Laur Jaerv
Manuel Hohmann
Martin Krssak
Christian Pfeifer

SageManifolds 1.0 released

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The SageManifolds project aims at extending the modern computer algebra system SageMath (http://www.sagemath.org/) towards differential geometry and tensor calculus. All SageManifolds 1.0 code is included in SageMath 7.5, so that it does not require any separate installation. Key features of SageMath are being open-source, using the Python language and running in the powerful Jupyter Notebook (http://jupyter.org/).

SageManifolds is devoted to explicit tensor calculus (as opposed to “abstract tensor calculus”): the dimension of the manifold must be specified and some atlas must be provided. SageManifolds 1.0 functionalities include
– topological manifolds: charts, open subsets, maps between manifolds, scalar fields
– differentiable manifolds: tangent spaces, vector frames, tensor fields, curves, pullback and pushforward operators
– standard tensor calculus (tensor product, contraction, symmetrization, etc.), even on non-parallelizable manifolds
– taking into account any monoterm tensor symmetry
– exterior calculus (wedge product, exterior derivative, Hodge duality)
– Lie derivatives of tensor fields
– affine connections (curvature, torsion)
– pseudo-Riemannian metrics
– some plotting capabilities (charts, points, curves, vector fields)

Example of use, in particular in the context of general relativity, are posted at
http://sagemanifolds.obspm.fr/examples.html
Visit http://sagemanifolds.obspm.fr/ for free download and run.

Eric Gourgoulhon (on behalf of the SageManifolds team: http://sagemanifolds.obspm.fr/authors.html )

SageManifolds

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The SageManifolds project aims at extending the modern computer algebra system SageMath (http://www.sagemath.org/) towards differential geometry and tensor calculus. All SageManifolds code is included in SageMath (from version 7.5), so that it does not require any separate installation. Key features of SageMath are
– being fully open-source
– using the Python language
– embarquing many high-quality tools of the Python ecosystem (NumPy, SymPy, SciPy, Matplotlib, etc.) and beyond (Maxima, R, GAP, GSL, etc.)
– running in the powerful Jupyter Notebook (http://jupyter.org/).

SageManifolds is devoted to explicit tensor calculus (as opposed to “abstract tensor calculus”): the dimension of the manifold must be specified and some atlas must be provided. SageManifolds 1.3 functionalities include
– topological manifolds: charts, open subsets, maps between manifolds, scalar fields
– differentiable manifolds: tangent spaces, vector frames, tensor fields, curves, pullback and pushforward operators
– standard tensor calculus (tensor product, contraction, symmetrization, etc.), even on non-parallelizable manifolds
– taking into account any monoterm tensor symmetry
– exterior calculus (wedge product, exterior derivative, Hodge duality)
– Lie derivatives of tensor fields
– affine connections (curvature, torsion)
– pseudo-Riemannian metrics
– numerical computation of geodesics
– some plotting capabilities (charts, points, curves, vector fields)
– submanifolds and their extrinsic geometry

See https://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.