Finding Riemann Components: Packages & Solutions

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Discussion Overview

The discussion revolves around finding suitable computational packages for calculating Riemann components in hypothetical spacetimes, specifically focusing on the calculation of ##R_{\mu \nu \rho \sigma}##, ##R_{\mu \nu}##, and ##R## values. Participants share their experiences with different software tools and packages relevant to general relativity and tensor analysis.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses urgency in finding a computational package for Riemann components and seeks advice from others.
  • Another participant recommends the Mathematica package OGRE for its capabilities in handling the required calculations.
  • A different participant mentions their preference for the Python package einsteinpy, highlighting its usability for general tensor analysis and integration with Jupyter.
  • One participant notes they created their own Mathematica file to perform the calculations, primarily for verifying exam answers.
  • Several participants confirm the effectiveness of OGRE, with one stating they successfully found all components using it and expressing interest in exploring Python packages later.

Areas of Agreement / Disagreement

Participants generally agree on the utility of Mathematica and its packages, particularly OGRE, while also presenting alternative views on using Python with einsteinpy. There is no consensus on a single best solution, as different tools are preferred based on individual experiences.

Contextual Notes

Some participants mention specific features of the packages that may or may not meet their needs, indicating potential limitations or dependencies on their specific computational requirements.

Who May Find This Useful

This discussion may be useful for researchers or students in the fields of general relativity, mathematical physics, or anyone interested in computational methods for tensor analysis.

ergospherical
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I'm working on a problem involving some hypothetical spacetimes (i.e. no tables/data-sheets available) and need to calculate a bunch of ##R_{\mu \nu \rho \sigma}## and ##R_{\mu \nu}## values, as well as ##R##. The metrics contain some arbitrary functions ##f(x^i)## of the spatial co-ordinates only. There's a little bit of urgency so I can't afford really to spend a great deal of time exploring which packages are best for this task; I hoped that somebody who feels confident with this could advise? Thanks!
 
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I just finally started to learn Python, and for computer algebra in GR (I guess it can easily be used for other general tensor-analysis work too) I like einsteinpy. Together with jupyter as the frontend it's very nice to work with:

https://einsteinpy.org/
 
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Dale said:
I use Mathematica for all things math-related. The best Mathematica package I have found is OGRE

https://arxiv.org/abs/2109.04193
Thank you, this looks promising. I noticed in the documentation that it seems to allow you to specify the co-ordinate dependencies of scalar fields, which is one thing I need.

Please allow me some time to install Mathematica and try to run the package!
 
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I just wrote my own mathematica file to do it for me. Mainly to double check exam answers before putting the exam to the students. It is not that extensive computations after all.
 
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Dale said:
I use Mathematica for all things math-related. The best Mathematica package I have found is OGRE

https://arxiv.org/abs/2109.04193
It's now working, I can find all of the components.
When I have more time I might experiment with a Python package.

Will shout if problems arise! :oldwink:
 
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