# Validate Your CM Invariants with Maple: Open Source Code Available for Testing

• Maple
• bcrowell
In summary, the Carminati-McLenaghan invariants are a set of 16 polynomial curvature invariants that have been implemented in a free Maple package by Carminati and McLenaghan. However, Maple is a proprietary software and cannot be used by everyone. The CM invariants have also been implemented as open-source code in the computer algebra system Maxima. The author has written various tests to check the validity of the code, but is unable to find any online tabulations of the CM invariants in cases where they are finite. They are specifically looking for results from the Maple implementation to compare with their own code. They have asked for help from anyone who owns Maple, and have also mentioned that @Ray Vickson may be
bcrowell
Staff Emeritus
Gold Member
There is a set of 16 polynomial curvature invariants called the Carminati-McLenaghan invariants, described here: https://en.wikipedia.org/wiki/Carminati–McLenaghan_invariants . They've been implemented (I think by Carminati and McLenaghan themselves) in a free Maple package described here: http://grtensor.phy.queensu.ca/Griihelp/cmscalar.help . Maple itself, however, is proprietary. I've implemented the CM invariants as open-source code https://github.com/bcrowell/cm_invariants that works in the open-source computer algebra system Maxima. I've written up a bunch of tests, e.g., calculating the invariants in spacetimes where I know that they should vanish, or spacetimes where I know that some of them should diverge at a curvature singularity. However, I haven't found any tabulations online of what the CM invariants are *supposed* to be in cases where they're finite. For example, there is an invariant called ##W_1##, and for the Schwarzschild spacetime I get ##W_1=6m^2/r^6##, but although this seems reasonable, I don't have any way to check whether it's right (e.g., whether the numerical coefficient should really be 6).

Would anyone who has a copy of Maple be willing to run the Maple implementation of the CM invariants and tell me some results that I could use to check whether my code is calculating correct output? The spacetimes that I have used so far for tests are in this test suite: https://github.com/bcrowell/cm_invariants/tree/master/tests .

Any help would be much appreciated!

Unfortunately, I don't own Maple. If I can help with some Mathematica package, let me know.

In another thread, I saw that @Ray Vickson uses Maple. He may be willing to help you.

bcrowell

## 1. How do I access Maple software?

In order to access Maple software, you need to purchase a license or obtain a free trial version from the official Maple website. Once you have the software installed on your computer, you can open it and start using it.

## 2. Can I get help with specific functions or commands in Maple?

Yes, there are several resources available for help with specific functions or commands in Maple. You can refer to the official Maple documentation, join online forums or communities, or seek help from Maple experts.

## 3. How can I import data into Maple?

To import data into Maple, you can use the "Import Data" command or use the "File" menu to open a data file. You can also copy and paste data from external sources into Maple. Additionally, Maple has built-in tools for importing data from various file formats.

## 4. Is there a way to customize the interface in Maple?

Yes, the Maple interface can be customized to suit your preferences. You can change the layout, colors, and fonts of the interface, as well as add or remove toolbars and menus. You can also create your own custom toolbars and shortcuts for frequently used commands.

## 5. Can I collaborate with others on a Maple project?

Yes, Maple offers collaboration features that allow you to work on a project with others in real-time. You can share your work with others and collaborate on a single document simultaneously. Additionally, Maple has built-in tools for commenting and reviewing shared documents.

• Special and General Relativity
Replies
2
Views
2K
• Special and General Relativity
Replies
13
Views
4K
• MATLAB, Maple, Mathematica, LaTeX
Replies
12
Views
1K
• Mechanical Engineering
Replies
4
Views
1K
• MATLAB, Maple, Mathematica, LaTeX
Replies
17
Views
2K
• MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
3K
• Special and General Relativity
Replies
1
Views
1K
• MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
• Programming and Computer Science
Replies
8
Views
2K
• Beyond the Standard Models
Replies
10
Views
2K