GrassmannCalculus
GrassmannCalculus - a Mathematica Application. Copyright 2020 by John Browne and David Park.
Grassmann Calculus is a powerful application for education or work in multilinear algebra, geometry, differential geometry, physics and engineering.
GrassmannCalculus is an Application that includes both, Grassmann algebra AND Grassmann calculus.
The Grassmann algebra contains exterior, regressive, interior, generalized, Clifford, and hypercomplex products. The Grassmann complement is a generalized Hodge star operator.
The calculus routines include vector operators, the exterior derivative and the generalized vector calculus operators.
There are various built-in spaces with their associated coordinates, bases (vector, differential form and orthonormal), metrics and symbols. It's possible to define spaces and then switch between various spaces on the fly.
The GrassmannCalculus Palette, available from the Mathematica Palettes menu is very useful when using the application.
Another useful palette is the Common Grassmann Operations palette available from the GrassmannCalculus Palette, drop-down Palettes menu.
The application contains all the theoretical work of John Browne on Grassmann algebra, which clarifies, extends but closely follows the work and thinking of Grassmann. David Park added calculus and differential forms, many convenience routines and did the overall application design.
The Presentations application is used in many of the example notebooks but not in GrassmannCalculus itself. If you already own Presentations do not download the FreePresentations.
The Application is still developmental but is now very solidly useful. The application utilizes Mathematica (10.1+. ??? update)
DOWNLOAD APPLICATION:
HELP: Notes on Getting Started
GrassmannCalculus - a Mathematica Application.
New users can download and install the GrassmannCalculusApplication and the GrassmannCalculusBook. The Application will probably be frequently updated and the book much more rarely.
Updates of either of the two portions can just be installed in the same manner as the original application and choosing to overwrite all existing files.
Grassmann-Dropbox Link folder contains the following files.
GrassmannCalculusApplication.zip (the basic application without the book.)
GrassmannCalculusBook.zip (The Grassmann Algebra book within the application.)
FreePresentations.zip (A free version of David's Presentation application.)
The Presentations application is used in many of the example notebooks but not in GrassmannCalculus itself. If you already own Presentations do not download the FreePresentations.
The book is John Browne's Grassmann Algebra plus draft chapters for the second volume. ???? IS THIS NEEDED NOW
In Mathematica, evaluate $UserBaseDirectory or $BaseDirectory to find the installation folder. It is important to use one of these locations because GrassmannCalculus looks for coordinate archive files at these location and won't find them if you install elsewhere.
In the $UserBaseDirectory or $BaseDirectory you will find an Applications folder.
Just unzip the appropriate files above directly into that Applications folder. The unzipping process will create a GrassmannCalculus and Presentations folders.
Updates can be unzipped in the same manner and you can simply replace existing files.
DOWNLOADING In more detail:
1) It is best to keep your downloads all in one place, - create a folder for GrassmannCalculus downloads.
2) Click on the Dropbox zip file to download; click the Download button; on the popup use the dropdown Save menu and SaveAs; maneuver to the Grassmann Calculus download folder and Save.
3) Repeat for all the files in download.
4) Open the download folder and the Mathematica Applications folder (or the folder that contains it).
5) Right click on the zip file to install and drag it to the Applications folder. There will be a WinZip item on the context menu. Choose it and "Extract to here".
6) If you are updating, WinZip will ask if you want to replace existing files. Choose "Yes to All".
7) Do this for each of the files to install. The GrassmannCalculusBook.zip will just overlay the Book chapters into the existing Documentation folder. The FreePresentations.zip will create a new application.
8) Your Applications folder should now contain a GrassmannCalculus folder, which constitutes the GrassmannCalculus Application. There will also be a Presentations folder, which is used in some of the example notebooks.
After installing, open Mathematica and go to Menu, Palettes, GrassmannCalculus and bring up the GrassmannCalculus Palette. This gives direct access to documentation, the book, and other features. Please explore the palette and we recommend that you have it open while using GrassmannCalculus because it keeps you abreast of the current state.
GrassmannCalculus comes with some style sheets. It is not necessary to use them, but they are very nice. For a new notebook, try out Menu, Format, Stylesheet, GrassmannCalculus, GrassmannCalculusToolbar.
The GrassmannCalculus Application folder contains a number of extra folders that contain notebooks exploring various aspects of GrassmannCalculus. We have included these as examples that might help you in getting started. These are Introductory Examples, Study Notebooks, and DifferentialGeometry. These notebooks may not all be up-to-date but as I work them over them may get better. You may add your own folders for your own work. The only caveat is that if you Uninstall the application or delete the GrassmannCalculus folder, you will lose your own folders provided you haven't backed them
up elsewhere.
Contact David Park for questions on installations and general use of the GrassmannCalculus Application.
David Park: djmparkjr [at] gmail dot com (replace at, dot)