SamplePublisher/GrassmannCalculus

GrassmannCalculus is an implementation of the work of Hermann Grassmann and John Browne in Mathematica

Contributed By: John Browne and David Park

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall[ResourceObject["https://wolfr.am/1bqxFmIQH"]]

To load the code after installation, evaluate this code:
Needs["SamplePublisher`GrassmannCalculus`"]

Paclet Guide

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The key attribute of Grassmann algebra is that it algebraicizes the notion and modeling of linear dependence and independence. It can be interpreted to many applications with contextual notation. The most important applications are mathematics, geometry, physics and engineering. Because of its basic antisymmetric nature, it is tensorial in nature being invariant to coordinate transformations. One can write coordinate free expressions applicable to all finite dimensions. A metric construct and measure arises from its basic axioms. One can compute with or without a metric. It can distinguish between points and free vectors. It can treat basis vectors as derivative operators, and reciprocal basis vectors as differential forms. It is, as John Browne writes: " a geometric calculus par excellence".

Grassmann Calculus is an Application for Grassmann algebra and 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.
Grassmann Calculus is thus a powerful application for education or work in multilinear algebra, geometry, differential geometry, physics and engineering.
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 extended Grassmann algebra theory and routines were developed by John Browne. The calculus routines were written by David Park who also designed the user interface.
You can contact David Park at djmparkjr@gmail.com. John Browne's (1942-2021) web site is at https://sites.google.com/view/grassmann-algebra/home

Grassmann Calculus Functionality

Grassmann Algebra Structure

Extras

Examples

Paclet Source

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