**AVF:** Exterior calculus with algebra value forms

**Authors:** Hugo D. Wahlquist © 2003-2020 under GPL,
mantained since 2011 by Frank B. Estabrook and José M. Martín-García

# Introduction

*AVF* is a Mathematica package for

- exterior calculus with indexed (or algebra-valued) sets of basis forms,
- Cartan moving frame theory in n-dimensional Riemannian geometry with arbitrary signature,
- the exterior differential systems of Cartan-Kähler theory and calculation of Cartan characters, and
- embedding of Riemannian manifolds.

There are specific programs for generation and use of Clifford algebra valued forms with moving frames, and generalizations.

The *AVF* package is essentially independent of the rest of the xAct packages.
It is included in the xAct framework because it covers a complementary area.
It does not yet talk to the other mathematical packages as it uses a different,
mostly index-free, approach.

Jose: This package is a small modification of a suite of programs written by Hugo D. Wahlquist in 2003,
used and tested by him and his collaborator Frank B. Estabrook.
The original programs, as written by Hugo D. Wahlquist, can be obtained from
http://www.emis.de/journals/SIGMA/2008/063/.
Hugo passed away in 2008, and Frank has kindly authorized *AVF* is included in the *xAct*
suite.

See AVF.History.

# Download and installation

Current version: 1.0.0 (as of 18 December 2011). It is recommended to
download the main *xAct* bundle, but
you can also download the different files separately:

- AVF.nb: source file with all definitions and comments. Many examples. You need this file if you want to understand and/or modify the internals of the package.
- AVF.m: package file. This file is automatically generated by Mathematica when AVF.nb is saved. This is the only essential file.
- AVFDoc.nb: main documentation file.
- General Public License

See the Installation notes.