Exterior Differential Calculus

and

Symbolic Matrix Algebra @ Mathematica



 

    Overview

     This package enables Mathematica to carry out calculations with differential forms. It defines the two basic operations - Exterior Product (Wedge) and Exterior Derivative (d)  - in such a way that:

  (1)  they can act on any valid Mathematica expression
  (2)  they allow the use of any symbols to denote differential forms
  (3)  input - output notation is as close as possible to standard usage

    There are two versions of this package: scalarEDC and matrixEDC. The first can handle scalar differential-form expressions only, while the second can also handle matrix-valued differential forms, i.e., matrices whose components are (scalar) differential forms. Both versions are included in the compressed files below.

    The matrix package, offering user-controlled application of trace identities and the Cayley-Hamilton theorem, can also be used for symbolic matrix calculations.

    Version 3.3.5 allows Wedge and d to act on expressions that are series expansions (SeriesData objects).
    Version 3.5.4 corrects a rare bug that can affect calculations with series, fixes a problem with SymbolPalette.nb and has minor speed improvements.

    Version 3.6.0 is a Mathematica 6 - compatible update.

   Version 3.6.1 corrects a problem causing Wedge to go in an infinite loop in Mathematica 6 when EDCcode is reevaluated without quitting the kernel. (The problem is due to an undocumented change in ClearAll in Mathematica 6 -- see MathGroup Message).

   The present version 3.7.0 corrects an error in the symbolic calculation of certain traces (matrix code only).

   The package requires Mathematica 3.0 or later.
   The notebook EDC_Manual.nb contains many examples illustrating the use of the functions defined in the package.



 

   Download (Version 3.7.0 - July 2009)


 

For comments, questions or suggestions please contact the author at sbonano@inp.demokritos.gr
 
 

advanced web statistics

Last modified  2009-07-21