Exterior Differential Calculus


Symbolic Matrix Algebra @ Mathematica



     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

    Another use of this package is for doing algebraic / differential calculations with "symbolic matrices", i.e., with symbols satisfying special multiplication rules, which can be interpreted as representing matrices, quantum operators, Lie algebra generators, Maurer-Cartan forms etc. In particular, it allows user-controlled application of trace identities and the Cayley-Hamilton theorem. Any symbol can be defined to be a "symbolic matrix", i.e., to have special multiplication properties. But in this case the user must give the extra multiplication (Wedge) rules that define his/her problem. This is illustrated with several examples.

   Version is 3.7.5 includes several auxiliary functions for manipulating explicit matrices. The notebook EDCmanual.nb has been rewritten ab initio and contains Definitions of all functions defined in the package and Examples illustrating their use.

   Version is 3.8.0 corrects some minor bugs and adds four new auxiliary functions.

   Version is 3.8.2 fixes some minor bugs.

   Version is 3.8.5 introduces two new functions: interiorProduct (contraction of a vector and a form) and LieDcartan (Lie derivative of forms using the Cartan identity).

   Version is 3.8.7 introduces the function FormCoef giving the "coefficient" of a differential form in a differential form expression.

   The present version is 3.8.9 corrects some minor bugs.

   The package is compatible with all Mathematica versions 3.0 or later.


   Download EDC (Version 3.8.9 - May 2013)