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Exterior Differential Calculus

Sotirios Bonanos
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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: scalarEDCcode.nb and matrixEDCcode.nb. 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.

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

The notebook EDC335Manual.nb contains many examples illustrating the use of the functions defined in the package.

*Mathematics > Calculus and Analysis > Differential Geometry

Wedge product, Exterior product, Exterior derivative, Grassmann algebra, Differential forms, Symbolic matrix algebra
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EDC360Manual.nb (185.2 KB) - Mathematica Notebook
SymbolPalette.nb (4.9 KB) - Mathematica Notebook
matrixEDC360code.nb (24.7 KB) - Mathematica Notebook
scalarEDC360code.nb (13.8 KB) - Mathematica Notebook