atlas 2 for Mathematica®

atlas package Documentation

Declaration operators

Calculation operators

Standard DG operators

Utility operators

General Tutorials

Visualization Tutorials

Atlas Palette Tutorials

Atlas Wizard Tutorials

Licenses & Pricing

Laplacian - Hodge-de Rham Laplacian operator

Laplacian[expr]
allows one to calculate the Hodge-de Rham Laplacian on an expression that is p-form.
  • expr - any expression.
  • The Hodge-de Rham Laplacian is the operator : p -> p where p and p are p-forms which are defined as follows:
  • If is a p-form then, ()=d(()) + (d()) where is the codifferential (see Codiff).