Atlas 2 - modern differential geometry
The Atlas 2 for Mathematica package is powerful Mathematica toolbox which allows you to do a wide range of modern differential geometry calculations: from formulating and solving 2D/3D problems to working with an N-dimensional manifold as a whole.
Atlas GUI
AtlasWizard Atlas package code generation
AtlasPalette advanced GUI application for Atlas package
Visualization visualization in Atlas package
Declaration operators
Use these operators to declare various differential geometry entities.
Domain Manifold and domain declaration
Constants Constants declaration
Functions Functions declaration
Tensors Tensors declaration
Forms Forms declaration
Vectors Vectors declaration
Mapping Declaration of a mapping between manifolds or domains
Coframe Coframe declaration
Frame Frame declaration
Metric Metric tensor declaration
Calculation operators
Use these operators for automatic calculation of various differential geometry objects.
Projectors Calculation of projectors of a mapping
Invariants Calculation of invariants of a mapping
Connection Calculation of connection 1-forms
Curvature Calculation of curvature 2-forms
Torsion Calculation of torsion 2-forms
Riemann Riemann tensor calculation
Ricci Ricci tensor calculation
RicciScalar Ricci scalar calculation
Differential geometry operators
Use these operators for standard differential geometry calculations.
d Exterior derivative operator
L Lie derivative
iota Interior product operator
Wedge Exterior product operator
CircleTimes Tensor product operator
Hodge Hodge operator
cov Covariant differentiation
grad Gradient operator
div Divergence operator
Codiff Codifferential operator
Laplacian Hodge-de Rham Laplacian
Pullback Pullback of a [0,k] tensor field under a mapping
Pushforward Pushforward (differential of a mapping)
Utility operators
Use these operators to control and manage your differential geometry entities.
ToBasis "ToBasis" decomposision
Who Lists of all declarations made and shows "who is who"
Kind Kind of a tensor
Nat Nat vector operator
Dual Dual operator
Delta Kronecker's delta symbol