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
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
TUTORIALS
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