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.
AtlasWizard— Atlas package code generation
AtlasPalette— advanced GUI application for Atlas package
Visualization— visualization in Atlas package
Use these operators to declare various differential geometry entities.
Domain— Manifold and domain declaration
Constants— Constants declaration
Functions— Functions declaration
Tensors— Tensors declaration
Vectors— Vectors declaration
Mapping— Declaration of a mapping between manifolds or domains
Coframe— Coframe declaration
Metric— Metric tensor declaration
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
iota— Interior product operator
Wedge— Exterior product operator
CircleTimes— Tensor product operator
cov— Covariant differentiation
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)
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"
Delta— Kronecker's delta symbol
- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
