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

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

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

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)

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"

Nat — Nat vector operator

Delta — Kronecker's delta symbol