atlas 2 - modern differential geometry for Maple

atlas 2D/3D Wizard - GUI AddO
atlas 2D/3D Wizard is powerful GUI AddOn for atlas package code generation.

This AddOn generates atlas package Maple™ code to solve typical 2D and 3D differential geometry problems:
- calculation of curvature, torsion, tangent, principal normal and binormal vectors for plane and space curves in any coordinate system
- calculation of metric, second fundamental form, mean curvature vectors, Laplace operator, connection, curvature Riemann and Ricci tensor, Gauss curvature for any surface in any 3D coordinate system
- calculation of metric, connection, Laplace operator for any 2D and 3D coordinate system
Just follow the Wizard steps, execute the generated Maple™ notebook and have your problem solved.
With this AddOn you can solve 2D and 3D differential geometry problems even with a little knowledge in differential geometry!

Modern differential geometry

Modern differential geometry is the basis for the atlas 2 package. Such entities as manifolds, mappings, p-forms, tensor fields, bundles, connections are very important in the modern differential geometry. The atlas 2 package allows to work with these entities without extra efforts, just define an entity with corresponding obvious definition and work with it just as you usually do.
The following declarations are trivial and self explanatory:
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

No programming just differential geometry

When working on your problem you think in terms of manifolds, mappings, embeddings, submersions, p-forms, tensor fields etc.
The atlas 2 package allows you concentrate on the differential geometry problem not on the programming.
You can use predefined declaration operators to declare various differential geometry objects, which are calculated on the fly:
Projectors - automatic calculation of projectors of a mapping
Invariants - automatic calculation of invariants of a mapping
Connection - automatic calculation of connection 1-forms
Curvature - automatic calculation of curvature 2-forms
Torsion - automatic calculation of torsion 2-forms
Riemann - automatic Riemann tensor calculation
Ricci - automatic Ricci tensor calculation
RicciScalar - automatic Ricci scalar calculation

No ugly output just standard notations

The atlas 2 package uses standard differential geometry notations: d - exterior derivative, Lie derivative- Lie derivative, ι - interior product, Exterior product- exterior product, Tensor product- tensor product, Hodge operator- Hodge star, Covariant derivative- covariant differentiation, δ - Kronecker's delta symbol etc. You always get output as you expected like the following:



Single solving path for almost any problem

With the atlas package you always have one and the same solving path for almost any of your differential geometry problem. You start with definitions of manifolds, vector and tensor fields, p- forms and mappings between the manifolds.
When you get your differential geometry entities defined, you use standard operators to get various quantities of your entities:
Projectors - automatic calculation of projectors of a mapping
Invariants - automatic calculation of invariants of a mapping
Connection - automatic calculation of connection 1-forms
Curvature - automatic calculation of curvature 2-forms
Torsion - automatic calculation of torsion 2-forms
Riemann - automatic Riemann tensor calculation
Ricci - automatic Ricci tensor calculation
RicciScalar - automatic Ricci scalar calculation