No ugly output just standard notations
The Atlas 2 package uses standard differential geometry notations: d - exterior derivative, - Lie derivative, ι - interior product, - exterior product, - tensor product, - Hodge star, - covariant differentiation, δ - Kronecker's delta symbol etc. You always get output as you expected like the following:
All calculations are as coordinate free as possible
In the package all calculations are performed in terms of tensors, vectors and p-forms (not their components!). For instance, conformally flat metric tensor of sphere is presented as
, where are coframe 1-forms and symbol - is tensor product operator (see examples below).
To get more information about the main principle of the package structure and to look through some complete examples see Examples.
To look through references list see References.
Some calculations with symbolic dimension are available
The package allows one to make some useful calculations even if the working dimension is symbolic. For example, if is the dimension, are coframe 1-forms and are frame vectors then decomposition
(of interior product of vector and 1-form ) - is one of the available calculation. Another example is Lie bracket decomposition:
To get more information about this possibility see Dimension.
Almost any differential geometry entity can be indexed
In the package any object (constant, tensor, p-form, manifold etc.) can be indexed. This is very flexible feature. For or more information on indexing facilities, see Indexing.
Easy customizable simplification of your results
Because computations with tensors and p-forms usually involve a great number of quantities, it is important to make simplification in each step of the computations. For this reason, the user can customize the simplification routine `atlas/simp` for a particular problem. For more information, see Simplification routine.