xCoba`, a companion package to xTensor`, provides several tools for working with bases and components. It allows the user to define bases on one or more vector bundles and to handle basis vectors, using basis indices notation. It performs component calculations such as expanding a tensor in a specified basis, changing the basis of an expression or tracing the contraction of basis dummies. xCoba` stores and handles component values efficiently, making full use of tensor symmetries. The package knows how to express derivatives and brackets of basis vectors in terms of Christoffel and torsion tensors and how to assign values to the components of a tensor. Support for charts (coordinate fields, restriction of a field to a point, etc.) is limited.

xCoba` is built on the twin package xTensor`, which is loaded automatically.

Load the package

0. xCoba` at a glance

1. Real and complex bases. Basis objects and basis indices

2. Manipulating basis indices: ContractBasis, SeparateBasis, ToBasis

3. Parallel derivatives and Christoffel tensors

4. Tensor densities; η and ε tensors and determinants

5. Tracing contractions

6. Working with components

7. Assigning values to components

8. Charts

9. Computing tensor values

10. Final comments

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