xCoba: General component tensor computer algebra. 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 manifolds 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. 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 still limited..