alGR is a general relativity package written in Mathematica. The code is brief so you can easily understand and modify it. Just input your metric and the package will calculate what you need. I have employed a convenient and powerful formalism for index notation. Common tensors are represented by Mathematica functions and positive indices are lower (covariant) indices and negative indices are upper (contravariant) indices. For example, $\dpi{300}\inline \Gamma^{1\ }_{\ 2}_{3}$, is represented by Γ[-1, 2, 3]. What if you have a tensor as list and you want to do raise or lower its indices? That is supported too. Just pay attention when you should be using a function representation or a list representation of a tensor. For most users, everything is already coded so you don’t have to worry about coding.

Features:

• A brief documentation
• Tensor inner product of all ranks and dimensions
• Raising and lowering indices of all ranks and dimensions
• Connection Parameters
• Connection Parameters
• Riemann curvature tensor
• Covariant derivative