einsteinpy / riccipy Goto Github PK

For a given vector , we need a method for calculating the covariant derivative given by:

The covariant derivative should be implemented as an operator, however, the contraction of the input vector with the Christoffel symbols implies that the covariant derivative is not compatible with the current API for tensors.

I propose to simply model the covariant derivative as a tensor operator similar to the DiffOperator in partial.py where it is a subclass of ~sympy.tensor.tensor.TensExpr and defines the __mul__ and __rmul__ magic methods to return an expression of the form provided by the equation above.

Python 3.5 is soon going to die. Let's not support Python 3.5 in this!

For some reason the API has it that

Currently, the left hand side yields the correct value while the right hand side sums the diagonal components of the array representing the tensor literally.

However this is only an issue with contractions on a single tensor (not a product of tensors), and when the contraction yields a scalar. Meaning that the calculation of the Ricci tensor is fine, but the Ricci scalar is not.

It's very important to provide a minimum bridge between the usefulness and compact symbolic manipulations provided by RicciPy and the numerical functions required by EinsteinPy. As such RicciPy should provide a convenient way to produce numpy-like functions with ~sympy.lambdify to return either numpy arrays or functions for individual components.

Having a global data structure for managing array replacement is not efficient and causes conflicts in multithreading/multiprocessing. It would be best to find a way to construct the necessary replacement dictionary from within expand_tensor from the arguments of the passed expression.

Create a directory for storing a collection of different exact solutions to the EFE and provide a means by which these files can be used to initialize a Metric object.