## Differential geometry in Rust

During the last few weeks I've been working on a library that would let the user do some differential-geometric calculations in Rust. By differential geometry I mean mostly the tensor calculus in curved spaces or space-times. I've already created something like that in C++, but I wanted to try and use some of the Rust features to create an improved version.

## What could Rust do better?

The most convenient representation of tensors for doing calculations is in the form of arrays of numbers. The problem is that representing a tensor numerically requires choosing a coordinate system. Various operations, like for example addition of two tensors, only make sens when the tensors involved are expressed in the same coordinate system. The only possibility of enforcing this rule in C++ was to encode the coordinate system as a property of the tensor object and checking for compatibility in the operator code. This way any errors will be detected at runtime.

Ok, so the errors were detectable, so what could be done better? Well, for examples the tensors expressed in different coordinate systems could not only have a different value of some property, but be objects of different types. This way the error can be detected at compile time, before the program is even translated into an executable form. ~~It wouldn't be very practical in C++, but the Rust type system allows to do it quite interestingly.~~

EDIT: It has been brought to my attention that C++'s templates also allow for this kind of thing. Nevertheless, doing it in Rust was a fun experiment :)