fizyk20/differential-geometry

A Rust crate for differential-geometric calculations.

differential-geometry's Issues

Implement metrics

The plan is to implement Metric trait for coordinate systems with the following methods:

• metric(Point)
• inv_metric(Point)
• christoffel(Point)

This will provide the basis on which it will be possible to implement covariant derivatives.

Implement default ConversionTo::inv_jacobian

That will complete the ConversionTo trait. Requires Matrix::inverse().

Add a trait abstracting the coordinate system away

Currently the only way of using a tensor requires knowing the coordinate system it is defined in statically. This may not always be possible.

Let's say I want to calculate a geodesic in a space partially described with one coordinate system, and partially with another. The current position and tangent vector might then be defined in each of the systems and the object containing them shouldn't have to worry about that - it should just know a point and a vector, period.

The solution will be a trait (or traits) implementing operations on tensors and points, providing an interface that doesn't depend on the coordinate system.

Improve the documentation

Current documentation is very basic, so it would be a good idea to develop it a bit before releasing the crate.

Implement helper functions for matrices

• inverse() - calculation of the inverse matrix
• transpose() - calculation of the transposed matrix
• identity() - returning the identity matrix

Any other ideas?