With Sympy we can write general symbolic expression by using symbols, functions, numbers,...., which are instances of the class Expr.

Similarly, we can write symbolic matrix expression using instances of the class MatrixExpr. We can also substitute dense or sparse matrices into those symbolic expressions.

Unfortunately, vector expressions (involving dot and cross products, magnitude, divergence, curl, ...) are not implemented yet. This is a highly experimental module to implement vector expressions. At the moment, only basic functionalities and printing are implemented. Take a look at the Jupyter notebooks Tutorial to learn how to use it. Also, feel free to help with the development.

I feel like the current implementation is not good enough to be extended anymore. In order to use matrices-tensors, the module need to be re-engineered and rewritten.

Take a look at the tests folder to see example of this module usage.

• Operation precedence.
• Printing need some works.
• Integrals of vector expressions.
• Solve for vector expressions.
• Gradient: the gradient of a vector field is a tensor (matrix). Is it possible to implement them in this module? Specifically, is it possible to substitute a tensor/matrix into a vector expression and perform the evaluation? Is it possible to integrate them with tensor and linear algebra modules?