diffforms 0.1.32

A symbolic differential form library with exterior calculus operations and sympy integration. Applications involve General Relativity and differentialform descriptions of Manifolds.

General

The Diffform python package implements differential forms and poly-forms from differential geometry. It includes some usual operations found in exterior calculus, include exterior product, differential operator. The main advantage of this package over other differential form packages ( e.g. pycartan ) is that it allows for polyforms and there is no dependence on basis forms.

This package is a part-time project during my PhD, updates should be suspected to end eventually. Bugs and mistakes may (possibly will) be prevalent.

Documentation will be implemented when I find the time, when I have time I will try to implement comments in the class/functions as a rudimentary form of documentation.

ToDo List

This is the list of possible implementation, in an approximate order of priority (interest to me):

• Differential Forms
• Exterior Product
• Simplification of Forms
• Exterior Differential Operator
• Substitution of factors/forms
• Vector fields
• Generic tensor product
• Insertion of vector fields
• Generic Tensor Contractions
• Implement substitution for Tensors
• Hodge star given metric/frame (Working?)
• Spin connection computation
• Lie Derivative on generic Tensor (add weight)
• Fallback to symbolic Hodge star without basis (or if form isn't in basis)
• Solving 1-form simple linear equations
• Vector Field Commutator

Dependencies

Make sure you have the following python packages:

• wheel (needed for installing through pip)
• sympy

Installation

Package should be uploaded to pip fairly frequently and is currently under diffforms