DFORMPY: A Python Library for visualising and zooming on differential forms

Abstract

A. We present the v1.0.1 release of DFormPy, the first Python library providing an interactive visualisation of differential forms. DFormPy is also capable of exterior algebra and vector calculus, building on the capabilities of NumPy and matplotlib. This short paper will demonstrate the functionalities of the library, briefly outlining the mathematics involved with our objects and the methods available to the user. DFormPy is an open source library with interactive GUI released under MIT license at https://github.com/MostaphaG/Summer_project-df. C 1. Introduction 2. Mathematical preliminaries 2.1. Differential p-forms 2.2. V * as tangent space 2.3. p-Forms exterior algebra 3. DFormPy objects 3.1. 1-Form 3.2. Vector field (VF) 3.3. 2-Form 3.4. 0-Form 4. DFormPy methods 4.1. Plotting 4.2. Zooming 4.3. Exterior derivative 4.4. Interior derivative 4.5. Hodge 4.6. Wedge 4.7. Covariant and contravariant 5. Conclusion and outlook Appendix A. Customisations A.