Russell Goyder has a new Python program simply called Analemma. But the program is far from simple as it is able to compute the shape and provide visualizations of the analemma for any planet in our solar system. His documentation and approach chooses to use the inertial frame of our solar system and apply vectors of position to determine the analemma and equation of time. "From the documentation, you can run and modify any [Python Jupyter] notebook yourself by clicking on the 'launch binder' button." Analemma uses SymPy and GAlgebra to encode and present the mathematics of the analemma.

His notebook is at: https://russellgoyder.github.io/sundial-latex/

A number of authors have used vector algebra to obtain trigonometric formulas many of us use. Goyder however uses the world of geometric algebra that consists of "outer products" and "bivectors". The terms are unfamiliar to many, but when explained, result in creating familiar trig formulas. An introduction to geometric algebra can be found at https://bivector.net/ with several informative videos.