Computing the homology of the motivic lambda algebra

I investigated generalizations of the Curtis algorithm, an inductive process for computing the homology of the lambda algebra, to determining motivic Adams \(E_2\) pages.

The lambda algebra is a differential graded algebra whose homology is the \(E_2\) page of the Adams spectral sequence for the sphere. Balderrama, Culver, and Quigley introduce a motivic version of the lambda algebra, and my project was to investigate a motivic analogue of the Curtis algorithm.

My REU paper gives an overview of the classical Curtis algorithm, and an appropriate motivic analogue. I managed to use the Curtis algorithm to automate the generation of classical Adams \(E_2\) charts, in the style of Isaksen, Wang and Xu. A Github repository containing some of my code is available here; currently rough and uncommented, but if you want to use it feel free to let me know and I can get you started.