Programs

yacop - yet another cohomology program

A SageMath package for large-scale Ext computations with small modules over the Steenrod algebra.

BP toy resolutions

Sage code to compute Ext over the BP Hopf algebroid from the bar resolution. The code is available on GitHub.

Steenrod algebra resolutions on the GPU

This was an attempt to use GPU computing power for the computation of the Adams \(E_2\)-term. I first created a Tcl wrapper for OpenCL to orchestrate the computation (vaguely modeled on Python’s pyopencl), then began translating my existing C+Tcl code to OpenCL. I later added OpenTelemetry instrumentation to debug the timings.

Sadly, the final code struggled just to match the performance of my older CPU-based code. The main reason, I believe, is that the required exact linear algebra routines over \({\mathbb F}_2\) just do not admit an efficient parallelization: at some point you always have to iterate over the rows of some matrix, pick a pivot, then reduce the rest of the matrix against it. It’s conceivable that Lin’s Gröbner basis algorithm could fare better here since it uses very little linear algebra.