Secondary Steenrod algebra calculations

This repository contains data files generated by ext-rs pertaining to the secondary Steenrod algebra algorithm. This supersedes https://zenodo.org/record/4766457 but is not a strict superset of the data.

This repository contains three files.

• d2-data.zip is a zip file containing the generated data, which are as follows:

  • d2: The d₂ differentials. If the target bidegree is empty, the differentials are omitted.

  • product_a: The secondary product of all elements with [a].

  • massey_a_b: The secondary Massey product <[a], [b], ->. The only exception is massey_P which contains the Adams periodicity operator <[h_3], [h_0^4], ->.

  • filtration_one: A list of all filtration one products.

  • charts.pdf: The Adams charts showing the d₂'s and the E₃ page, drawn by TikZ.

  • clean_charts.pdf: The same charts but without showing h₂ products.

  • differentials.gz: The differentials in our minimal resolution, in a human-readable plain text format.

  • change_of_basis: The correspondence between our basis and Bruner's basis in arXiv:2109.13117. Each row expresses one of our basis element in terms of Bruner's basis.

  Unless otherwise suggested by the file extension, all files are plain text (utf-8) files. The script and the save file are known to be compatible with the version of the code in https://zenodo.org/record/5898397

• script.sh is a script that generates the files above, except for change_of_basis and the charts. This is to be run in the `ext/` directory of sseq. If the execution of the script is interrupted halfway through, it is safe to simply run the script again with the safe parameters to resume computation; the vast majority of the computation would have been saved in the save directory and need not be recomputed (If a save file was corrupted due to the interruption, the program will panic instead of silently propagate errors). Similarly, the script can be run with a larger/different range and previous computations would be reused.

• S_2_milnor.tar is an archive containing the algorithm's save file for the above computation, up to (n, s) = (140, 72).