Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups
Web Page for Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups
Claudio Gómez-Gonzáles, Alexander J. Sutherland, and Jesse Wolfson
This paper uses computations completed in SageMath [SageMath2022] by accessing GAP [GAP2022]. The SageMath script compute_molien.sage lets you pick a sporadic group G and either
computes the Molien series M (ρ_G;z) as a rational function, prints the numerator p_G(z) and the denominator q_G(z), and stores p_G(z) and q_G(z) in the file G_output.txt ; or
takes in the data for G from the GAP character table library (saved in the file G_data.txt) and computes the first 20 coefficients m_1(ρ_G), . . . , m_{20}(ρ_G) of the Molien series M (ρ_G;t), prints m_1(ρ_G), . . . , m_{20}(ρ_G) , and stores m_1(ρ_G), . . . , m_{20}(ρ_G) in the file G_output.txt.
Outcome 1 happens when G = M11, M12, M22, M23, M24, Co3, Co2, Co1, J1, J2, J3, Suz, HS, McL, Ru, or He.
Outcome 2 happens when G = J4, Fi22, Fi23, Fi24', HN, Th, O'N, Ly, B, and M.
Here are the data files, output files, the script, and a ZIP file containing all aforementioned files:
Script File
Output Files (Rational Functions)
Data Files (Coefficients)
Output Files (Coefficients)
[GAP2022] The GAP Group, GAP -- Groups, Algorithms, and Programming, Version 4.12.2; 2022, https://www.gap-system.org.
[Sag22] The Sage Developers, SageMath, the Sage Mathematics Software System; 9.5, 2022, https://www.sagemath.org.