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Here we share the C++ code used to analyze the GIT problems for the Mukai models of \(\overline{\mathrm{M}}_7\) and \(\overline{\mathrm{M}}_8\).
Input file containing the set \(A_3\).
The set \(A_3\) contains 852 characters. Algorithm 5.1 finds one-parameter subgroups that are orthogonal to four linearly independent characters in \(A_3\). To do so, it searches over all subsets of size 4 of the set of indices \(\{0,\ldots,851\}\).
The program takes one input, an integer \(i_0\). The input \(i_0\) must be between 0 and 848. The program then analyzes each subset of size four of the form \( \{i_0,i_1,i_2,i_3\}\) where \(i_0 < i_1 < i_2 < i_3 \leq 851\). If the four characters indexed by this subset are linearly independent, and if the line orthogonal to their span meets the fundamental chamber \(F\), then the program prints this one-parameter subgroup and these four indices. It also outputs a log summarizing how many unique one-parameter subgroups have been found during the program's run.
For example, here are the output one-parameter subgroups and log when \(i_0=836\).
We ran the program for each input \(0 \leq i_0 \leq 848\) and collected the results. We obtained 10,620,905 distinct one-parameter subgroups, and the resulting file is 161MB. Here are the first 100 one-parameter subgroups. Email the fourth author, Dave Swinarski, for the full output file if you are interested.