GAP Computations

After solving enough correspondences, convert the monodromy data to a GAP permutation group and ask GAP for group-theoretic information.

The monodromy solve does not have to be fully successful before you inspect the group data. If tracking stops with only partial correspondences, build_gap_group uses the valid permutations determined by the correspondences currently stored in the result. The returned group is therefore the group generated by the available information, not a certificate that all monodromy permutations have been found.

result = solve_monodromy(compiled, vertices; max_roots=4)

G = build_gap_group(4, result)
GAP.Globals.StructureDescription(G)
galois_width(G)

build_gap_group returns nothing if the available correspondences do not define any valid permutations.

G === nothing

CertifiedHomotopyTracking.build_gap_group — Function

build_gap_group(max_roots, edges_or_result)

Construct a GAP permutation group from monodromy edge correspondences.

Returns nothing if no valid permutations are available.

source

CertifiedHomotopyTracking.galois_width — Function

galois_width(G::GAP.GapObj)

Calculate the Galois width of a GAP group using a GAP helper function.

source