If a pcgs pcgs is known for a group G, then orbits and stabilizers can be computed by a special method which is particularly efficient. Note that within this function only the elements in pcgs and the relative orders of pcgs are needed. Hence this function works effectively even if the elementary operations for pcgs are slow.
StabilizerPcgs( pcgs, pt )
Pcgs_OrbitStabilizer( pcgs, domain, pnt, oprs, opr ) F
runs a solvable group orbit-stabilizer algorithm on pnt with pcgs
acting via the images oprs and the operation function opr.
The domain domain can be used to speed up search, if it is not known,
false can be given instead.
The function
returns a record with components orbit, stabpcgs and lengths, the
latter indicating the lengths of the orbit whenever it got extended.
This can be used to recompute transversal elements.
This function should be used only inside algorithms when speed is
essential.
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GAP 4 manual