Dear GAP-Forum,
Dear Ashvin,
On Fri, 21 Jun 2002, ashvin db wrote: --> I gave the following commands in GAP. --> gap> z := ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16) --> gap> h :=(1,4,6,7); --> gap> test := h^-1 * z; --> ( 1, 2, 8, 9,10,11,12,13,14,15,16)( 3, 4)( 5, 6)
Actually, I got a slightly different result from GAP at this point:
( 1, 8, 9,10,11,12,13,14,15,16)( 2, 3, 4)( 5, 6)
Anyway ...
--> assuming ( 1, 2, 8, 9,10,11,12,13,14,15,16)( 3, 4)( 5, 6) are the k --> surviving subpaths after using the splitting template h for z. --> what command do I use to get a k-cycle of all the heads of the surviving --> arcs. --> in this case I have to get a 4 cycle (1,3,5,7).
... from your example it seems clear to me what you are interested in.
The desired 4-cycle consists of the "starting points" of the orbits on
the range [1..16] under the permutation 'test'. You can produce this
cycle by the following commands:
#-------------------- determine starting points: sp := []; for orbit in OrbitsPerms( [test], [1..16] ) do Add( sp, orbit[1] ); od; #---------------------------------- build cycle: k := Length( sp ); cyc_list := [1..sp[k]]; ## describes identity for i in [1..k-1] do cyc_list[sp[i]] := sp[i+1]; od; cyc_list[sp[k]] := sp[1]; ## now 'cyc_list' describes the desired k-cycle cyc := PermList( cyc_list );
Please note also that considering "Orbits( Group([test]) )" instead of
"OrbitsPerms( [test], [1..16] )" in the first for-loop would ignore
the fixed point 7 because orbits of a group <G> are orbits on the set
MovedPoints( <G> ) by default!
Best regards
Mathias
---------------------------------------------------------------------- Dr. Mathias Kratzer | I_nstitute for E-Mail: kratzer@exp-math.uni-essen.de | E_xperimental Phone : +49-201-183-7680 | M_athematics Ellernstr. 29 Visit : IEM, Room 205 | D-45326 ESSEN