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Dear Forum and Heiko Thei{\ss}en and Martin Sch\"onert:
Thanks for your response.
You said:
I have used the `AbStab.g' library quite a bit for Rubik's Cube. I
never encountered a problem at all. Could it be that the problems you
have with ``solutions'' not working in Maple arise because the model
you use in Maple is slightly different from the one used in GAP (e.g.,
different order of generators)? Note that the ``solutions'' found by
I don't believe so. I carefully determined all the generators used by abstab.g
in terms of my generators.
`AbStab.g' are still not optimal. In the case of Rubik's Cube, they
are usually about an order of magnitude too long.
I'll explain why I think abstab.g has an error. I used GAP and abstab.g
for the group of the masterball, which has size ~4.3x10^26. I usually
can eventually get the masterball into one of two ``nearly solved''
positions: one requiring a 2-cycle and the other requiring a 3-cycle.
Shrink in abstab.g gives a ~90 move long solution to the 3-cycle position
which works. I checked this on my maple implementation and by hand.
Shrink gives a slightly longer solution for the 2-cycle. It does
not work by my maple computer implementation nor by hand. Moreover,
the ``word'' returned by Shrink is *not* equal to the ``word'' returned
by FactorPermGroupElement. This makes me suspicious.
By the way: While trying to play with `AbStab.g' I have noticed that
the function `MakeAbStabChain' runs into an error in GAP V3R4P3, but
succeeds in GAP V3R4P2. The reason is that third update included a
modification of the function `List'. In GAP V3R4P2 the first argument
could have holes (even though the manual forbids this), so e.g.List( [, 1 ], x -> x ^ 2 ) returned [ 1 ]while in GAP V3R4P3 this now results in an error. I suppose that your
experiments with `AbStab.g' were done in GAP V3R4P2 (or earlier). Is
this right?
I used gap3r4p2 at work and I used gap3r4p3 with the 3r4p2 library
at home with no errors of this kind.
Attached by a sun mailtool attachment is a history of a gap session
which produces the above described problem. Also included is a .g
file containing the group-theoretical data for the masterball group,
for anyone interested. I'm enclosing this because, based on this session,
I conjecture that Shrink in abstab.g has a bug. However, I would be
happy to hear of some other explanation for the problem.
- David Joyner ---------- X-Sun-Data-Type: default X-Sun-Data-Description: default X-Sun-Data-Name: bug.txt X-Sun-Charset: us-ascii X-Sun-Content-Lines: 86 51 math65:/home/math6/wdj> gap
######## Lehrstuhl D fuer Mathematik ### #### RWTH Aachen ## ## ## # ####### ######### ## # ## ## # ## ## # # ## # ## #### ## ## # # ## ##### ### ## ## ## ## ######### # ######### ####### # # ## Version 3 # ### Release 2 # ## # 10 Feb 93 # ## # ## # Alice Niemeyer, Werner Nickel, Martin Schoenert ## # Johannes Meier, Alex Wegner, Thomas Bischops ## # Frank Celler, Juergen Mnich, Udo Polis ### ## Thomas Breuer, Goetz Pfeiffer, Hans U. Besche ###### Volkmar Felsch, Heiko Theissen, Alexander Hulpke Ansgar Kaup, Akos Seress
For help enter: ?<return> gap> LogTo("/home/math6/wdj/gap/games/bug.log"); gap> Read("/home/math6/wdj/gap/games/grpdata.g"); gap> Read("/home/math6/wdj/gap/new/AbStab.g"); The record 'descriptions' contains brief descriptions of the functions in this file. Functions of importance: MakeAbStabChain, FactorPermGroupElement, Shrink gap> gen:=Set([f1,f2,f3,f4,r1,r2,r3,r4]); [ (25,26,27,28,29,30,31,32), (17,18,19,20,21,22,23,24), ( 9,10,11,12,13,14,15,16), ( 4,31)( 5,30)( 6,29)( 7,28)(12,23)(13,22)(14,21) (15,20), ( 3,30)( 4,29)( 5,28)( 6,27)(11,22)(12,21)(13,20)(14,19), ( 2,29)( 3,28)( 4,27)( 5,26)(10,21)(11,22)(12,23)(13,24), (1,2,3,4,5,6,7,8), ( 1,28)( 2,27)( 3,26)( 4,25)( 9,20)(10,19)(11,18)(12,17) ] gap> G:=MinGenSet(gen); Group( (25,26,27,28,29,30,31,32), (17,18,19,20,21,22,23,24), ( 9,10,11,12,13, 14,15,16), ( 4,31)( 5,30)( 6,29)( 7,28)(12,23)(13,22)(14,21)(15,20), ( 3,30) ( 4,29)( 5,28)( 6,27)(11,22)(12,21)(13,20)(14,19), ( 2,29)( 3,28)( 4,27) ( 5,26)(10,21)(11,22)(12,23)(13,24), (1,2,3,4,5,6,7,8) ) gap> 2_cycle:=(1,2); (1,2) gap> cycle2a:=FactorPermGroupElement(G,2_cycle); g1^2*g5*g7*g5^-1*g1*g5*g7^-1*g5^-1*g1^-1*g5*g7*g5^-1*g1^-2*g5*g7^-1*g5^-1*g1^-\ 1*g5*g7*g5^-1*g1^3*g5*g7^-1*g5^-1*g1*g5*g7*g5^-1*g1^-1*g5*g7^-1*g5^-1*g1^-3*g5\ *g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1^-2*g5*g7^-1*g5^-1*g1*g5*g7^3*g5^-1*g1*g5*g7^-\ 3*g5^-1*g1^-1*g5*g7*g5^-1*g1^-2*g5*g7*g5^-1*g1^3*g5*g7^-1*g5^-1*g1^-2*g5*g7^-1\ *g5^-1*g1*g5*g7^3*g5^-1*g1*g5*g7^-3*g5^-1*g1^-1*g5*g7*g5^-1*g1^-1*g5*g7*g5^-1*\ g1^2*g5*g7^-1*g5^-1*g1*g5*g7*g5^-1*g1^-1*g5*g7^-1*g5^-1*g1^-3*g5*g7*g5^-1*g1^2\ *g5*g7^-1*g5^-1*g1^-2*g5*g7^-1*g5^-1*g1*g5*g7^3*g5^-1*g1*g5*g7^-3*g5^-1*g1^-1*\ g5*g7*g5^-1*g1^-1*g5*g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1^-2*g5*g7^-1*g5^-1*g1*g5*g\ 7^3*g5^-1*g1*g5*g7^-3*g5^-1*g1^-1*g5*g7*g5^-1*g1^-2*g5*g7*g5^-1*g1^3*g5*g7^-1*\ g5^-1*g1^-2*g5*g7^-1*g5^-1*g1*g5*g7^3*g5^-1*g1*g5*g7^-3*g5^-1*g1^-1*g5*g7*g5^-\ 1*g1^-1*g5*g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1*g5*g7*g5^-1*g1^-1*g5*g7^-1*g5^-1*g1\ ^-3*g5*g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1^-2*g5*g7^-1*g5^-1*g1*g5*g7^3*g5^-1*g1*g\ 5*g7^-3*g5^-1*g1^-1*g5*g7*g5^-1*g1^-1*g5*g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1^-2*g5\ *g7^-1*g5^-1*g1*g5*g7^3*g5^-1*g1*g5*g7^-3*g5^-1*g1^-1*g5*g7*g5^-1*g1^-2*g5*g7*\ g5^-1*g1^3*g5*g7^-1*g5^-1*g1^-2*g5*g7^-1*g5^-1*g1*g5*g7^3*g5^-1*g1*g5*g7^-3*g5\ ^-1*g1^-1*g5*g7*g5^-1*g1^-1*g5*g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1*g5*g7*g5^-1*g1^\ -1*g5*g7^-1*g5^-1*g1^-3*g5*g7*g5^-1*g1^2*g5*g7^-1*g5^-1*g1^-2*g5*g7^-1*g5^-1*g\ 1*g5*g7^3*g5^-1*g1*g5*g7^-3*g5^-1*g1^-1*g5*g7*g5^-1*g1^2*g5*g7*g5^-1*g1*g5*g7^\ -1*g5^-1*g1^-1*g5*g7*g5^-1*g1^-3*g5*g7^-1*g5^-1*g1*g5*g7*g5^-1*g1^2*g5*g7^-1*g\ 5^-1*g1*g5*g7*g5^-1*g1^-1*g5*g7^-1*g5^-1*g1^-2 gap> cycle2b:=Shrink(G,cycle2a); g1^-2*g5^-1*g1*g4^-1*g1*g4^-1*g1^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-3*g5^-1*g1^-1*g\ 5^-1*g7*g5^-1*g1^2*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7*g5^-1*\ g1^-1*g5^-1*g7^-1*g5^-1*g1^-4*g5^-1*g7*g5^-1*g1*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^\ -2*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7^4*g5^-1*g1\ *g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^2*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^3*g\ 5^-1*g1*g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1 gap> cycle2a=cycle2b; false gap> cycle2c:=Shrink(G,2_cycle); g1^-2*g5^-1*g1*g4^-1*g1*g4^-1*g1^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-3*g5^-1*g1^-1*g\ 5^-1*g7*g5^-1*g1^2*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7*g5^-1*\ g1^-1*g5^-1*g7^-1*g5^-1*g1^-4*g5^-1*g7*g5^-1*g1*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^\ -2*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7^4*g5^-1*g1\ *g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^2*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^3*g\ 5^-1*g1*g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1 gap> cycle2b=cycle2c; true gap> quit; 258.33u 75.28s 33:19.81 16.6% 52 math65:/home/math6/wdj> ---------- X-Sun-Data-Type: default X-Sun-Data-Description: default X-Sun-Data-Name: grpdata.g X-Sun-Charset: us-ascii X-Sun-Content-Lines: 14 r1 := (1, 2, 3, 4, 5, 6, 7, 8); r2 := (9, 10, 11, 12, 13, 14, 15, 16); r3 := (17, 18, 19, 20, 21, 22, 23, 24); r4 := (25, 26, 27, 28, 29, 30, 31, 32); f1 := (1, 28)(2, 27)(3, 26)(4, 25)(9, 20)(10, 19)(11, 18)(12, 17); f2 := (2, 29)(3, 28)(4, 27)(5, 26)(10, 21)(11, 22)(12, 23)(13, 24); f3 := (3, 30)(4, 29)(5, 28)(6, 27)(11, 22)(12, 21)(13, 20)(14, 19); f4 := (4, 31)(5, 30)(6, 29)(7, 28)(12, 23)(13, 22)(14, 21)(15, 20); f5 := (5, 32)(6, 31)(7, 30)(8, 29)(13, 24)(14, 23)(15, 22)(16, 21); f6 := (6, 25)(7, 32)(8, 31)(1, 30)(14, 17)(15, 24)(16, 23)(9, 22); f7 := (7, 26)(8, 25)(1, 32)(2, 31)(15, 18)(16, 17)(9, 24)(10, 23); f8 := (8, 27)(1, 26)(2, 25)(3, 32)(16, 19)(9, 18)(10, 17)(11, 24); order_of_group := 437763136697395052544000000; geners := Set([r1,r2,r3,r4,f1,f2,f3,f4,f5,f6,f7,f8]);