I have downloaded GAP version 4.7.8. for windows, and installed everything (all packages, including"ACE") with the installer. Now I want to do a simple task, enumerating the cosets. To create a group and a subgroup I execute:
gap> G := SymmetricGroup( 8 ); Sym( [ 1 .. 8 ] ) gap> U := Subgroup( G, [ (1,2), (3,4), (3,4,5) ] ); Group([ (1,2), (3,4), (3,4,5) ])
which works fine. Now for coset enumeration I found in the GAP Manual for Version 4.7.8 the function CosetTable, but when I trying to execute in analogy with the example given there I get:
gap> tab := CosetTable(G, U); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CosetTable' on 2 arguments called from <function "HANDLE_METHOD_NOT_FOUND">( <arguments> ) called from read-eval loop at line 3 of *stdin* you can 'quit;' to quit to outer loop, or you can 'return;' to continue
which leaves me with a big question sign? Using "? Coset Table" directly in GAP just gives me also the above section in the manual. Now looking further through the manual I found the function "CosetTableBySubgroup", executing gives me
gap> CosetTableBySubgroup(G,U); [ [ 2, 4, 1, 6, 8, 3, 5, 10, 7, 9 ], [ 3, 1, 6, 2, 7, 4, 9, 5, 10, 8 ], [ 1, 5, 7, 4, 2, 6, 3, 9, 8, 10 ], [ 1, 5, 7, 4, 2, 6, 3, 9, 8, 10 ] ]
So luckily something that works, but what would be preferable would be a list of cosets, something like this GAP Code which unluckily does not work (maybe because it refers to an old version), because it gives:
gap> LeftCosets(G, U); Error, Variable: 'LeftCosets' must have a value not in any function at line 6 of *stdin*
While searching through the web I found this document, stating that you have to define the function "CosetTable" first, but when I try to execute the code there I get:
gap> CosetTable:=function(g,n) > local x,y,tmp; > tmp:=Flat(List(LeftCosets(g,n),x->Elements(x))); Syntax error: warning: unbound global variable tmp:=Flat(List(LeftCosets(g,n),x->Elements(x))); ^
So does not help. Then I found the package "ACE", and tried to use it, but this package, despite being installed, does not load on my system:
gap> LoadPackage("ace"); #I Package ``ACE'': The program `ace' is not compiled fail
How should I compile, I have no compiler on my Windows 8.1 system, and I used the installer, which should have all packages pre-installed on it?
So how can I enumerate the cosets in GAP?????