Dear Alexander— Yes, I’m well aware of the breadth of your contributions to GAP4. Thank you for that, and for your detailed response.
First, I’m a little confused about some of the statements you made. I am running GAP, Version 4.7.5 of 24-May-2014. There are really two answers to your question. > The first is the actual question — how to change the stored values of > dictionaries. Here my choice (as the person who implemented much of the > code for dictionaries) would be to not to attempt to change the values at > all, but use as values the entries in a (changeable) value list. While this > requires one indirection it is safe and requires no modification of data > structures that might not have been set up for this, or might change in > future releases (in fact is almost guaranteed to do so as there are still > some issues in the code). > I tried doing this, but once I stored the list in the dictionary I found I could no longer change the list. gap> l := [3]; [ 3 ] gap> d := NewDictionary(false, true, [1,2,3]); <object> gap> IsMutable(l); true gap> AddDictionary(d, 2, l); gap> IsMutable(l); false gap> Am I confused? The second answer goes closer to what you are actually doing, namely > identifying double cosets. > > At the moment GAP has no specific hash key code for double cosets, so the > best dictionaries can do is to compare using the `<‘ order. For double > cosets, this comparison is done by determining the (minimal) > representatives for all the contained right cosets, and comparing the > smallest of the minimal coset representatives. While this ordering is > equivalent to the ordering as sets of elements, if means that in fact you > store representatives for all right cosets. Given that this is the case, I > would try the following approach (assuming the subgroups are A and B): > Here again I think I must be confused: gap> g:=SymmetricGroup(4);; gap> u:=Subgroup(g,[(1,2,3),(1,2)]);; gap> v:=Subgroup(g,[(3,4)]);; gap> cos:=DoubleCosets(g, u, v); [ DoubleCoset(Group( [ (1,2,3), (1,2) ] ),(),Group( [ (3,4) ] )), DoubleCoset(Group( [ (1,2,3), (1,2) ] ),(1,4),Group( [ (3,4) ] )), DoubleCoset(Group( [ (1,2,3), (1,2) ] ),(1,4,2),Group( [ (3,4) ] )) ] gap> cos[1] < cos[2]; Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `<' on 2 arguments called from <function "HANDLE_METHOD_NOT_FOUND">( <arguments> ) called from read-eval loop at line 40 of *stdin* you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> Thank you for your help, and suggestions below, which I will think about once we get the above sorted out. Regarding publications, etc, we will be submitting a paper in early April to the FOCS CS conference, and will put it on the arXiv. I’d love to help out in any way I can. Erick > Calculate t:=RightTransversal(G,A) > This is an object that behaves like a list, but often needs less storage. > > Create a second list DCNumber that for each right coset of A stores the > number (in some arbitrary indexing) of the double coset AxB that contains A. > > If you find an element r, let > > p:=PositionCanonical(t,r); # number of the right coset for the element > if IsBound(DCNumber[p]) then > result:=DCNumber[p]; > else > newnum:=New index number for double coset; > result:=newnum; > DCNumber[p]:=newnum; > o:=Orbit(B,t[p],function(rep,g) return > CanonicalRightCosetElement(A,rep*g);end); > for i in o do > DCNumber[PositionCanonical(t,i)]:=newnum; # mark all right cosets > within the same double coset. > od; > fi; > > and then process result — the number of the double coset — as if it came > as dictionary value. This is less slick code than dictinaries, but I’d > suspect this will work notably faster. > > Best, > > Alexander Hulpke > > Frederick "Erick" Matsen, Assistant Member > > Fred Hutchinson Cancer Research Center > > > Is there a chance you have a citable article or presentation that connects > permutation group calculations with (the ultimate ``usefulness’’ argument > for higher administration) attempts on dealing with cancer? This could come > very helpful when questions of ``broader impace’’ etc. come up. Thanks! > > > -- Alexander Hulpke. Department of Mathematics, Colorado State University, > Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA > email: hul...@math.colostate.edu, Phone: ++1-970-4914288 > http://www.math.colostate.edu/~hulpke > > -- Frederick "Erick" Matsen, Assistant Member Fred Hutchinson Cancer Research Center http://matsen.fredhutch.org/ _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
