Very briefly (sorry, don't have time for a larger explanation today) - in this case, see IteratorOfCartesianProduct. For example, after
lists := []; lists[1] := [1,2,3]; lists[2] := [4,5]; try this: gap> for x in IteratorOfCartesianProduct(lists) do Print(x,"\n");od; [ 1, 4 ] [ 1, 5 ] [ 2, 4 ] [ 2, 5 ] [ 3, 4 ] [ 3, 5 ] This iterates over the cartesian product without generating the list of all tuples from it, and should work fast enough. Best wishes Alexander On 16 Jan 2014, at 22:13, "Wolstenholme, Robert" <robert.wolstenholm...@imperial.ac.uk> wrote: > Thanks for the reply. I don't think I was clear enough with my initial > question though so have given the example below: > > ################################################################################### > Consider > > lists := [] > lists[1] := [1,2,3] > lists[2] := [4,5] > > I would now like to iterate over the cartesian product of `lists[1]` and > `lists[2]` i.e. `[[1,4],[1,5],[2,4],[2,5],[3,4],[3,5]]`. > > For an example this small, you could simply store the cartesian product > itself in a list and iterate over that. This obviously becomes very > inefficient if we have more lists with a larger number of values. > > > A better way is, if we have `n` lists and `size_rc[i] := Size(list[i])`, we > can avoid storing/calculating the Cartesian product with > > base := List([1..n], x -> 1); #We store the iteration step state in base > while base <> size_rc do > > #Perform whatever list[i][base[i]] calculations here > > #Execute the incrementor > base[1] := base[1] + 1; > for j in [2..n] do > if base[j-1] = size_rc[j-1] + 1 then > base[j] := base[j] + 1; > base[j-1] := 1; > fi; > od; > od; > > then at each loop of the while `base` contains the values we need. > > However this is still far slower than the Python implementation I mentioned > before. I was wondering if there was a way in GAP to speed up this iteration > (maybe by pointing to the memory locations of the lists)? > > Thanks, > Rob > > ________________________________________ > From: Alexander Konovalov [alexander.konova...@gmail.com] > Sent: 16 January 2014 22:01 > To: Wolstenholme, Robert > Cc: forum@mail.gap-system.org > Subject: Re: [GAP Forum] Iteration Over Lists of Lists > > On 16 Jan 2014, at 20:03, "Wolstenholme, Robert" > <robert.wolstenholm...@imperial.ac.uk> wrote: > >> Is there a way in GAP to 'quickly' iterate of lists of lists i.e. like the >> Python itertools.product() function? >> > > Yes, see `21.20 Operations for Lists' from the GAP Reference Manual. You may > enter `?Operations for Lists' in GAP or see it online at > > http://www.gap-system.org/Manuals/doc/ref/chap21.html#X7DF510F7848CBBFD > > A random example just to expose the syntax and some functions: > > gap> l:=List([1..10],i -> [1..i]); > [ [ 1 ], [ 1, 2 ], [ 1 .. 3 ], [ 1 .. 4 ], [ 1 .. 5 ], [ 1 .. 6 ], > [ 1 .. 7 ], [ 1 .. 8 ], [ 1 .. 9 ], [ 1 .. 10 ] ] > gap> Sum( List( l, x -> Product( List( x, Fibonacci ) ) ) ); > 124819000 > > > HTH, > Alexander > > > > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
