Re: Cartesian product of n sets of lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg5940] Re: [mg5860] Cartesian product of n sets of lists*From*: seanross at worldnet.att.net*Date*: Tue, 4 Feb 1997 00:04:50 -0500*Sender*: owner-wri-mathgroup at wolfram.com

Jean-Christophe Deschamps wrote: > > PLEASE: be kind to mail answers to <jchd at worldnet.fr> as well. > I do _not_ receive this list at all here (I wonder why, since I got the > welcome automated message) and the feed for the Mma newsgroup is utterly > unreliable at this end, sigh! Sorry for that unconvenience. > > Using Mma v2.x, I never found the proper way to get the cartesian > product of several sets whose elements are themselves Lists. > > In other terms, I would like to write something like this (using List as > operator): > > p =3D CartProd[List, { {a, b, c}, {1, 2, 3} }, > { {d, e, f}, {4, 5, 6} }] > > and obtain four matrices: > > a b c a b c d e f d e f > 1 2 3 4 5 6 1 2 3 4 5 6 > > Outer is of little use since it acts beyond level 1 of its arguments, e.g= > .: > > Outer[List, { {a, b}, {1, 2} }, > { {c, d}, {3, 4} }] > > {{{{{a, c}, {a, d}}, {{a, 3}, {a, 4}}}, {{{b, c}, {b, d}}, {{b, 3}, {b, > 4}}}},=20 > {{{{1, c}, {1, d}}, {{1, 3}, {1, 4}}}, {{{2, c}, {2, d}}, {{2, 3}, {2, > 4}}}}} > > Of course, it's possible to define a bunch of functions (one taking 2 > sets, one taking 3 sets, ...) like: > > CartProd[f_, s1_List, S2_List] :=3D Block[{ii,jj}, > Flatten[ Table[ f[s1[[ii]], s2[[jj]] ], > {ii,Length[s1]}, {jj,Length[s2]} ], 1]] > > but I find it a little ugly. > > Thank you for your hints. > -- > jchd at worldnet.fr | Jean-Chistophe Deschamps > | 14, rue Hermel > T=E9l.: (33) 01 42 55 01 93 | 75018 Paris Have you looked at the MatrixManipulation package? That may contain some functions that might fit your need. I would also suggest experimenting around with various Map and MapThread combinations using List or Join as the mapping function.