Cartesian product of n sets of lists
- To: mathgroup at smc.vnet.net
- Subject: [mg5860] Cartesian product of n sets of lists
- From: Jean-Christophe Deschamps <jchd at worldnet.fr>
- Date: Sun, 2 Feb 1997 01:30:35 -0500
- Sender: owner-wri-mathgroup at wolfram.com
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.
--
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