Re: Relation Problem in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg108449] Re: Relation Problem in Mathematica
- From: Peter Pein <petsie at dordos.net>
- Date: Thu, 18 Mar 2010 04:32:33 -0500 (EST)
- References: <hnqd1k$ql$1@smc.vnet.net>
Or define e.g. SmallCircle:
In[1]:= X={1,2,3,4};
R=Transpose[{X,RotateLeft[X]}];
S=Reverse/@R;
SmallCircle[{} | Sequence[], rel: {{_Integer, _} ...}] := rel;
SmallCircle[rel1: ({{_Integer, _} ...} ...), rel2: {{_Integer, _} ...}] :=
SmallCircle[Sequence @@ Most[{rel1}],
rel2 /. {a_Integer, b_} :> {a, b /. Rule @@@ Last[{rel1}]}
]
In[5]:= S \[SmallCircle] R
Out[5]= {{1, 1}, {2, 2}, {3, 3}, {4, 4}}
(* enter the following as SmallCircle[R, S, R, S, R] and press
<Strg><Shift><n> while the cursor is in the input-line *)
In[6]:= R \[SmallCircle] S \[SmallCircle] R \[SmallCircle] S
\[SmallCircle] R
Out[6]= {{1, 2}, {2, 3}, {3, 4}, {4, 1}}
Peter
On 17.03.2010 12:05, Bob Hanlon wrote:
> R = {{1, 2}, {2, 3}, {3, 4}, {4, 1}};
>
> S = {{2, 1}, {3, 2}, {4, 3}, {1, 4}};
>
> f[{a_, b_}, {b_, c_}] = {a, c};
> f[__] = Sequence[];
>
> Flatten[Outer[f, R, S, 1], 1]
>
> {{1, 1}, {2, 2}, {3, 3}, {4, 4}}
>
>
> Bob Hanlon
>
> ---- Paul Slevin<slevvio at hotmail.com> wrote:
>
> =============
> Hello - I was wondering if somebody could help me with this problem. I have the set X = {1,2,3,4}, and have computed the Cartesian Product X^2.
>
> Let R = {(1,2),(2,3),(3,4),(4,1)}
> S = {(2,1),(3,2),(4,3),(1,4)}
>
> be relations on X.
>
> I want to compute the product S o R...