Re: Q: Union and SameTest Option

• To: mathgroup at smc.vnet.net
• Subject: [mg16048] Re: [mg16016] Q: Union and SameTest Option
• From: BobHanlon at aol.com
• Date: Sun, 21 Feb 1999 00:15:21 -0500
• Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2/20/99 6:43:15 AM, btml01 at uni-bayreuth.de writes:

>Can anybody explain to me what's going on here ?
>
>In[270]:=
>Union[ {{a,b,1},{a,c,1},{x,y,2},{a,b,2}},
>       SameTest->(#1[[2]]===#2[[2]]&) ]
>Out[270]=
>{{a,b,1},{a,c,1},{x,y,2}}
>
>is ok since the first and the last list element have the same second
>component. But what is wrong here now ?
>
>In[272]:=
>Union[ {{a,b,1},{a,c,1},{x,y,2},{a,b,2}},
>       SameTest->(#1[[3]]===#2[[3]]&) ]
>Out[272]=
>{{a,b,1},{a,b,2},{a,c,1},{x,y,2}}
>

Clemens,

test = {{a,b,1},{a,c,1},{x,y,2},{a,b,2}};

Union[ test, SameTest->(#1[[2]]===#2[[2]]&) ]

{{a, b, 1}, {a, c, 1}, {x, y, 2}}

Union[ test, SameTest->(#1[[3]]===#2[[3]]&) ]

{{a, b, 1}, {a, b, 2}, {a, c, 1}, {x, y, 2}}

The first case worked not because the second elements were equal,
but because the first elements were also equal.  Note that the
first case does not work if {a, b, 2} is changed to {e, b, 2}.

Union[ {{a,b,1},{a,c,1},{x,y,2},{e,b,2}},
SameTest->(#1[[2]]===#2[[2]]&) ]

{{a, b, 1}, {a, c, 1}, {e, b, 2}, {x, y, 2}}

Based on this behavior, I would guess that Mathematica first sorts
the elements, then compares only adjacent elements for "sameness".
Consequently, to implement the "Union" that you want, you need to
modify the approach.

myUnion[x_List, n_Integer?Positive] := Module[
{temp = RotateLeft[#, n-1]& /@ x},
temp = Union[temp, SameTest -> (#1[[1]] === #2[[1]]&)];
RotateRight[#, n-1]& /@ temp];

Table[myUnion[test, k], {k, 3}]//ColumnForm

{{a, b, 1}, {x, y, 2}}
{{a, b, 1}, {a, c, 1}, {x, y, 2}}
{{a, b, 1}, {a, b, 2}}

Bob Hanlon

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