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