Re: Re: logical inconsistency in Union

*To*: mathgroup at smc.vnet.net*Subject*: [mg13194] Re: [mg13109] Re: [mg13069] logical inconsistency in Union*From*: "Jrgen Tischer" <jtischer at col2.telecom.com.co>*Date*: Mon, 13 Jul 1998 07:42:43 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Hi David, this union1 is so awfully slow, so I tried to speed it up a bit. I supposþd that two elements are considered equal if they give the same result to a criterion crit. My union4 is quite a bit faster even than union3 of Union.html. union4[p_List,crit_]:ÿdule[{result,link,new}, resultÿnk[]; new[_]ÿue; Table[If[new[crit[p[[n]]]],new[crit[p[[n]]]]úlse; resultÿnk[result,p[[n]]]],{n,Length[p]}]; List@@Flatten[result,\[Infinity],link]] I hope you like it. Jürgen -----Original Message----- From: David Withoff <withoff at wolfram.com> To: mathgroup at smc.vnet.net Subject: [mg13194] [mg13109] Re: [mg13069] logical inconsistency in Union >> The Union function gives logically inconsistent results when used with >> certain SameTest rules. The problem is that the argument of Union is >> first sorted into Mathematica's canonical order, which may be >> inconsistent with the supplied SameTest. Here's an innocent example of >> the problem: >> >> In[1]:ÿ* 3 points in the plane *) >> añ,1}; >> bñ.2,1}; >> cñ.1,2}; >> >> In[2]:ÿ* rule which says two points are the same if each coordinate >> differs by at most 0.5 *) >> approxSame[x_,y_]:ÿund[x-y]ÿ0,0} >> >> In[5]:>> Union[{a,b,c},SameTest->approxSame] >> >> Out[5]>> {{1,1},{1.1,2},{1.2,1}} (* incorrect result ! *) > >This has been discussed a few times in mathgroup before, so you may be >able to find some useful information in the mathgroup archives. See >also the Wolfram Research web site: > >http://www.wolfram.com/support/Kernel/Symbols/System/Union.html > >It is likely that Union will be extended in a future version of >Mathematica so that it will work as you describe. Comparing all pairs >of elements is of course a lot slower for large sets than sorting and >comparing only adjacent pairs, which is why Union is designed as it is, >but sometimes there isn't much choice. In the meantime, until that >functionality is built in, it can be programmed into existing versions >of Mathematica without too much difficulty. One of the programs from >the Wolfram Research web site is > >union1[p_List, test_] :ÿodule[{result, link}, > result ÿink[]; > Scan[Module[{rþsult}, > While[If[rÿlink[], result ÿink[result, #]; False, > !test[Last[r], #]], r ÿirst[r]]] &, p]; > List @@ Flatten[result, Infinity, link] > ] > >but there are other ways to achieve the same effect. > >Dave Withoff >Wolfram Research >