Re: Sort with -Infinity fails

*To*: mathgroup at smc.vnet.net*Subject*: [mg73856] Re: Sort with -Infinity fails*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Fri, 2 Mar 2007 06:28:51 -0500 (EST)*References*: <es6d0l$rmr$1@smc.vnet.net>

Read carefully the documentation for Sort (*execute the following command*) In[85]:= FrontEndExecute[{HelpBrowserLookup["RefGuide", "Sort"]}] There we read among other things... Sort[list, p] applies the function p to pairs of elements in list to determine whether they are in order. The default function p is OrderedQ[{#1, #2}]&. So for example In[86]:= Sort[{-1, 3, -4, 5}] Out[86]= {-4, -1, 3, 5} is identical to In[90]:= Sort[{-1, 3, -4, 5}, OrderedQ[{#1, #2}] & ] Out[90]= {-4, -1, 3, 5} Using Trace you can see the process of sorting In[91]:= Trace[Sort[{-1, 3, -4, 5}, OrderedQ[{#1, #2}] & ]] (*omitting Output*) Now In[92]:= -Infinity < -8 < 8 < Infinity Out[92]= True But In[93]:= OrderedQ[{-Infinity, -8}] Out[93]= False So in view of all these, you can understand now the following output In[94]:= Sort[{-Infinity, -5, -8, 9, Infinity}] Out[94]= {-8, -5, 9, -Infinity, Infinity} If you want you can use again Trace In[96]:= Trace[Sort[{-Infinity,-5,-8,9,Infinity},OrderedQ[{#1,#2}]&]] (*omitting Output*) Why now OrderedQ works in this way is beyond my knowledge. Reading in the Section A.3.9 of Mathematica Book (*execute the following command to go there!) In[97]:= FrontEndExecute[{HelpBrowserLookup["MainBook", "A.3.9"]}] about the canonical ordering I was not able to figure out the reason. Anyway...I think you want "the way to be done" and not "why must be done in this way"... So... Your desirable result can be achieved as follows In[98]:= Sort[{-Infinity, -5, -8, 9, Infinity}, #1 < #2 & ] Out[98]= {-Infinity, -8, -5, 9, Infinity} or In[100]:= Sort[{-Infinity, -5, -8, 9, Infinity}, #2 > #1 & ] Out[100]= {-Infinity, -8, -5, 9, Infinity} =CE=9F/=CE=97 Tom Aldenberg =CE=AD=CE=B3=CF=81=CE=B1=CF=88=CE=B5: > Dear MathGroup, > > Minus Infinity (-Infinity) is smaller than -8, but Sort does not sort it = as > expected. > Is there a Real minus Infinity? > > > In[75]:= > -Infinity < -8 > Out[75]= > True > > In[76]:= > Sort[{-Infinity, -8, 5}] > Out[76]= > {-8, 5, -=E2=88=9E} > > > Regards, > > Tom Aldenberg > > _________________________________________________________________________= ___ > > DISCLAIMER: http://www.rivm.nl/disclaimer.htm