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Re: Re: Select and Cases Give Different Answers

Gregory Lypny wrote:
> Good stuff, Andrzej.  This certainly calls for a bug report.  Maybe  
> it's best if the tech people at Wolfram are simply directed to this  
> thread.
> 
> 	Gregory

The inconsistent behavior was reported yesterday and fixed in the 
development kernel of Mathematica. Strings, rationals, and reals are all 
"atomic" types in mathematica, hence Unequal should (and in a future 
release will) return True.

Daniel Lichtblau
Wolfram Research


> On Tue, Apr 28, 2009, at 8:38 AM, Andrzej Kozlowski wrote:
> 
>> On 28 Apr 2009, at 17:42, Gregory Lypny wrote:
>>
>>> Hello everyone,
>>>
>>> Suppose I have the following list that is a mixture of the string  
>>> "NA"
>>> and five numeric quantities.
>>>
>>> 	theList = {"NA", "NA", -0.01315, 0.0120957, -1/41, 0.00625, "NA",
>>> "NA", 5/8,  "NA"}
>>>
>>> I want to weed out the NAs, and all of the following
>>>
>>> 	Cases[theList, _?NumericQ]
>>>
>>> 	DeleteCases[theList, _?StringQ]
>>>
>>> 	Select[theList, # =E2=88=88 Reals &]
>>>
>>> 	Select[theList, # =!= "NA" &]
>>>
>>> work fine because each returns {-0.01315, 0.0120957, -(1/41),  
>>> 0.00625,
>>> 5/8}.
>>>
>>> But I don't understand why Unequal, when used as the criterion for
>>> Select as in
>>>
>>> 	Select[theList, # != "NA" &],
>>>
>>> fails to return the rationals, and I get only three elements
>>> {-0.01315, 0.0120957, 0.00625}.  I'd appreciate any clarification on
>>> the difference between UnsameQ and Unequal because my inclination in
>>> most circumstances is to use an equal sign or an unequal sign to make
>>> simple comparisons yet it doesn't give me the answer I expect, and  
>>> I'd
>>> hate to make a costly mistake somewhere down the road!
>>>
>>> Regards,
>>>
>>> 	Gregory
>>>
>>
>> I think that there is indeed something strange here, but it it the  
>> opposite of what you seem to find strange. To me the strange thing  
>> here is the difference between strings and symbols and between exact  
>> and approximate numbers . Replace your strings "NA" by symbols NA  
>> and note that now you get:
>>
>> Select[theList2, #1 != NA & ]
>> {}
>>
>> which is what I would have expected also in your example. In the  
>> case of a symbol Unequal and UnsameQ are different, as one would  
>> expect:
>>
>> UnsameQ[x, 2]
>> True
>>
>> Unequal[x, 2]
>> x != 2
>>
>> An undefined symbol x is certainly "not the same as" (i.e. not  
>> identical) the number 2, but it could be equal to it (depending on  
>> the context) so Unequal[x,2] can't be answered. But when we replace  
>> x by the string "x" things become mysterious. First of all we have:
>>
>> UnsameQ["x", 2]
>> True
>>
>> Unequal["x", 2]
>> True
>>
>> so now there is no difference between UnsameQ and Unequal. One might  
>> think that Strings are never equal to numbers (which would be  
>> reasonable, since they can't be assigned values) but then:
>>
>> "x" =!= 2/3
>> True
>>
>> "x" != 2/3
>> "x" != 2/3
>>
>> so when we have a rational on the RHS strings behave the same as  
>> symbols! But not so with reals:
>>
>> "x" =!= N[2/3]
>> True
>> "x" != N[2/3]
>> True
>>
>> By the way, if we replace Rational[2,3] with Complex[2,3] the  
>> behaviour will remain the same. All this is puzzling to me and I  
>> can't see any other explanation but that this is just an unintended  
>> side-effect of something. Obviously it does not make any  
>> mathematical sense to ask the question whether a string is equal to  
>> a rational number of a real, so I would not attach any semantic  
>> significance to these answers.
>>
>> Andrzej Kozlowski
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