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Re: Rational[a,b] vs Rational[1,2]

• To: mathgroup at smc.vnet.net
• Subject: [mg116644] Re: Rational[a,b] vs Rational[1,2]
• From: Richard Fateman <fateman at eecs.berkeley.edu>
• Date: Tue, 22 Feb 2011 04:45:36 -0500 (EST)

On 2/21/2011 6:04 PM, DrMajorBob wrote:
> The head of 1/2 is Rational, but the head of a/b is Times.
I know that.
What is the head of Rational[a,b]?    where  a, b  are symbols, not 
numbers...

FullForm[Rational[a,b]]
says
Rational[a,b]
  also
Head  says it is Rational.


  BUT IT IS NOT A Rational.
For example, Numerator[Rational[a,b]]  is not a, but   Rational[a,b]


I am aware of the info about atoms and Rational, and Complex too.

However, the situation above looks to me like it is hazardous.  Do you
see what I am getting at?
Regards
RJF



>
> a/b//FullForm
>
> Times[a,Power[b,-1]]
>
> Replace looks at the arguments of Times, but it doesn't look within 
> "atoms". Rationals are "atoms", so there you go.
>
> Help explains this under "Possible Issues", and under "More 
> Information", it says:
>
> "You have to use Numerator and Denominator to extract parts of 
> Rational numbers."
>
> Apparently that's the ONLY way to extract parts of a Rational, and 
> that's what we're supposed to glean from "have to".
>
> First[1/2] returns 1/2 and an error message, for instance.
>
> Bobby
>
> On Mon, 21 Feb 2011 18:30:54 -0600, Richard Fateman 
> <fateman at eecs.berkeley.edu> wrote:
>
>> I find it potentially hazardous that Head[]
>> does not distinguish the cases of Head[1/2]
>>
>> and Head[Rational[a,b]]
>>
>> Thus these both get transformed...
>>
>> 1/2  /. Rational[r_,s_]-> foo[r,s]
>>
>> Rational[a,b] /. Rational[r_,s_] -> foo[r,s]
>>
>>
>> but compare ...
>>
>> 1/2  /. 2->4
>>
>> Rational[a,2] /. 2->4
>>
>> I'm not saying I'm surprised by this, of course.
>>
>> Perhaps Rational[a,b] should be converted to a/b unless both
>> a and b are numbers.
>>
>> Oh, for some fun, try Rational[1/2,4].
>>
>>
>> RJF
>>
>> PS, I used version 7.
>>
>>
>
>