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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116641] Re: Rational[a,b] vs Rational[1,2]
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Tue, 22 Feb 2011 04:45:03 -0500 (EST)

The head of 1/2 is Rational, but the head of a/b is Times.

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.
>
>


-- 
DrMajorBob at yahoo.com


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