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

*To*: mathgroup at smc.vnet.net*Subject*: [mg116652] Re: Rational[a,b] vs Rational[1,2]*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 22 Feb 2011 06:25:56 -0500 (EST)

Yes, but are there any likely circumstances under which someone might type "Rational[a,b]" (rather than a/b - which is quite different) unless that person knew quite well what he was doing? Andrzej Kozlowski On 22 Feb 2011, at 10:45, Richard Fateman wrote: > 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. >>> >>> >> >> > >

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

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