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Re: unevaluated, hold, holdform

• To: mathgroup at smc.vnet.net
• Subject: [mg50912] Re: unevaluated, hold, holdform
• From: highegg at seznam.cz (highegg)
• Date: Mon, 27 Sep 2004 00:42:28 -0400 (EDT)
• References: <vas7uiw8wg82@legacy>
• Sender: owner-wri-mathgroup at wolfram.com

On 24 Sep 04 09:46:19 -0400 (EDT), D. Gomez wrote:
>Dear all,
>
>A friend of mine need to get both the numerator and denominator of
any
>expression but he does not want it to be reduced to its lowest 
>form, i.e.: given the expression (4 x^2)/(2 x), he needs to extract
>its Numerator:
>Numerator[(4*x^2)/(2*x)]= 4 x^2,
>however Mathematica always simplify it to its lowest form yielding:
>(2*x)
>as its Numerator, that's not what we are looking for.
>We all know about the Hold, HoldForm, Unevaluated functions but
>don't know how to get the Numerator by using at the same time those
>hold functions.
>Many thanks for your help, indeed.
>D. Gomez

hello Gomez,

might not be what you will need,
but in general, arguments given to a function are evaluated first
(as an expression in brackets)
if you want to prevent an argument from evaluation,
Wrap it with the _Unevaluated_ function:
Numerator[Unevaluated[(4*x^2)/(2*x)]]

but be careful, if you use this as a function:
f[x_]:=Numerator[Unevaluated[x]],

f[(4*x^2)/(2*x)] won't work, the argument is pre-evaluated again!

the best way to sort this out is to assign an argumant to the function
f:
AppendTo[Attributes[f],HoldAll]

now f[(4*x^2)/(2*x)] will give us what we want!
(but note that f[x_]:=Numerator[x] still won't work!)