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Re: Replacement Rule with Sqrt in denominator
*To*: mathgroup at smc.vnet.net
*Subject*: [mg114677] Re: Replacement Rule with Sqrt in denominator
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Sun, 12 Dec 2010 05:47:09 -0500 (EST)
On 11 Dec 2010, at 07:52, Jack L Goldberg 1 wrote:
>
> a) Input as typed: 2<==x<==4. Look at its fullform. On my Mac
> running ver. 7 of Mathematica, I get returned,
> LessEqual[2,x,4].
>
> b) Now type in Reduce[2<==x<==4]. You will get
> Inequality[2,LessEqual,x,LessEqual,4].
>
> These are are different expressions! How can one program replacement
> rules when one can not be sure of the FullForm? These structures are
> entirely different. Which fullform can one assume is the one Mathematica sees
> in some complicated module wherein one step is a replacement rule?
>
> Jack Goldberg
> Mathematics
> University of Michigan
>
O.K. but I don't see anything here that in any way contradicts anything that has been said about the need for
for looking at FullForm before trying pattern matching. Actually, it is als
o an argument against using Copy and Paste. To see that, evaluate Reduce[2<==x<==4]. Now, copy the output and paste it into another cell and wrap FullForm around it, then evaluate. You will get LessEqual[2,x,4].
I don't see this as a problem, do you? You can certainly match both forms with a single pattern:
{2 <== x <== 4, Reduce[2 <== x <== 4]} /.
(a_) <== x <== (b_) | Inequality[a_, LessEqual, x, LessEqual, b_] :> {a, b}
{{2, 4}, {2, 4}}
Andrzej Kozlowski
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