Re: Re: Replacement equivalence?

• To: mathgroup at smc.vnet.net
• Subject: [mg63252] Re: [mg63239] Re: Replacement equivalence?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 20 Dec 2005 23:35:36 -0500 (EST)
• References: <do6892\$b1t\$1@smc.vnet.net> <200512200919.EAA28528@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 20 Dec 2005, at 18:19, David Bailey wrote:

>> This is a spinoff of an ongoing thread in s.m.s.  Could the nonlinear
>> replacement
>>
>>                            b^2 -> 1
>>
>> be changed to the linear one
>>
>>                            b-> 1||-1
>>
>> Similarly
>>              x^4 -> 16     to    x ->  2||-2||2*I||-2*I
>>
>> Any possible side effects?
>>
> Hello,
>
> Quite a few really, for example:
>
> b^2 /. b -> 1 || -1
>
>       (1 || -1)^2
>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>

The only interpretation of the original post that makes any sense to
me is that what the poster was trying to get at is the fact that the
pattern _?(#^2 == 1 &) is equivalent to the pattern 1 | -1. Indeed:

Cases[{1, -1, 2, -1, 3}, _?(#^2 == 1 &)]

{1, -1, -1}

Cases[{1, -1, 2, -1, 3}, 1 | -1]

{1, -1, -1}

Andrzej Kozlowski

```

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