Re: Re: Replacement equivalence?

• To: mathgroup at smc.vnet.net
• Subject: [mg63253] Re: [mg63239] Re: Replacement equivalence?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 20 Dec 2005 23:35:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```On 20 Dec 2005, at 23:43, Andrzej Kozlowski wrote:

>
> 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
>
>
>

In fact, however, things are not as simple:

b /: b^2 = 1;

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

{b, 1, -1, -1}

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

{1, -1, -1}

Andrzej Kozlowski

```

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