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Re: Re: Log[4]==2*Log[2]

• To: mathgroup at smc.vnet.net
• Subject: [mg50599] Re: [mg50557] Re: [mg50520] Log[4]==2*Log[2]
• From: Andrzej Kozlowski <andrzej at akikoz.net>
• Date: Sun, 12 Sep 2004 04:42:10 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Actually, I don't think Mathematica does any real "determining" since 
it does not replace the exact values given in the input by
numerical approximations. The message issued is, I think, purely 
formal. Mathematica could not determine anything because it tries to 
compare the numbers "numerically" without using approximate numerical 
values, which can't be done. (You have to apply N for it to use 
numerical values). That't what I meant by "not surprisingly". I don't 
think I  really understand your point?

ANdrzej


On 11 Sep 2004, at 01:52, DrBob wrote:


>>> Mathematica does not apply any simplification rules but just tries to 
>>> evaluate the expression numerically and, not
>>> surprisingly, it can't determine if the LHS is zero or not
>>> up to the required precision.
>
> On the contrary, I think the error message itself clearly indicates 
> the difference IS zero to "the required precision". If 50 digits extra 
> precision isn't enough to determine that the difference ISN'T zero, 
> why doesn't Equal return True?
>
> Bobby
>
> On Fri, 10 Sep 2004 04:05:56 -0400 (EDT), Andrzej Kozlowski 
> <andrzej at akikoz.net> wrote:
>
>> On 9 Sep 2004, at 18:17, Andreas Stahel wrote:
>>
>>>
>>> To whom it may concern
>>>
>>> the following answer of Mathematica 5.0 puzzeled me
>>>
>>> Log[4]==2*Log[2]
>>> leads to
>>>
>>> N::meprec: Internal precision limit $MaxExtraPrecision = 50.` reached
>>> while \
>>> evaluating -2\Log[2]+Log[4]
>>>
>>> with the inputs given as answer. But the input
>>>
>>> Log[4.0]==2*Log[2]
>>>
>>> leads to a sound "True"
>>>
>>> Simplify[Log[4]-2*Log[2]]
>>> leads to the correct 0, but
>>> Simplify[Log[4]-2*Log[2]==0]
>>> yields no result
>>>
>>> There must be some systematic behind thid surprising behaviour.
>>> Could somebody give me a hint please
>>>
>>> With best regards
>>>
>>> Andreas
>>> --
>>> Andreas Stahel       E-Mail: Andreas.Stahel at [ANTI-SPAM]hti.bfh.ch
>>> Mathematics, HTI     Phone: ++41 +32 32 16 258
>>> Quellgasse 21        Fax:   ++41 +32 321 500
>>> CH-2501 Biel         WWW:   www.hta-bi.bfh.ch/~sha
>>> Switzerland
>>>
>>>
>>
>> When you enter
>>
>> Log[4] - 2*Log[2] == 0
>>
>> Mathematica does not apply any simplification rules but just tries to
>> evaluate the expression numerically and, not surprisingly, it can't
>> determine if the LHS is zero or not up to the required precision.
>>
>> If you use
>>
>> Simplify[Log[4] - 2*Log[2] == 0]
>>
>> Mathematica first tries to evaluate the argument of Simplify and the
>> same thig happens as above, but then it actually applies Simplify to
>> the output and gets the right answer True.
>>
>> The best thing to do is:
>>
>>
>> Simplify[Unevaluated[Log[4]-2*Log[2]==0]]
>>
>>
>> True
>>
>> which avoids evaluation of the argument and instead uses Simplify on
>> the unevaluated input.
>>
>>
>>
>> Andrzej Kozlowski
>> Chiba, Japan
>> http://www.akikoz.net/~andrzej/
>> http://www.mimuw.edu.pl/~akoz/
>>
>>
>>
>
>
>
> -- 
> DrBob at bigfoot.com
> www.eclecticdreams.net
>

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    • From: DrBob <drbob@bigfoot.com>