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MathGroup Archive 2004

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50619] Re: [mg50599] Re: [mg50557] Re: [mg50520] Log[4]==2*Log[2]
  • From: DrBob <drbob at bigfoot.com>
  • Date: Mon, 13 Sep 2004 02:19:37 -0400 (EDT)
  • References: <200409120842.EAA01340@smc.vnet.net> <opsd8augkviz9bcq@monster.cox-internet.com> <9144B6AA-0511-11D9-9D11-000A95B4967A@akikoz.net>
  • Reply-to: drbob at bigfoot.com
  • Sender: owner-wri-mathgroup at wolfram.com

>> it seems to me that it is a good idea
>> for errors to produce error  messages

It's not an error. If we ask Simplify to recognize an equality, we (usually) don't get an error message if it fails; we just get back the original expression. This is NO different.

In fact, for the expression Log[4]==2Log[2], Simplify returns True as it should--but too late to avoid the "error" message from Equal. That's just dumb.

Log[4]==2Log[2]//Simplify

\!\(\*
   RowBox[{\(N::"meprec"\), \(\(:\)\(\ \)\), "\<\"Internal precision
       limit $MaxExtraPrecision = \\!\\(50.`\\) reached while evaluating \
\\!\\(\\(\\(\\(\\(-2\\)\\)\\\\ \\(\\(Log[2]\\)\\)\\)\\) + \
\\(\\(Log[4]\\)\\)\\). \\!\\(\\*ButtonBox[\\\"More?\\\", \
ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
ButtonData:>\\\"General::meprec\\\"]\\)\"\>"}]\)

True

Bobby

On Mon, 13 Sep 2004 08:14:59 +0900, Andrzej Kozlowski <andrzej at akikoz.net> wrote:

> *This message was transferred with a trial version of CommuniGate(tm) Pro*
>
> On 13 Sep 2004, at 04:24, DrBob wrote:
>
>>
>> If Equal can't decide equality for exact expressions, then it should
>> return unevaluated. It shouldn't interrupt everything with a useless
>> error message.
>>
>> Bobby
>
> I am not sure about that. You are right as far as the "aesthetics" of
> the interface of CAS  is concerned. But when this sort of thing happens
> in a program it is likely to be the result of an error (probably not
> intended by the programmer) and it seems to me that it is a good idea
> for errors to produce error  messages since it makes it debugging
> easier (such messages can be caught with Check).
>
> Andrzej
>
>>
>>
>> On Sun, 12 Sep 2004 04:42:10 -0400 (EDT), Andrzej Kozlowski
>> <andrzej at akikoz.net> wrote:
>>
>>> 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
>>>>
>>>
>>>
>>>
>>
>>
>>
>> --
>> DrBob at bigfoot.com
>> www.eclecticdreams.net
>>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net


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