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Re: Re: Re: Log[4]==2*Log[2]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50624] Re: [mg50599] Re: [mg50557] Re: [mg50520] Log[4]==2*Log[2]
*From*: DrBob <drbob at bigfoot.com>
*Date*: Wed, 15 Sep 2004 01:49:17 -0400 (EDT)
*References*: <200409120842.EAA01340@smc.vnet.net> <opsd8augkviz9bcq@monster.cox-internet.com> <9144B6AA-0511-11D9-9D11-000A95B4967A@akikoz.net> <opsd8qdyosiz9bcq@monster.cox-internet.com> <3ADADD30-0534-11D9-AE14-000A95B4967A@akikoz.net> <opsd857nociz9bcq@monster.cox-internet.com> <FC5C5A8F-0550-11D9-A0AA-000A95B4967A@akikoz.net>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
You went to some trouble to use Unevaluated; I didn't go out of my way to commit "*premature* evaluation". (That sounds so evil, doesn't it?)
Simplify[Log[4]==2Log[2]] asks Mathematica to simplify an expression. If Equal left the expression unevaluated (because it can't decide the question) then Simplify could come along and settle it.
And it DOES do exactly that, just as I would expect it to.
But the error message rings a great big meaningless bell, giving me a completely unnecessary headache.
(Tell me again why Simplify shouldn't ring bells when it can't simplify something?)
Anyway, if Equal really HAS to throw an error, why shouldn't it be a meaningful one, like "These expressions are equal to $MaxExtraPrecision, but we're unwilling to declare them equal, because we'd never declare them equal anyway, we only declare things unequal."
I think I'll add Off[N::meprec] to my Init file.
Bobby
On Mon, 13 Sep 2004 15:48:57 +0900, Andrzej Kozlowski <andrzej at akikoz.net> wrote:
> *This message was transferred with a trial version of CommuniGate(tm) Pro*
> But this is all due to your using *premature* evaluation (as I
> explained in m y original reply):
>
> In[1]:=
> N[Unevaluated[Log[4]==2Log[2]]]
>
> Out[1]=
> True
>
> In[2]:=
> Simplify[Unevaluated[Log[4]==2Log[2]]]
>
> Out[2]=
> True
>
> So this time it is really the case of "user error" and, as far as I am
> concerned at least, this behaviour is clear, logical and I see no good
> reason to change it.
>
> Andrzej
>
>
>
> On 13 Sep 2004, at 15:41, DrBob wrote:
>
>> *This message was transferred with a trial version of CommuniGate(tm)
>> Pro*
>>>> When I wrote an "error" I meant a (likely) programmer's error, not
>>>> Mathematica's error.
>>
>> So did I.
>>
>>>> in real life situations, when, in a program and equality appears
>>>> that Mathematica is unable to verify
>>>> it is very likely to be something unintended; most probably the
>>>> programmer forgot to use N.
>>
>> If I use N, don't I still get an error message, even though
>> Mathematica DOES verify the equality?
>>
>> Log[4]\[Equal]2Log[2]//N
>>
>> \!\(\*
>> 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
>>
>>>> On the other hand whenever you use Simplify you are (or at least
>>>> should be) aware that Mathematica may fail to
>>>> return what you are expecting (or hoping for).
>>
>> If I use Simplify, don't I still get an error message, even though I
>> _do_ get what I'm expecting, otherwise?
>>
>> Simplify[Log[4]==2Log[2]]
>>
>> \!\(\*
>> 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
>>
>> Tell me again why that isn't dumb?
>>
>> Bobby
>>
>> On Mon, 13 Sep 2004 12:23:06 +0900, Andrzej Kozlowski
>> <andrzej at akikoz.net> wrote:
>>
>>> *This message was transferred with a trial version of CommuniGate(tm)
>>> Pro*
>>> I disagree, though of course this is a matter of design, which is to
>>> some extent is a matter of taste and judgement, not mathematics.
>>> When I wrote an "error" I meant a (likely) programmer's error, not
>>> Mathematica's error. In my judgement, in real life situations, when,
>>> in a program and equality appears that Mathematica is unable to verify
>>> it is very likely to be something unintended; most probably the
>>> programmer forgot to use N. On the other hand whenever you use
>>> Simplify
>>> you are (or at least should be) aware that Mathematica may fail to
>>> return what you are expecting (or hoping for). That is in the nature
>>> of
>>> Simplify and realizing this fact is an essential aspect of
>>> understanding Mathematica. So, in my opinion, there is a good reason
>>> for treating these two cases differently.
>>>
>>> Andrzej
>>>
>>>
>>>
>>> On 13 Sep 2004, at 09:59, DrBob wrote:
>>>
>>>> *This message was transferred with a trial version of CommuniGate(tm)
>>>> Pro*
>>>>>> 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
>>>>
>>>
>>>
>>>
>>
>>
>>
>> --
>> DrBob at bigfoot.com
>> www.eclecticdreams.net
>>
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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