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Re: Solve never calls Equal?

  • To: mathgroup at
  • Subject: [mg120318] Re: Solve never calls Equal?
  • From: Richard Fateman <fateman at>
  • Date: Tue, 19 Jul 2011 06:54:06 -0400 (EDT)
  • References: <> <ivovvt$qpa$> <> <> <ivuc93$gth$> <> <j0115b$qao$>

On 7/18/2011 3:16 AM, Andrzej Kozlowski wrote:
>> I think it is hard to claim that these test could be done only with
> Significance arithmetic.  However, DanL has indicated that tracing Equal
> may not be effective if the system programs utilize some internal call
> to a system entry into PossibleZeroQ.  The point remains that
>> redefining Equal as done here does not seem to adversely affect
> NSolve, Reduce, NIntegrate. Nor does it seem to take much time.
>> RJF
> As usual, your reply avoids the only important thing, which is the
> example that I posted.
> Reduce[Exp[x] - x == 1/2&&   Abs[x]<   1, x]
> Try it again yourself, with Equal replaced by SameQ and without. What do
> you see?

As posted, my note on 7/18 just preceding yours, shows what happens when 
I tried it again, with the definition of Equal that I proposed, that 
compares numbers with full accuracy.  (Redefining Equal as SameQ is NOT 
something I recommended because SameQ is hardly better. Furthermore, to 
use SameQ for non-numbers is a very bad idea indeed since it has quite a 
different semantics from Equal in that case. Equal[x,y] returns 
unchanged if x,y are unknown. SameQ[x,y] returns False.)
> It's amazing that you can deny what you can and everyone can see and
> still claim that "Reduce has not been effected". It is also clear that
> you do not understand why I chose this particular example and why your
> improvement broke it.

Since my improvement did not break it, what can I say in response?
> Hint: this equation is being solved *exactly* and yet your "improvement"
> breaks it.
I should mention that the note I sent to mathgroup was accidentally not 
sent to Andrzej at the same time, as I usually do. Perhaps he would not 
have written with such certainty then.

> The main problem is that you don't understand the mathematics involved
> here.   The fact that you than produces a lot of examples that have
> obviously no relevance to this issue confirms this.

What can I say, "I'm rubber you're glue"?

> This sort of thing is not new Richard. I have already offered, to
> re-post some of your past posts which show you lack of understanding of
> the basics of Mathematica. But I can also post some examples, like this
> one, that show that you do not understand the mathematics behind it, and
> yet arrogantly presume to be instructing those who do (at least better
> than you).

More often I think that I understand what is going on in Mathematica, 
but believe it to be wrong.  You choose to interpret it as not 
understanding Mathematica.


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