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Re: Solve never calls Equal?

On 07/18/2011 05:13 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?
> [...]
> Hint: this equation is being solved *exactly* and yet your "improvement"
> breaks it.
> [...]

I think a minor variant of the Equal-->SameQ might be safer. One needs 
to restrict to cases where both arguments have finite precision.

    b_?NumericQ] /; (Precision[a] =!= Infinity &&
     Precision[b] =!= Infinity) := SameQ[a, b]

With this version the Reduce example will work. Not sure what will be 
the effect in gerneral though.

Daniel Lichtblau
Wolfram Research

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