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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.
Unprotect[Equal];
Equal[a_?NumericQ,
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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