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Re: Solve never calls Equal?

On 7/18/2011 6:55 AM, Andrzej Kozlowski wrote:
> On 18 Jul 2011, at 12:14, Richard Fateman wrote:
>> Clearly one cannot, in general, find an
>> exact solution to a transcendental equation using rational arithmetic,
>> so I was a little surprised by Reduce working just fine, here.
> Of course one does not use "arithmetic".
Of course Reduce uses arithmetic in
Reduce[Exp[x] - x == 1/2 && Abs[x] < 1, x] // N

How else to explain that in it, proven by tracing Equal, it compares 
numbers like 0 and 0.907560823521493954198929899042.
Of course I did not convert all its internal arithmetic to rational 
arithmetic, just comparisons.
So in fact Reduce was doing its regular same-old thing, most of the 
time; if I had thought of that
I wouldn't have been surprised.  Testing for termination conditions 
using rationals didn't seem to hurt.
Again, that is not totally surprising since it seems a bit unlikely that 
Reduce relies, for
termination, on loss of precision.  But who knows.

> You still don't understand what is going on here, but I am now at an airport during a break in a long flight so won't be able to educated you how it is really done (and why your fix "works") just yet. But if you ask nicely, maybe in the future ;-)
Sure you write an explanation of how you think Reduce works, you can 
post it on a web page and provide a link here.
Otherwise we would just be left with the documentation, e.g.


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