Re: Solve never calls Equal?

*To*: mathgroup at smc.vnet.net*Subject*: [mg120318] Re: Solve never calls Equal?*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Tue, 19 Jul 2011 06:54:06 -0400 (EDT)*References*: <201107150118.VAA23606@smc.vnet.net> <ivovvt$qpa$1@smc.vnet.net> <201107160941.FAA08237@smc.vnet.net> <7BBB2BCC-0234-4BDA-A129-3270EBA623CE@mimuw.edu.pl> <ivuc93$gth$1@smc.vnet.net> <4E2377E3.2010606@cs.berkeley.edu> <j0115b$qao$1@smc.vnet.net>

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. RJF >

**References**:**Re: Numerical accuracy/precision - this is a bug or a feature?***From:*"Christoph Lhotka" <christoph.lhotka@univie.ac.at>

**Solve never calls Equal?***From:*Richard Fateman <fateman@cs.berkeley.edu>