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Re: Replacement Rule with Sqrt in denominator. Also Bug in Series
I'd like to chime in that I appreciate Richard Fateman's analysis of the behavior of replacement rules. (See his paper www.cs.berkeley.edu/~fateman/papers/better-rules.pdf. I've been using mathematica since version 1 (or even before, when Steve Wolfram was still involved with SMP), and I've often been annoyed at the difficulties he's discussed. My interest in Mathematica is as a peripheral tool; I don't want to have to know too much about its quirks and its inner workings. I'm a mathematician, I don't want to be a mathematica-ologist. Usually if I start looking at FullForm[expression], I feel like I'm wading in more deeply than I want to or should. It quickly becomes very frustrating, since as Richard noted, FullForm doesn't tell the whole story, the whole story is not public and not documented, and the undocumented internal behavior can and does change from version to version --- so I'd prefer to have to think about it as little as possible. Because of problems like those cited, I've often ended up just giving up on mathematica finding formal solutions even when I know in principle it can find them, and instead I attack them from other directions or by alternate tools. Mathematica has done many things well for me, but I've been tripped up miserably on others. Bill Thurston On Dec 9, 2010, at 6:01 AM, Richard Fateman wrote: > > As for Andrzej's assertion that no one agrees with my perspective, > I suppose it is sufficient to point out that Andrzej would have > no way of knowing that. And to some extent it is pointless to > support my perspective (on this newsgroup) as long as I am willing to > do so myself.