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Re: Re: another Bug in Reduce ?
On 20 Sep 2005, at 06:35, Adam Strzebonski wrote: >> As for the rest of the problems they seem to me very difficult to >> deal with. Essentially the algorithms used by Reduce, >> CylindricalAlgebraicDecomposition and Quantifier ELimination are >> purely algebraic; they work for polynomial expressions. It seems >> to me that all other types of expressions have to be deal with >> by heuristic methods and probably can never be made fully >> reliable (which is not to say they can't be made better). >> > > Cylindrical algebraic decomposition can handle real algebraic > functions > (Root objects and radical expressions) in full generality. It should > always give the correct answer (provided there are no bugs...). > > Best Regards, > > Adam Strzebonski > Wolfram Research > By the "rest of the problems" I meant the problems with Reduce discussed in Maxim's post. They involve things like Im[Sqrt[x]], Infinities etc, so they do not use CAD, and it seems to me that some sort of "heuristics" (by whch I mean "special case" based techniques rather than general algorithms like CAD) have to be used in these situations. Andrzej Kozlowski