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Re: Re: another Bug in Reduce ?

• To: mathgroup at smc.vnet.net
• Subject: [mg60566] Re: [mg60533] Re: another Bug in Reduce ?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 20 Sep 2005 05:19:52 -0400 (EDT)
• References: <dgit7h$2ag$1@smc.vnet.net> <200509190845.EAA23572@smc.vnet.net> <ED1C56B6-A552-4CA6-A365-562B710B4271@mimuw.edu.pl> <432F2F3F.1030106@wolfram.com>
• Sender: owner-wri-mathgroup at wolfram.com

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

• References:
  • Re: another Bug in Reduce ?
    • From: Maxim <ab_def@prontomail.com>