On Tuesday, December 11, 2012 6:52:53 PM UTC-5, JamesHDavenport wrote:
>
>
>
> On Tuesday, 11 December 2012 13:15:09 UTC, kcrisman wrote:
>>
>> I wouldn't worry about it, since in general there is no way to define 
>> "simpler" expression that is fully useful at all times, and for more 
>> complicated expressions more detail work would be needed anyway.
>>
> Pedantic Note. Jacques Carette's paper: Understanding Expression 
> Simplification.
> Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79.
> http://www.cas.mcmaster.ca/~carette/publications/simplification.pdf.
> defines it in a useful way, just not in a computable way (that I can see 
> in practice).
>

Very interesting paper.  I guess I was referring to the sense that 

(1+x)(1-x)

and

1-x^2

might each be considered "simpler" depending on the context, which is the 
way a lot of people who don't know about decidability would perceive this 
question (or so my experience has been interacting with a lot of people who 
ask about why Sage doesn't "simplify" this or that).  I suppose the answer 
to my example would depend on what you pick for your axiomoids?  RJF always 
seems to have a useful comment about these things as well.

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