Re: Simplifying radicals
- From: JohnCreighton_@xxxxxxxxxxx
- Date: 25 Aug 2005 07:34:53 -0700
Christopher Creutzig wrote:
> JohnCreighton_@xxxxxxxxxxx wrote:
> > should be able to change the simplifying rules so it can. Or you should
> > perform the calculations where you want them to cancel using something
> > like:
> > assuming(myExpresion,"extra assumptions only for this calculation")
>
> MuPAD and Maple use
>
> myExpression assuming whatever
>
> and I believe Mathematica does something similar with its optional
> arguments to Simplify and FullSimplify. But that only helps for a very
> short path of the way, since most of the expression simplification will
> take place internally and the user simply won't know to assume that C251
> is neither PI/2 nor 0 - nor would it help to ask her, since C251 didn't
> exist in the problem as stated to the system.
>
> It may be "wrong" in some specific mathematical contexts (but correct
> in many others), but for programmatical reasons it has turned out to be
> good for a system to normalize x^2/x to x. Note that there are even
> contexts where x-x=0 is wrong, yet we do want a CAS to perform this
> simplification automatically.
>
>
> Christopher Creutzig
I believe the most recent version of maple changed this (what is it
maple 11?) because it is not true that x-x=0 if x is a random function.
My answer is there should be a default set of rules and we should be
able to tell the CAS to change these rules if needed. As for things
happening internally perhaps you could specify rules in a given
context. For instance we could tell the CAS that you can only cancel
roots when doing limit computations. If all the contexts are well
documented and the programmer could create there own context then this
might work. A function could even override contexts set externally if
it was known that this would lead to a wrong answer.
.
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