|
|
Re: Symbolic manipulation with Sqrt[-1] ?
Posted:
Dec 6, 2009 4:34 PM
|
|
Nasser M. Abbasi wrote:
>
> I was wondering which CAS system is considered the "best" when it comes to
> the issue of substitution then?
The problem of substitution is the name of a 1968 paper by A.C. Hearn,
the author of the CAS Reduce.
I could not find a copy of this paper online, however.
I wrote about "ratsubst" (in Macsyma) in my thesis, published in 1971.
Some people consider that the issue of simplification with respect to
polynomial side conditions is solved by Grobner bases.
>
> Some have issues with how Mathematica does it for some cases.
That is apparent.
So, is there
> then considered a best or a canonical way to approach this whole issue
> instead of looking at as a case by case?
>
For polynomials, especially smallish ones, there probably is a canonical
way, (or a collection of them) based on Grobner bases. In general this
is not necessarily helpful, nor does it address the full breadth of
expressions that are possible. Personally, I think that ratsubst (in
Maxima) is a pretty good tool; other systems now have similar facilities
I think. Look for simplification with respect to polynomial side relations.
....
> And this seems to me to be as a canonical way to do this as it would be
> possible?
You haven't defined canonical. The general concept is that for a CAS
form to be canonical, two mathematically equivalent expressions must
look identical when converted to that form. FullForm is not canonical
at all. FullForm[2*Cos[x]*Sin[x]] is different from FullForm[Sin[2*x]].
If you want to learn about simplification and substitution, I suggest
you go to the library (or look on the internet) and read, instead of
relying on the responses of people who happen to spend their afternoons
writing essays on sci.math.symbolic :)
|
|
