terminology
J. Papp
"computer algebra" and "computational algebra"?
Is there a textbook where the meanings of these phrases are delimited?
Richard Fateman
> What is in your opinion the difference between "symbolic computation",
> "computer algebra" and "computational algebra"?
Not much.
> Is there a textbook where the meanings of these phrases are delimited?
>
Probably not. If there is, it was probably just made up without particular
authority. Just because something appears in some textbook in this field
does not mean it has been checked by even one other person.
Historically, the phrase Symbolic and Algebraic Manipulation (SAM) was used,
as in the name for SIGSAM, the ACM special interest group, dating back
to 1966 or so. And I think it should still be used.
The term "algebra" is, in my view, somewhat inaccurate since
one can do other parts of math on computers, e.g. analysis, geometry...
(though one could argue that one can do "analysis" or "geometry"
only by reducing it to "algebra").
The phrase "symbolic computation" has occasionally been used to denote
non-arithmetical computing; at one time a group of people tried to
start a journal on this topic which was devoted to graphics.
The term manipulation is far more accurate but perhaps has connotations
that people would like to avoid.
financial manipulation implies not-quite-legal activities.
I think it is even worse in some other languages.
For reasons unknown to me "CAS" for Computer Algebra System seems to
have caught on to describe computer programs such as Mathematica, Maple,
etc.
RJF
Robert Israel
Richard Fateman <fat...@cs.berkeley.edu> wrote:
>The term manipulation is far more accurate but perhaps has connotations
>that people would like to avoid.
>financial manipulation implies not-quite-legal activities.
>I think it is even worse in some other languages.
Within mathematics, "manipulation" has the connotation that you're
just pushing symbols around without regard to their meaning. In a
sense, this is all that computers can ever do, but we try to
program computer algebra systems so that they at least provide
some illusion of intelligence.
Robert Israel isr...@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
J. Papp
>Within mathematics, "manipulation" has the connotation that you're
>just pushing symbols around without regard to their meaning. In a
>sense, this is all that computers can ever do, but we try to
>program computer algebra systems so that they at least provide
>some illusion of intelligence.
So "manipulation" would fit better for the "inner kernel" of
a CAS, like the LISP engine of Reduce, Maple's op, subsop, subs,...
and "computation" to those functions (in the kernel or the library)
that have mathematical meaning?
Richard Fateman
Not in my view. The Lisp "engine" in Reduce, Macsyma, Maxima, Axiom,
as well as the partial implementation of Lisp inside Mathematica,
Maple, Mupad, .... would be underlying data structures and programs.
I would not call this "manipulation" especially.
These operations in lisp are perfectly well defined, operationally and
theoretically in terms of several computer science formalism, and
are subject to type systems, theorem proving etc. (I cannot speak
for the kernel of Mathematica or Maple... if they are well defined,
their definition is probably not public.)
The more "mathematical" operations are the ones that consist of
pushing symbols around. For example, replacing sin(2*x) by 2*cos(x)*sin(x),
or the reverse transformation are what I would characterize as
manipulation. Mathematically speaking, you can substitute equals
for equals, and thus there is no difference between the two.
For a computer algebra system there is obviously a difference.
If you want to talk about syntactic transformations, perhaps using
pattern matching and rules, or tree-computations or ... then maybe
you could formalize the notion of manipulation. Most reasonable
people end up using notions like "canonical forms" which you
can read about in various texts.
If you are seriously interested in the subject I suggest you find
another way to approach it rather than trying to define terms
from under their already-ambiguous usage to try to clarify them.
Have fun.
RJF
J. Papp
>If you are seriously interested in the subject I suggest you find
>another way to approach it rather than trying to define terms
>from under their already-ambiguous usage to try to clarify them.
Thank you for opening my eyes! I was under impression that I just
wanted to clarify the meaning of terms so I won't use them
improperly for my project book on Maple & Mechanics. But since
it is so obvious to you I have to "approach this field", I'm
considering going back to some Ph.D. Maybe undergraduate?
Richard Fateman
> Richard Fateman <fat...@cs.berkeley.edu> wrote:
>
>>If you are seriously interested in the subject I suggest you find
>>another way to approach it rather than trying to define terms
>
>>from under their already-ambiguous usage to try to clarify them.
>
> Thank you for opening my eyes! I was under impression that I just
> wanted to clarify the meaning of terms so I won't use them
> improperly for my project book on Maple & Mechanics.
That's great!
I hope that you have had an opportunity to
look at the book by Sussman and Wisdom: Structure and Interpretation
of Classical Mechanics. A copy of it is free on-line.
But since
> it is so obvious to you I have to "approach this field", I'm
> considering going back to some Ph.D. Maybe undergraduate?
If you are committed to using Maple, then you presumably have
to find a phrase to describe "what Maple does". In which case
it seems you should just look at the official Maple documentation.
That is much better defined.
RJF
>