Simplification - Richard J. Fateman: Essays in Algebraic Simplification
Vladimir Bondarenko
This famous classic work can be downloaded for free here [5 Mb]
http://www.lcs.mit.edu/publications/specpub.php?id=663
Richard J. Fateman
Essays in Algebraic Simplification, 195 pp, 4-1-1972
Abstract:
This thesis consists of essays on several aspects of the problem
of algebraic simplification by computer. Since simplification is
at the core of most algebraic manipulations, efficient and
effective simplification procedures are essential to building
useful computer systems for non-numerical mathematics.
Efficiency is attained through carefully designed and engineered
algorithms, heuristics, and data types, while effectiveness is
assured through theoretical considerations.
Chapter 1 is an introduction to the field of algebraic
manipulation, and serves to place the following chapters
in perspective.
Chapter 2 reports on an original design for, and programming
implementation of, a pattern matching system intended to
recognize non-obvious occurrences of patterns within algebraic
expressions. A user of such a system can "teach" the computer
new simplification rules.
Chapter 3 reports on new applications of standard mathematical
algorithms used for canonical simplifications of rational
expressions. These applications, in combinations, allow a
computer system to contain a fair amount of expertise in several
areas of algebraic manipulation.
Chapter 4 reports on a new, practical, canonical simplification
algorithm for radical expressions (i.e. algebraic expressions
including roots of polynomials). The effectiveness of the
procedure is assured through proofs of appropriate properties
of these simplified expressions.
Chapter 5 is a brief summary and a discussion of potential
research areas. Two appendices describe MACSYMA, a computer
system for symbolic manipulation, an effort of some dozen
researchers (including the author) which has served as the
vehicle for this work.
Richard J. Fateman. "Essays in algebraic simplification".
Technical report MIT-LCS-TR-095, 1972.
.................................................................
Simplification - Joel Moses: Algebraic Simplification:
A Guide for the Perplexed, 1971
http://groups.google.com/group/sci.math.symbolic/msg/e81b8db8dd551d70
.................................................................
Richard J. Fateman
9 pages were mis-scanned (entirely black). The MIT
publications people have expressed some interest in fixing
this and several other technical reports with similar scan errors.
So maybe you should wait to download it.
More concise reports of the results in this thesis were published
in various papers, and it turns out that one table (comparing times to
CAMAL) is unfair to CAMAL, which was faster than I wanted to believe.
I do not know why VB thinks the existence of this is newsworthy for 5
newsgroups.
Richard Fateman
Ronald Bruck
<fat...@eecs.berkeley.edu> wrote:
> By coincidence, I looked at this yesterday and found that
> 9 pages were mis-scanned (entirely black). The MIT
> publications people have expressed some interest in fixing
> this and several other technical reports with similar scan errors.
> So maybe you should wait to download it.
>
> More concise reports of the results in this thesis were published
> in various papers, and it turns out that one table (comparing times to
> CAMAL) is unfair to CAMAL, which was faster than I wanted to believe.
>
> I do not know why VB thinks the existence of this is newsworthy for 5
> newsgroups.
Oh, come, Richard, you're too modest--I've often wondered how you got
your detailed knowledge of Macsyma, and now I know.
--Ron Bruck
[I've trimmed the newsgroup list]
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Craig Carey
>I do not know why VB thinks the existence of this is newsworthy for 5
>newsgroups.
I request that Mr Bondarenko state the fact on why he copied the
message on simplifaction. It is apparent that the copying Simferopol
man, does not have a taxononomy of bugs (or defects) applicable to
products of Maplsesoft GMBH, for sci.maths.symbolic to examine.
Mr Bondarenko does not pick up on hints. To out-do the Ukrainian
in the development of a taxonomy of mistakes, here I trial this:
* is response to implicit question of Mr Fateman, et al,
* by mistake the noisy Simferopol ISP user missed it
* the question was not implicit [as occurs here in this 'post',
with the question asking for reasoning for copying outwards
(6 types of copying: a replication of transfers in 2 directions
with Bondarenko at the centre, and 3 states: residual,
electronic documents in motion, and the residual 'pre-questioning'
state....
Implementation of symbolic algebra simplifications is much produced
using trial and error programming.
Failure to do a little more trial and error style programming does not
seem to be a "bug".
Also Bondarenko can provide the exact hsitorical reasoning procedure
that was used when creating that message alerting sci.math.symbolic
to some previously unsuspected need for religious awe at the
allegedly visual fact of a painting on a curved upper ceiling of
some Christian church building.
Did Mr Bondarenko intend to have a response?. Perhaps Bondarekno
incorect expects sci.math.symbolic and Maple to respond, and
wrongly does not respond himself, and Usenet irrational buggy
thinking in Ukraine is calling for spiking. Questions over to
VB are likely to be sparse.
Only have two floors nd no curved ceiling.
http://www.maplesoft.com/company/about/images/Patio.jpg
Maybe later Mathematica's Ancow can disclose more on whether Mr Wolfram
should have removed Miranda from Mathematica by now ?..
>Vladimir Bondarenko wrote:
>> .................................................................
>>
>> This famous classic work can be downloaded for free here [5 Mb]
>>
>> http://www.lcs.mit.edu/publications/specpub.php?id=663
>>
It is worse than 0^0