SymbolicNumeric Reflections:
One Person's 35year Perspective
Keith Geddes
SNC '07
The University of Western Ontario
27 July 2007
Abstract
This will be an informal afterdinner talk recalling some events of past years related to scientific computation and computer algebra.
What this is not: This is not a comprehensive overview of historical developments in numerical analysis and computer algebra, nor of the development of "symbolicnumeric computation".
It is more casual and lighthearted (as expected for an afterdinner talk), but with some mention of significant historical developments.
The SNC Landscape
Approximate Timelines
My Personal Timelines
Early Milestones related to SNC
J. H. Wilkinson
Key concepts:
W. Kahan
Among many contributions, I mention
Key concepts:
B. Buchberger
Key concept:
The Maple Project: Some recollections
PreMaple
The "red room" in the Math and Computer building at UW
Early Computer Algebra Systems
How large do integers need to be?
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Note: The maximum length of integers above is 10 digits.
The old algorithm `gcd/reduced` (which uses a PRS algorithm) yields the same result. It even seems fast enough on modern computers.However, notice the large integers that can be generated by intermediate calculations!
We very soon ran into GCD computations that could not be completed on a system that limits the size of integers to only 100 digits.
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{> enter gcd/reduced, args = 2500000*x^4487995500*x^32442003501*x^2+308523500*x+4504301, 125000*x^3+1110250*x^2+2426470*x+2501 
{> enter gcd/reduced/prs, args = 2500000*x^4487995500*x^32442003501*x^2+308523500*x+4504301, 125000*x^3+1110250*x^2+2426470*x+2501  
{> enter gcd/reduced/prs, args = 2500000, 487995500  
< exit gcd/reduced/prs (now in gcd/reduced/content) = 500}
{> enter gcd/reduced/prs, args = 500, 2442003501 

< exit gcd/reduced/prs (now in gcd/reduced/content) = 1}  
{> enter gcd/reduced/prs, args = 125000, 1110250  
< exit gcd/reduced/prs (now in gcd/reduced/content) = 250}
{> enter gcd/reduced/prs, args = 250, 2426470 

< exit gcd/reduced/prs (now in gcd/reduced/content) = 10}
{> enter gcd/reduced/prs, args = 10, 2501 

< exit gcd/reduced/prs (now in gcd/reduced/content) = 1}  
{> enter gcd/reduced/prs, args = 1, 1  
< exit gcd/reduced/prs (now in gcd/reduced/prs) = 1}  
{> enter gcd/reduced/prs, args = 12931048027941398437500000000000, 64681102235762874984375000000000  
< exit gcd/reduced/prs (now in gcd/reduced/content) = 25862096055882796875000000000}  
< exit gcd/reduced/prs (now in gcd/reduced) = 2501+500*x}  
< exit gcd/reduced (now at top level) = 2501+500*x}  
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1980: The Maple Project Begins
In the beginning (1980) there were two of us: Gaston Gonnet and Keith Geddes
How many PersonYears of R&D for Maple?
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Voila!
19811984: A Few Pictures
Michael Monagan and Greg Fee
Benton Leong and Howard Johnson
A good view of the "ASCII Maple logo"
An Aside
Since this is a joint banquet for SNC and PASCO 
Stephen Watt's PhD Thesis
The 1980 Parallel Maple Question
Another relationship to PASCO
The 2007 Parallel Maple Question
More seriously,
19851997: More Pictures
Stan Devitt, Stephen Watt, Bruce Char, Benton Leong, Keith Geddes
(in Linz, Austria for the 1985 Eurocal conference)
A geeky picture of me in Linz, Austria (1985)
ISSAC '88 in Rome  the first to be named "ISSAC"
Rome 1988
Bruce Char and Mark Mutrie, Maple Retreat 1989
Maple booth, NCTM 1992, Quebec City
A view of the competition, NCTM 1992, Quebec City
Stephen Watt and I with hosts, Kiev 1993
Kiev 1993
The vodka banquet, Kiev 1993
W. Kahan, K. Geddes, D. Jeffrey, G. Labahn, Ha Le, Maple Retreat 1994
Rob Corless family, Maple Retreat 1994
Erich Kaltofen with Allan Bonadio and ??, Maple Retreat 1994
Group picture, Maple Retreat 1994
Hard at work at the Maple Retreat, Sparrow Lake, Ontario, 1997
SNC Today
Conferences/Workshops
(among others)
H. J. Stetter
Hans Stetter, Keith Geddes, Stephen Watt, 2005
Remarks on Stetter's Book
As I found in first encounters as a graduate student with Wilkinson's books,
and with the works of Kahan and many others ...
Key concepts
Conclusions