Approximate Timelines 

• Numerical Analysis:  Approx. 1950 to the present
  

• Computer Algebra:  Approx. 1960 to the present
  

• Symbolic-Numeric Computation:  Approx. 1990 to the present

My Personal Timelines 

• 1970s:  Numerical Analysis
  
  - PhD Thesis, Algorithms for Analytic Approximation, 1973
  
  - My 1970s papers primarily in Numerical Approximation
   with particular interest in
   - Chebyshev series
   - Chebyshev-Pade approximation
   - Clenshaw-Curtis quadrature
  

• 1980s:  Computer Algebra
  
  - The Maple project, started about November 1980
  
  - Textbook, Algorithms for Computer Algebra (Geddes, Czapor, Labahn),
     publication date 1992
  

• 1990s and 2000s:  More emphasis on Symbolic-Numeric Computation
  
  - Numerical integration using symbolic analysis,
     incorporated into Maple's numerical integration facility
  
  - Recent work with former PhD student Fred Chapman
     on bivariate approximation
     also numerical multidimensional integration

J. H. Wilkinson 

• Rounding Errors in Algebraic Processes, 1963

• The Algebraic Eigenvalue Problem, 1965

Key concepts: 

• introduced backward error analysis

• also numerically stable algorithms for eigenproblems

W. Kahan 

Among many contributions, I mention 

• Conserving Confluence Curbs Ill-Condition, 1972 Tech Rep (Berkeley)

Key concepts: 

• root-finding becomes ill-conditioned for multiple or nearly-equal roots but

• determining the location of an m-fold cluster of roots is well-conditioned

B. Buchberger 

• An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal (German), PhD Thesis, 1965

• subsequent papers in the 1970s, 1980s, etc.

Key concept: 

• Groebner bases

Pre-Maple 

• In the 1970s I used early systems for Computer Algebra
  - for teaching and research work
  

• In those days we called it "symbolic computation"

• or "algebraic manipulation"

• Witness: ACM SIGSAM (for "symbolic and algebraic manipulation")

• The computers were "large" (but lacking in speed and memory space!!)

The "red room" in the Math and Computer building at UW 

Early Computer Algebra Systems 

• Formac (a preprocessor to PL/1)

• batch processing

• ALTRAN (a preprocessor to Fortran)

• very Fortran-like programming

• batch processing

• restricted to polynomial and rational function manipulation

• Communicate to the mainframe from a terminal

• I recall the so-called "silent 700"
  (not very silent, but compared to an IBM 2741 type-ball terminal!)

• I had a Teleterm terminal
  (cost $5200 in 1974)

• connect to campus mainframe at 300 baud

• The issue of memory size

• we used a Honeywell time-sharing mainframe

• 50K words (i.e., 200K bytes) of memory usage was "very large"

• often wait overnight for processing to finish

• would lead to high charges to my research grant

• could not use more than a half-megabyte of memory

• The point of the above trace of a computation: Large intermediate integers arise, much larger than the size of integers in the input and the output
  
  

• By the late 1970s, I made some use of MACSYMA

• Developed at MIT

• How did I use it?
  By dialing long-distance to a DEC 10 computer at MIT in Boston

• My question to my Computer Science colleagues:

• How can we get a computer that would run MACSYMA at U of Waterloo?

• My colleagues answer: That is the wrong question!
  

1980: The Maple Project Begins 

In the beginning (1980) there were two of us: Gaston Gonnet and Keith Geddes 

• I was on sabbatical at Berkeley during the first half of 1980, hosted by Richard Fatemanstarted writing a textbook on algebraic algorithmswhich eventually got completed (with co-authors) in 1992 :
  

• But back to 1980!
  

• I called a meeting of my CS colleagues at UW in November 1980
  

• My question: Can we apply for research grant to buy a computer large enough to run MACSYMA?
  

• The answer (typical of UW): You should build your own system, and (avoiding LISP as an implementation language) try to do much more with fewer computing resources.
  

• In short, using a BCPL-language (eventually, this meant the C language) we did develop the Maple system which could do more with less!
  

• It was at this November 1980 meeting where I learned that fellow faculty member, Gaston Gonnet, was also interested in algebraic computation.
  

• Gaston had already developed a mini-CA system (WAMA -- Waterloo Algebraic Manipulation) during 1979-80, for doing asymptotic analysis calculations related to the analysis of algorithms.
  

• By the first week of December 1980, Gaston had put together the first running system to which we gave the name "Maple".
  

• Where does the name "Maple" come from?
  It is just a Canadian name -- after first thinking of acronyms for "Mathematical Programming Language", for example.
  

• Now I could proceed with my interest in "Algorithms for Computer Algebra" by implementing the algorithms in Maple.

How many Person-Years of R&D for Maple? 

• Start date is 1 Dec 1980.

• Of course, we need a Maple calculation to figure out the number of person-years of R&D effort.

• Note: The numbers for PersonsPerYear below are fictitious -- but maybe something like this!

>

 

>

 

>

 

>

 

>

 

>

 

(3)

 

>

 

>

 

(4)

 

>

 

(5)

 

>

 

(6)

 

>

 

>

 

>

 

>

 

>

 

(7)

 

>

 

Voila! 

1981-1984: A Few Pictures 

Michael Monagan and Greg Fee 

• Michael Monagan arrived at UW (from New Zealand) as a graduate student in 1982.
  

• By the end of the 1980s when we calculated the contributions to Maple code by various authors, Michael was one of the "top three" contributors (Gaston, Keith and Michael) -- in some order (I believe that Michael was ahead of one or both of us).
  

• Greg Fee and Benton Leong were hired to work on the Maple project about 1981 and remained with the project for many years.

Benton Leong and Howard Johnson 

A good view of the "ASCII Maple logo" 

• Credit for inventing the "ASCII Maple logo" goes to Stephen Watt, who did his PhD degree under my supervision in the early 1980s.

An Aside 

• There is no truth to the rumour that Stephen got his PhD for inventing the ASCII Maple logo!

Since this is a joint banquet for SNC and PASCO -- 

• My presentation has not related to the PASCO conference, so let me give some "parallel" relationships.

1985-1997: 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 

Conferences/Workshops 

(among others) 

• SNAP '96, Sophia Antipolis, France, Jul 1996
  (Symbolic-Numeric Algebra for Polynomials)

• SNSC '99, RISC-Linz, Aug 1999
  (Symbolic and Numerical Scientific Computation)

• SNSC '01, RISC-Linz, Sep 2001

• SNC '05, Xi'an, China, Jul 2005
  (Symbolic-Numeric Computation)

• SNC '07, London, Ontario, Canada, Jul 2007

• Significant contributions are being presented at these meetings

H. J. Stetter 

• Numerical Polynomial Algebra, 2004.

Hans Stetter, Keith Geddes, Stephen Watt, 2005 

Conclusions 

• Hopefully over time, the fundamental concepts presented by Stetter (and being further developed by others) will become "common knowledge" in scientific computing.

• Of course, there is more to Symbolic-Numeric Computation than the topics of Stetter's book!

• Progress continues on many aspects. As indicated at the outset, I have not attempted to be comprehensive about mentioning the significant contributions to this field.