Curriculum Vitae
Dr. W. A. Naylor
Name  William Arthur Naylor
Date of birth  6th October 1968
Country of birth  Canada
Nationality  British/Canadian
Sex  Male
Current occupation  Post Doctoral Fellow: Ontario Research
Centre for Computer Algebra, at the University of Western
Ontario.
Field of Expertise  Symbolic Computation
Work Address  


Room 327E, 

The Computer Science Department, 

Middlesex College, 

The University of Western Ontario, 

London, Ontario, Canada N6A 5B7 
Telephone  015196614298
Institution 
Qualifications Gained 
Date of attendance 
University of Bath 
PhD entitled: 
 2000 

`Polynomial GCD Using Straight Line Program
Representation'. 


See section 4 

University of Bath 
MSc in Symbolic Computation with honours 
 1993 
University of Bath 
BSc in Computers & Mathematics with honours 
 1992 
Olchfa Comprehensive School 
4 A' level passes 
 1987 
Bishopston Comprehensive School 
10 O'level passes 
 1985 
My past employment includes:
 September 2000  present; My employment is with
the Ontario Research Centre for Computer Algebra, at the University
of Western Ontario as a postdoctoral research fellow
under the supervision of Professor S.M. Watt. My current research
interests are detailed in section 6.
 December 1999  August 2000; I was employed on
the OpenMath project. My foremost duty was to correct and update the
base Content Dictionaries (CDs). These are the files intended to
define `symbols' which represent certain basic mathematical operators
and objects in the OpenMath XML application. The base set of CDs are
specifically the CDs designed to perform alignment with the MathML
project.
 October 1993  October 1995; I was employed by
Bath University under a Teaching Company Scheme to work with NAG
Ltd. The work involved:
 Writing a mathematical front end to aid the use of some
NAG routines designed for solving systems of hyperbolic Partial
Differential Equations. This front end system is written in the
symbolic algebra system AXIOM, and makes use of the builtin FORTRAN
generation mechanisms of AXIOM. The NAG routines require the user to
provide some fairly complex mathematical objects instantiated as
FORTRAN routines, an example being a solver for the Riemann problem
associated with the specific problem. Routines were written in the
AXIOM compiler language (Aldor) which then automatically generated
these objects.
 October 1990  October 1991; I completed a years placement working for the
software house Micro Automation developing a Crane Monitoring Base Station system
(CMBS). This was a central system that performed a poll of a
number of outlying Crane Monitoring Systems (CMSs) over a radio
link. The CMBS then collated the data collected from the
CMSs, and logged any mechanical failures reported. It was necessary
to develop a protocol to send and receive this data.
Synopsis of my PhD
My PhD work, under the supervision of Professor J. H. Davenport,
involved writing a Straight Line Program (SLP) implementation which
could be used for representing and manipulating polynomials. The
implementation was written in Aldor under the AXIOM computer algebra system
environment. Further routines to calculate gcds of polynomials
represented as SLPs were written. Much attention was paid to the
efficiency of these routines.
 Conventional languages: Fortran, Pascal, Java, Javascript, C, Perl.
 Computer algebra related languages: Lisp, Aldor, Maple, Reduce.
 XML languages (applications): OpenMath, XSL(T), MathML.
 Miscellaneous: LATEX, HTML, shell script (bash).
Current Research Interests
Current research interests include:
 the UWO coordinator for the ongoing Canadian/European MONET project.
 implementing Unicode encodings within the Aldor system,
including UTF8, UTF16, etc. at a machine level,
 implementing an XML hierarchy on top of the aforementioned
encodings,
 implementing translation between MathML objects and Aldor
objects,
 implementing domains for structured matrices in Aldor,
 implementing a MonteCarlo category structure in Aldor,
 developing an implementation of straight line programs which
include nodes for exponential, logarithmic and radical functions in Aldor,
 developing a Special Function set of Content Dictionaries,
 writing XSLT stylesheets for translation of XML documents to
other XML and nonXML forms, in particular translation of OpenMath
documents and metastylesheets.
 extension of the Maple module XMLTools to encorporate
functionality which is useful for namespace aware processes (to be
included as part of the Maple 9 release).
 providing interfaces between Aldor and Maple using an external
language of MathML and utilising the XML namespace mechanism to
provide separation of the namespaces.
 constructing an on line OpenMath calculator that performs
reductions of OpenMath expressions. It has a html front end
and utilises a Java back end for performing the underlying
calculations, with XSLT preprocessing of the results:
http://orcca.on.ca/~bill/Tmp/index.html
My teaching experience includes the following:
 Part of the team teaching CS 422b/539b (Foundations of Computer
Algebra), 2000  2001 at UWO (under Dr. Ilias Kotsireas, head instructor).
 A one week workshop for senior honours students at the
University of Western Ontario teaching the basics of XML, MathML and
OpenMath.
 Three years of tutoring computer courses at the University of
Bath, to undergraduate honours students.
 Designing and teaching a course on the Aldor programming language at
the Universidad d'Ingenieros de Madrid, to professors from that
institution.
 Polynomial GCD Using Straight Line Program Representation,
PhD Thesis, University of Bath, 2000.
 Report on various Zero Structure Decompositions, MSc
dissertation, University of Bath, 1993.
 Mappings between presentation markup and semantic
markup for variable size objects, to be presented at the MathML and
Technologies for Math on the Web conference, June 2002. Chicago, Illinois.
 Meta stylesheets for the conversion of Mathematical
documents into multiple forms, joint author S.Watt, presented
at the Mathematical Knowledge Management conference 2001.
http://www.risc.unilinz.ac.at/conferences/MKM2001/Proceedings/naylor.ps
Accepted for publication in the Special Issue on Mathematical
Knowledge Management of the Annals of Mathematics and Artificial
Intelligence 2003.
 On the relationship between OpenMath and MathML, joint
author S.Watt, proceedings IAMC 2001.
http://icm.mcs.kent.edu/research/iamc2001.papers/nay.ps.gz
 A physical Application of Computer Algebra, joint author
Meikle, I.D., T.C.S. seminar, for the application of advanced I.T. 1994.
 Conversion Between MathML and OpenMath
D. Carlisle, J. Davenport, M.Dewar, N. Hur, W. Naylor. OpenMath deliverable 1.2.7:
http://www.nag.co.uk/projects/openmath/final/reports/ommml.pdf
 A MonteCarlo Extension to a CategoryBased Type System,
joint author J.H. Davenport.
 A Symbolic Interface for an advanced hyperbolic PDE
solver.
 Interactions between OpenMath and MathML under the Maple
environment to be presented as a poster at the MathML and
Technologies for Math on the Web conference, June 2002. Chicago,
Illinois.
 A MonteCarlo Extension to a CategoryBased Type System,
published as a poster at ISSAC 2000.
 A Symbolic Interface for an advanced hyperbolic PDE
solver published as a poster at ISSAC 1995.
Sporting hobbies in which I pursue an active interest include rock
climbing and cave exploration.
Amongst my nonsporting hobbies, I play the Highland bagpipes.
Curriculum Vitae
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Bill Naylor
20020509