Skip to the content of the web site.

 

Keith O Geddes

List of Publications

Refereed Papers (Journals and Conference Proceedings):

Papers in Refereed Newsletters

Books

Technical Reports:

Refereed Papers: 2000—2009

  1. F.W. Chapman and K.O. Geddes, An improved algorithm for the automatic derivation and proof of tensor product identities via computer algebra. Proceedings of Calculemus'06 (Genoa, Italy, Jul 2006), Anna Bigatti and Silvio Ranise (ed.), 2006, pp. 52—67.

  2. O.A. Carvajal, F.W. Chapman and K.O. Geddes, Hybrid symbolic-numeric integration in multiple dimensions via tensor-product series. Proceedings of ISSAC'05 (International Symposium on Symbolic and Algebraic Computation), Manuel Kauers (ed.), ACM Press, New York, 2005, pp. 84—91.

  3. Tom Robinson and K.O. Geddes, Automated generation of numerical evaluation routines. Maple Conference 2005, Ilias S. Kotsireas (ed.), Maplesoft, Waterloo, Ontario, Canada, 2005, pp. 383—398.

  4. Yu.A. Brychkov and K.O. Geddes, On the derivatives of the Bessel and Struve functions with respect to the order. Integral Transforms and Special Functions, 16 (3), Apr 2005, pp. 187—198.

  5. S.A. Abramov, J.J. Carette, K.O. Geddes and H.Q. Le, Telescoping in the context of symbolic summation in Maple. Journal of Symbolic Computation, 38 (4), Oct 2004, pp. 1303—1326.

  6. K.O. Geddes, H.Q. Le and Z. Li, Differential rational normal forms and a reduction algorithm for hyperexponential functions. Proceedings of ISSAC'04 (International Symposium on Symbolic and Algebraic Computation), J. Gutierrez (ed.), ACM Press, New York, 2004, pp. 183—190.

  7. Yu.A. Brychkov and K.O. Geddes, Differentiation of hypergeometric functions with respect to parameters. Appears in Abstract and Applied Analysis (Proceedings of the International Conference, Hanoi, Vietnam), N.M. Chuong, L. Nirenberg and W. Tutschke (ed.), World Scientific, 2004, pp. 15—28.

  8. K.O. Geddes and W.W. Zheng, Exploiting fast hardware floating point in high precision computation. Proceedings of ISSAC'03 (International Symposium on Symbolic and Algebraic Computation), J.R. Sendra (ed.), ACM Press, New York, 2003, pp. 111—118.

  9. S.A. Abramov, K.O. Geddes and H.Q. Le, Computer algebra library for the construction of the minimal telescopers. International Congress of Mathematical Software, A.M. Cohen, X. Gao, N. Takayama (ed.), World Scientific, 2002, pp. 319—329.

  10. K.O. Geddes and H.Q. Le, An algorithm to compute the minimal telescopers for rational functions (Differential-integral case). International Congress of Mathematical Software, A.M. Cohen, X. Gao, N. Takayama (ed.), World Scientific, 2002, pp. 453—463.

  11. K.O. Geddes, Algorithms for indefinite and definite integration in Maple. Appears in Applications of Computer Algebra (Proceedings of the International Symposium on Applications of Computer Algebra, Kolhapur, India, Oct 2000), R. Akerkar (ed.), Allied Publishers Ltd, Mumbai, 2001, pp. 51—84.

  12. K.O. Geddes, Hybrid symbolic-numeric methods applied to definite integrals and ODEs. Appears in Applications of Computer Algebra (Proceedings of the International Symposium on Applications of Computer Algebra, Kolhapur, India, Oct 2000), R. Akerkar (ed.), Allied Publishers Ltd, Mumbai, 2001, pp. 85—108.

Back to top

Refereed Papers: 1990—1999

  1. K.O. Geddes, Generating numerical ODE formulas via a symbolic calculus of divided differences. SIGSAM Bulletin: Communications on Computer Algebra, 33 (2), 1999, pp. 29—42.

  2. K.O. Geddes, Symbolic math and the hybrid symbolic-numeric paradigm in scientific computation. Proceedings of the International Conference on Computational Mathematics, Bangkok, Thailand, Dec 1997.

  3. M. Kavian, R.G. McLenaghan and K.O. Geddes, Application of genetic algorithms to the algebraic simplification of tensor polynomials. Proceedings of ISSAC'97, W.W. Kuechlin (ed.), ACM Press, New York, 1997, pp. 93—100.

  4. M. Kavian, R.G. McLenaghan and K.O. Geddes, MapleTensor: A new system for performing indicial and component tensor calculations by computer. Fields Institute Comm., 15, 1997, pp. 269—272.

  5. M. Kavian, R.G. McLenaghan and K.O. Geddes, MapleTensor: Progress report on a new system for performing indicial and component tensor calculations using symbolic computation. Proceedings of ISSAC'96, Lakshman Y.N. (ed.), ACM Press, New York, 1996, pp. 204—211.

  6. K.O. Geddes and G. Labahn, Symbolic and numeric integration in Maple. Appears in Innovative Use of Technology for Teaching and Research in Mathematics (Proceedings of The First Asian Technology Conference in Mathematics, Dec 1995), The Association of Mathematics Educators, Singapore, 1995, pp. 377—386.

  7. K.O. Geddes and G. Labahn, The Maple computer algebra system. Appears in Innovative Use of Technology for Teaching and Research in Mathematics (Proceedings of The First Asian Technology Conference in Mathematics, Dec 1995), The Association of Mathematics Educators, Singapore, 1995, pp. 367—376.

  8. M. Kavian, R.G. McLenaghan and K.O. Geddes, Mapletensor: A new system for performing indicial and component tensor calculations by computer. Proceedings of the 7th Marcel Grossman Conference, World Scientific, Singapore, 1995.

  9. M. Kavian, R.G. McLenaghan and K.O. Geddes, Mapletensor: A new system for performing indicial and component tensor calculations by computer. Proceedings of the 14th International Conference on General Relativity and Gravitation, Florence, Italy, 1995.

  10. K.O. Geddes, Hybrid symbolic-numeric algorithms for scientific and engineering problem solving. CD-ROM Proceedings of SEAM'95 (Scientific and Engineering Applications of the Macintosh), MacSciTech, Worcester, MA, 1995, 34 pages.

  11. K.O. Geddes and G.J. Fee, Hybrid symbolic-numeric integration in Maple. Proceedings of ISSAC'92, P.S. Wang (ed.), ACM Press, New York, 1992, pp. 36—41.

  12. K.O. Geddes, M.L. Glasser, R.A. Moore and T.C. Scott, Evaluation of classes of definite integrals involving elementary functions via differentiation of special functions. Applicable Algebra in Engineering, Communication and Computing, 1 (2), Nov 1990, pp. 149—165.

  13. T.C. Scott, R.A. Moore, G.J. Fee, M.B. Monagan, G. Labahn and K.O. Geddes, Perturbative Solutions of Quantum Mechanical Problems by Symbolic Computation: A review. Int. J. Mod. Phys. C, 1, 1990, pp. 53—76.

Back to top

Refereed Papers: 1980—1989

  1. K.O. Geddes and L.Y. Stefanus, On the Risch-Norman integration method and its implementation in Maple. Proceedings of ISSAC'89, ACM Press, New York, 1989, pp. 212—217.

  2. K.O. Geddes and T.C. Scott, Recipes for classes of definite integrals involving exponentials and logarithms. Computers and Mathematics, E. Kaltofen and S.M. Watt (ed.), Springer-Verlag, New York, 1989, pp. 192—201.

  3. K.O. Geddes and G.H. Gonnet, A new algorithm for computing symbolic limits using hierarchical series. Appears in Symbolic and Algebraic Computation, P. Gianni (ed.), Lecture Notes in Computer Science, No. 358, Springer-Verlag, Berlin, 1989, pp. 490—495.

  4. K.O. Geddes, G.H. Gonnet and T.J. Smedley, Heuristic methods for operations with algebraic numbers. Appears in Symbolic and Algebraic Computation, P. Gianni (ed.), Lecture Notes in Computer Science, No. 358, Springer-Verlag, Berlin, 1989, pp. 475—480.

  5. B.W. Char, K.O. Geddes and G.H. Gonnet, GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation. J. Symbolic Computation, 7, 1989, pp. 31—48.

  6. K.O. Geddes, Numerical integration in a symbolic context. Proceedings of SYMSAC'86, B.W. Char (ed.), ACM Press, New York, 1986, pp. 185—191.

  7. S.R. Czapor and K.O. Geddes, On implementing Buchberger's algorithm for Groebner bases. Proceedings of SYMSAC'86, B.W. Char (ed.), ACM Press, New York, 1986, pp. 233—238.

  8. B.W. Char, K.O. Geddes, G.H. Gonnet, B.J. Marshman and P.J. Ponzo, Computer algebra in the undergraduate mathematics classroom. Proceedings of SYMSAC'86, B.W. Char (ed.), ACM Press, New York, 1986, pp. 135—140.

  9. B.W. Char, G.J. Fee, K.O. Geddes, G.H. Gonnet and M.B. Monagan, A tutorial introduction to Maple. J. Symbolic Computation, 2 (2), Jun 1986, pp. 179—200.

  10. B.W. Char, G.J. Fee, K.O. Geddes, G.H. Gonnet, M.B. Monagan and S.M. Watt, On the design and performance of the Maple system. Proceedings of the 1984 MACSYMA Users' Conference, V. Ellen Golden (ed.), General Electric, Schenectady, New York, 1984, pp. 199—219.

    Online paper: Design84

    Extended version: Technical Report CS-84-13, 1984 http://www.cs.uwaterloo.ca/research/tr/

  11. B.W. Char, K.O. Geddes and G.H. Gonnet, GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation. Extended abstract in Proceedings of EUROSAM'84, J. Fitch (ed.), Lecture Notes in Computer Science, No. 174, Springer-Verlag, Berlin, 1984, pp. 285—296.

  12. S.R. Czapor and K.O. Geddes, A comparison of algorithms for the symbolic computation of Padé approximants. Proceedings of EUROSAM'84, J. Fitch (ed.), Lecture Notes in Computer Science, No. 174, Springer-Verlag, Berlin, 1984, pp. 248—259.

  13. B.W. Char, K.O. Geddes, W.M. Gentleman and G.H. Gonnet, The design of Maple: A compact, portable and powerful computer algebra system. Appears in Computer Algebra (Proceedings of EUROCAL'83), J.A. van Hulzen (ed.), Lecture Notes in Computer Science, No. 162, Springer-Verlag, Berlin, 1983, pp. 101—115.

    See also: Technical Report CS-83-06, 1983 http://www.cs.uwaterloo.ca/research/tr/

  14. K.O. Geddes, Block structure in the Chebyshev-Padé table. SIAM J. Numer. Anal., 18 (5), Oct 1981, pp. 844—861.

Back to top

Refereed Papers: 1970—1979

  1. K.O. Geddes, Convergence behaviour of the Newton iteration for first-order differential equations. Appears in Symbolic and Algebraic Computation (Proceedings of EUROSAM'79), E.W. Ng (ed.), Springer-Verlag, Berlin, 1979, pp. 189—199.

  2. K.O. Geddes, Symbolic computation of Padé approximants. ACM Trans. Math. Software, 5 (2), Jun 1979, pp. 218—233.

  3. K.O. Geddes, Remark on Algorithm 424: Clenshaw-Curtis quadrature. ACM Trans. Math. Software, 5 (2), Jun 1979, p. 240.

  4. K.O. Geddes, Near-minimax polynomial approximation in an elliptical region. SIAM J. Numer. Anal., 15 (6), Dec 1978, pp. 1225—1233.

  5. M.O. Afolabi and K.O. Geddes, Near-minimax interpolation of analytic functions on regular polygons. Proceedings of the Seventh Manitoba Conference on Numerical Math. and Computing, University of Manitoba, Sep 29 — Oct 1, 1977, pp. 163—176.

  6. K.O. Geddes, Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. Proceedings of the 1977 MACSYMA User's Conference, Carl M. Andersen (ed.), University of California, Berkeley, CA, Jul 27—29, 1977, NASA CP-2012, pp. 405—423.

  7. K.O. Geddes, Chebyshev nodes for interpolation on a class of ellipses. Appears in Theory of Approximation, A.G. Law and B.N. Sahney (ed.), Academic Press, New York, 1976, pp. 155—170.

  8. K.O. Geddes and J.C. Mason, Polynomial approximation by projections on the unit circle. SIAM J. Numer. Anal., 12 (1), Mar 1975, pp. 111—120.

Back to top

Papers in Refereed Newsletters

  1. K.O. Geddes, A package for numerical approximation. MapleTech (The Maple Technical Newsletter), Issue 10, Fall 1993, pp. 28—36.

  2. T.C. Scott, Y.B. Band and K.O. Geddes, Recipes for solving broad classes of definite integrals and applications. MapleTech (The Maple Technical Newsletter), Issue 10, Fall 1993, pp. 19—27.

  3. K.O. Geddes, Numerical integration using symbolic analysis. MapleTech (The Maple Technical Newsletter), Issue 6, Fall 1991, pp. 8—17.

Back to top

Books

Back to top

Technical Reports: 2000—2009

  1. K.O. Geddes and W.W. Zheng, Exploiting fast hardware floating point in high precision computation. Technical Report CS-2002-41, School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 2002. http://www.cs.uwaterloo.ca/research/tr/

  2. S.A. Abramov, J.J. Carette, K.O. Geddes and H.Q. Le, Symbolic summation in Maple. Technical Report CS-2002-32, School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 2002. http://www.cs.uwaterloo.ca/research/tr/

  3. H.Q. Le, S.A. Abramov and K.O. Geddes, A direct algorithm to construct the minimal telescopers for rational functions (q-difference case). Technical Report CS-2001-25, School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 2001. http://www.cs.uwaterloo.ca/research/tr/

  4. H.Q. Le, S.A. Abramov and K.O. Geddes, HypergeometricSum: A Maple package for finding closed forms of indefinite and definite sums of hypergeometric type. Technical Report CS-2001-24, School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 2001. http://www.cs.uwaterloo.ca/research/tr/

  5. X. Liu, R.M. Corless and K.O. Geddes, Computation of center manifolds. Technical Report TR-00-15, Ontario Research Centre for Computer Algebra, London, Ontario, Canada, 2000. http://www.orcca.on.ca/TechReports/

Back to top

Technical Reports: 1990—1999

  1. K.O. Geddes and G.J. Fee, Hybrid symbolic-numeric integration in Maple. Research Report CS-92-31, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, May 1992.

  2. T.C. Scott and K.O. Geddes, Recipes for solving broad classes of definite integrals. Research Report CS-92-05, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Feb 1992.

  3. D.E.G. Hare, K.O. Geddes and G.J. Fee, Arbitrary precision evaluation of the complex error function. Research Report CS-91-60, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Oct 1991.

  4. K.O. Geddes et. al. (Symbolic Computation Group), Maple V: A Sample Interactive Session. Research Report CS-91-51, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Oct 1991.

Back to top

Technical Reports: 1980—1989

  1. B.W. Char, G.J. Fee, K.O. Geddes, G.H. Gonnet, M.B. Monagan and S.M. Watt, On the Design and Performance of the Maple System. Research Report CS-84-13, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Jun 1984. http://www.cs.uwaterloo.ca/research/tr/

  2. B.W. Char, K.O. Geddes and G.H. Gonnet, An Introduction to Maple: Sample Interactive Session. Research Report CS-84-04, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Jan 1984.

  3. K.O. Geddes, Newton's iteration and the Hensel construction. Research Report CS-83-36, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Nov 1983.

  4. B.W. Char, K.O. Geddes and G.H. Gonnet, Record of the First Annual Maple Workshop. Research Report CS-83-31, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Jun 1983.

  5. B.W. Char, K.O. Geddes, W.M. Gentleman and G.H. Gonnet, The Design of Maple: A Compact, Portable and Powerful Computer Algebra System. Research Report CS-83-06, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Apr 1983. http://www.cs.uwaterloo.ca/research/tr/

  6. K.O. Geddes, Symbolic Computation 5: Homomorphisms and Chinese Remainder Algorithms. Research Report CS-81-35, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Dec 1981.
  7. K.O. Geddes, Symbolic Computation 3: Normal forms and data structures. Research Report CS-81-29, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Sep 1981.

  8. K.O. Geddes, Symbolic Computation 2: Algebra of polynomials, rational functions and power series. Research Report CS-81-27, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Sep 1981.

  9. K.O. Geddes and G.H. Gonnet, Maple User's Manual. Research Report CS-81-25, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Jul 1981.

  10. K.O. Geddes, Block structure in the Chebyshev-Padé table. Research Report CS-80-16, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Mar 1980.

Back to top

Technical Reports: 1970—1979

  1. K.O. Geddes, Non-truncated power series solution of linear ODE's in ALTRAN. Research Report CS-79-09, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Feb 1979.

  2. K.O. Geddes, An ALTRAN implementation of the fraction-free Padé algorithm. Research Report CS-78-10, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Feb 1978.

  3. K.O. Geddes, ALTRAN procedures for the Chebyshev series solution of linear ODE's. Research Report CS-77-05, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Feb 1977.

  4. K.O. Geddes, Algorithms for Analytic Approximation. (Ph.D Thesis). Technical Report No. 56, Department of Computer Science, University of Toronto, Toronto, Canada, Aug 1973.

Back to top