- The authors of the following paper acknowledge the joint work
of Lihong Zhi in relation to Section 8 on approximate ideal membership and on
structured methods to converge to nearby involutive systems.
The latter is the subject of ongoing joint work which should have been
referenced in the paper below. The authors sincerely regret
and apologize for this omission and the lack of prior consultation
with Lihong Zhi before the submission of the paper below.
- Wenyuan Wu and Greg Reid (2006),
*Application of Numerical Algebraic Geometry and Numerical Linear Algebrato PDE*, Proc. ISSAC 2006, ACM Press, New York, 345-352. [Retrieve PDF] . - G. Reid, J. Tang, and L. Zhi (2003),
*A complete Symbolic-Numeric Linear Method for Camera Pose Determination*, Proc. ISSAC 2003, ACM Press, New York, 215-223. [Retrieve PostScript] [Retrieve PDF] . - K. Hazaveh, D.J. Jeffrey, G.J. Reid, S.M. Watt & A.D. Wittkopf (2003),
*An exploration of homotopy solving in Maple*. Proc. of the Sixth Asian Symp. on Computer Math. (ASCM 2003). Lect. Notes Series on Computing by World Sci. Publ.**10**edited by Z. Li & W. Sit (Singapore/River Edge, USA) 145-162. [Retrieve Postscript] . - G. J. Reid, C. Smith and J. Verschelde (2002),
*Geometric Completion of Differential Systems using Numeric-Symbolic Continuation*, SIGSAM Bulletin**36**(2): 1-17. (article was formally reviewed according to SIGSAM policy). [Abstract] [Retrieve PostScript] [Retrieve PDF] - M. W. Giesbrecht, G. J. Reid & Y. Zhang (2002).
*Non-commutative Grobner bases in Poincaré-Birkhoff-Witt extensions*. Proc. of the Fifth Inter. Workshop on Computer Algebra in Scientific Computing (CASC 2002, Yalta, Ukraine), edited by V.G. Ganzha, E.W. Mayr & E.V. Vorozhtsov (Pub: Technical University of Munich) 97-106. [Retrieve PostScript] [Retrieve PDF] . - A. D. Wittkopf and G. J. Reid (2001),
*Fast Differential Elimination in C: The CDiffElim Environment*, Computer Physics Communications**139**(2) 192-217.

Associated Package: approximately 16,000 lines of code in C, reviewed accepted and distributed in the Computer Physics Communications (CPC) Program Library. [Retrieve PostScript] . - G. J. Reid, P. Lin and A. D. Wittkopf (2001),
*Differential-Elimination Completion Algorithms for DAE and PDAE*, Studies in Applied Mathematics**106**(1): 1-45. [Retrieve PostScript] [Retrieve PostScript Diagrams] . - G. J. Reid and A. D. Wittkopf (2000),
*Determination of Maximal Symmetry Groups of Classes of Differential Equations*, Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation, 272-280 (acm press, New York). [Retrieve PostScript] [Retrieve PDF] . - I. G. Lisle and G. J. Reid (2000),
*Cartan Structure of Infinite Lie Pseudogroups*, To appear in*Geometric Approaches to Differential Equations*, edited by P. J. Vassiliou and I. G. Lisle, pp. 116-145 (Cambridge University Press). [Retrieve PostScript] [Retrieve PDF] . - C. J. Rust, G. J. Reid and A. D. Wittkopf (1999),
*Existence and Uniqueness Theorems for Formal Power Series Solutions of Analytic Differential Systems*, Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation, 105-112 (acm press, New York). [Retrieve PostScript] [Retrieve PDF] . - E. L. Mansfield, G. J. Reid and P. A. Clarkson (1998),
*Nonclassical Reductions of a 3+1-Cubic Nonlinear Schrödinger System*, Computer Physics Communications**115**, 460-488. [Retrieve PostScript] . - I. G. Lisle and G. J. Reid (1998),
*Geometry and structure from infinitesimal defining equations*, Journal of Symbolic Computation**26**, 355-379. [Retrieve gzipped PostScript] . - C. J. Rust and G. J. Reid (1997),
*Rankings of Partial Derivatives*, Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, 9-16 (acm press, New York). [Retrieve PostScript] [Retrieve DVI] . - G. J. Reid, A. D. Wittkopf and A. Boulton (1996),
*Reduction of systems of nonlinear partial differential equations to simplified involutive forms*. Eur. J. of Appl. Math.**7**604 - 635. [Retrieve gzipped PostScript] . - I. G. Lisle, G. J. Reid and A. Boulton (1995),
*Algorithmic determination of the structure of infinite symmetry groups of differential equations*, in Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation (acm press, New York). [Retrieve PostScript] [Retrieve DVI] . - G. J. Reid, D. T. Weih and A. D. Wittkopf (1993),
*A point symmetry group of a differential equation which can not be found using infinitesimal methods*, in Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, N. H. Ibragimov, M. Torrisi and A. Valenti (eds.), 311-316 (Kluwer Academic Publishers, Amsterdam). [Retrieve PostScript] [Retrieve DVI] . - G. J. Reid, I. G. Lisle, A. Boulton and A. D. Wittkopf
(1992),
*Algorithmic determination of commutation relations for Lie symmetry algebras of PDEs*, in Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation, edited by P. S. Wang, 63-68 (acm press, New York). [One of 50 accepted papers from over 130 submissions]. [Retrieve PostScript] [Retrieve DVI] . - G. J. Reid and A. Boulton (1991),
*Reduction of systems of differential equations to standard form and their integration using directed graphs*, in Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, edited by S. M. Watt, 308-312 (acm press, Bonn). [One of 55 accepted papers out of 208 submissions, see page iv of this reference]. - G. J. Reid (1991),
*Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution*, Eur. J. of Appl. Math.**2**, 293-318. - G. J. Reid (1991),
*Finding abstract Lie symmetry algebras of differential equations without integrating determining equations*, Eur. J. of Appl. Math.**2**, 319-340. - G. J. Reid (1990),
*A triangularization algorithm which determines the Lie symmetry algebra of any system of PDEs*, J. Phys. A: Math. Gen.**23**, 853-859. - G. W. Bluman and G. J. Reid (1989),
*Sequences of related linear PDEs*, J. of Math. Anal. and its Applns.,**144**, 565-585. - G. W. Bluman and G. J. Reid (1988),
*New classes of symmetries for ordinary differential equations*, IMA J. of Appl. Math.,**40**, 87-94. - G. W. Bluman, S. Kumei and G. J. Reid (1988),
*New classes of symmetries for partial differential equations*, J. of Math. Phys.,**29**, 806-811. - G. J. Reid (1988),
*Determination of the symmetries characterising separable systems in Euclidean spaces*, J. Phys. A: Math and Gen.,**21**, 353-362. - E. K. Blum and G. J. Reid (1988),
*On the numerical solution of three-dimensional boundary value problems by separation of variables*, SIAM J. Numerical Anal.,**25**, 75-90. - G. J. Reid (1986),
*R-separation for heat and Schrödinger equations*, SIAM J. Math. Anal.,**17**, 646-687. - E. G. Kalnins, W. Miller Jr. and G. J. Reid (1984),
*Separation of variables for complex Riemannian spaces of constant curvature I. Orthogonal coordinates for and*, Proceedings of the Royal Society,**394**, 183-206. - E. G. Kalnins and G. J. Reid (1982),
*R-separation for the Hamilton-Jacobi equation*, Letters in Math. Phys.**6**, 97-100.