Several decades have passed since J. F. Ritt and E. R. Kolchin introduced algebraic methods to study differential equations and their solutions. An early application of their theory is the well-known Risch algorithm for integration in finite terms. Another, more recent, one is Kovacic's algorithm for solving a second order ordinary differential equation. While these algorithms (and their generalizations) work in theory, implementation posts many challenging algorithmic subproblems, many of which are purely algebraic in nature.

After the phenomenal success of Buchberger's algorithm and its many generalizations, some researchers began to turn to similar techniques for algebraic differential equations. It was quickly realized that the differential analogues, where these exist, are far more complicated than their algebraic counterparts.

The time is ripe to focus on the recent advances and make these results and problems known to the general symbolic computation community. We invite submissions for a special issue on Differential Equations and Differential Algebra.

The special issue will be a collection of mostly original works that report new research results in the area of differential equations and differential algebra. These will be supplemented with one or more tutorials that survey the field. Each original paper should contribute to the mathematical foundation for symbolic computation algorithms in these areas. Results should promote the advancement in the design and implementation of algorithms for related problems. Topics relevant to the special issue include, but are not restricted to:

- symbolic methods for simplifying or solving ordinary or partial differential polynomial systems;
- algorithms for factoring linear differential operators;
- differential Galois theory, the inverse problem, and symbolic algorithms for linear ordinary differential equations;
- algorithms for symbolic integration;
- differential Grobner bases, characteristic sets, differential resultants, and decision problems for differential polynomial ideals;
- general component and singular components of differential polynomial systems;
- differential dimensions and differential birational invariants of differential polynomial systems;
- applications of pure mathematics (such as combinatorics and hopf algebra) to algorithmic aspects of differential equations and differential algebra;
- difference algebra, symbolic summation, difference Galois theory, symbolic algorithms for difference and q-difference equations;
- applications requiring symbolic manipulation of differential equations or of their solutions (for example, in control systems or error correcting codes);
- symbolic computations of differential algebraic groups;
- algorithms for computing first integrals of dynamical systems;
- software design problems specific to symbolic methods in differential equations;
- efficient implementation of such algorithms, and their interface with existing computer algebra libraries;

Guidelines for submittal of JSC manuscripts and the JSC style files can be found at the URL http://www.cis.udel.edu/~caviness/jsc.html.

Manuscripts may be submitted electronically in TeX, LaTeX, AMSTeX, or uuencoded-gzipped PS, but LaTeX using the JSC style files is preferred. Please send these to one of the two guest-editors who will handle the preparation of this special issue. All manuscripts will be peer-reviewed according to the rules of JSC. A letter (or e-mail) of intent to submit a paper (including author(s) information, a title, an abstract, and an estimated number of pages) will be much appreciated. We strongly encourage early submissions.

Revised deadline for submission of full papers: 14 September, 1997 Notification of acceptance/rejection: 1 March, 1998 Final revised manuscripts due: 1 July, 1998 Appearance of special issue: 1998/1999

Guest Editors:

William Sit Manuel Bronstein Department of Mathematics Scientific Computation Institute The City College of New York ETH Zentrum IFW 160 Convent Avenue CH-8092 Zurich New York, NY 10031 Switzerland United States of America bronstein@inf.ethz.chwyscc@cunyvm.cuny.edu