Foreword

This Special Issue is dedicated to the memory of Vladimir P. Gerdt (January 21, 1947–January 5, 2021), distinguished researcher, collaborator, communicator, teacher, and friend. He was a full professor at the Joint Institute for Nuclear Research (JINR), Dubna, Russia, and head (from 1983) of the Computer Algebra Research Group, resp. the Research Group on Algebraic and Quantum Computation, at JINR, and a well known and respected member of the computer algebra community.

Both editors of this Special Issue got to know Vladimir very well through his regular visits to Germany (in particular, to Aachen and to Kassel), joint research projects, workshop organization, and not least, meetings at conferences. In fact, both of us had immediate next steps on our agendas for our respective collaborations with Vladimir, which came to a sudden end.

On January 5, 2021, we very sadly received a message from his son Anton informing us about Vladimir’s death earlier on that day. In the months to come, various activities commemorating Vladimir took place internationally, of which we mention, e.g., a pre-conference workshop of ISSAC 2021, organized as a hybrid event in St. Petersburg. At ACA conferences a contributed session on computational aspects and applications of differential algebra and difference algebra has regularly been organized by Vladimir and co-organizers. The ACA 2021 edition (online) of this session, organized by Roberto La Scala, Alexander Levin and Daniel Robertz, was dedicated to his memory. Vladimir having been the co-founder (with Ernst W. Mayr) of the CASC conference series, the proceedings of the 23rd CASC conference in Sochi 2021, published as volume 12865 of the Springer series Lecture Notes in Computer Science, contains an extensive obituary (also reprinted in Journal of Symbolic Computation 109 (2022), pp. 50–56).

For this Special Issue we have collected contributions of two kinds: refereed research papers as well as short memory notes. The latter may resonate with those readers familiar with Vladimir and may shed a light on Vladimir’s character for those who were not.

We appreciate both kinds of contributions and would like to thank the authors for their valuable work and for their generosity to share their memories of Vladimir. We also would like to thank the referees of the research papers.

While we are not able to cover all aspects of Vladimir’s research interest—we miss, e.g., quantum computation—we do hope that the articles in this issue altogether convey an impression of the research themes that Vladimir cared about deeply. Of course, these themes are in the realm of computer algebra and scientific computing, often related to differential equations, or difference equations, and to polynomial systems, their exact and numerical solutions, their symmetries, and their applications to physics, etc. Vladimir and collaborators coined the notion of involutive division and involutive basis. Hence, two research papers in this special issue contribute to this topic as well.