Objectif Completion to involution is a fundamental technology for dealing with general systems of partial differential equations. This can already be seen from their close relationship to Gröbner bases for polynomial ideals. Completion alone does not directly answer many questions about a given system; but without a suitable basis many questions cannot be answered at all. It is not difficult to forecast that very soon involution will play in the theory of differential equations a similar role as Gröbner bases already do now in commutative algebra and algebraic geometry.The project is divided into three equally important tasks: fundamental theory, completion algorithms, applications. The main objective of the first task is to obtain a deeper understanding of the meaning of involution. Involution will be compared to classical concepts in differential algebra like Gröbner bases or characteristic sets; in addition the Spencer cohomology will be studied in detail. As a result the foundation of involution will become much clearer which is not only of considerable scientific interest but also very important for the design of algorithms.The objective of the second task is to provide efficient implementations of completion algorithms for linear and non-linear differential systems (algebraic equations are considered as a special case of linear differential systems) on several platforms. This includes a geometric version of the algorithms which allows for the computation of intrinsic results independent of the used co-ordinate system.As in the purely algebraic case, the complexity of the completion represents a major obstacle. For this reason so much emphasis is put on algorithmic aspects. Without fast computer algebra programs no progress can be achieved in this field. Consequently, the teams deliberately did not choose to select just one specific computer algebra system for implementing the algorithms. Instead, efficient implementations for a number of systems will result from the project which is crucial for spreading the use of involutive techniques in applied mathematics.The objective of the third task is to demonstrate the power of involution in applications. Both group analysis of differential equations (with special emphasis on viscous heat conducting gas dynamics) and the symbolic and numerical analysis of constrained mechanical systems will be studied. In the first case, the results will not only be new exact solutions of an important physical model but also new techniques to handle extremely large differential systems. In the latter case, the main theoretical result will be the unification of some physical and numerical theories in a single framework. In addition, the prototype of a combined symbolic-numerical environment for treating constrained systems will be developed.The project unites some of the leading teams in the field of involution. All participating teams have already made important contributions in this field. Their collaboration within the project will lead to further significant progress. Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Thème(s) 4 - Life Sciences OPEN - OPEN Call Appel à propositions Data not available Régime de financement Data not available Coordinateur University of Wales, Aberystwyth Contribution de l’UE Aucune donnée Adresse Edward Lloyd Building SY23 3DA Aberystwyth Royaume-Uni Voir sur la carte Coût total Aucune donnée Participants (5) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire Horticulture Research International Royaume-Uni Contribution de l’UE Aucune donnée Adresse Wellesbourne CV35 9EF Warwick Voir sur la carte Coût total Aucune donnée Leiden University Pays-Bas Contribution de l’UE Aucune donnée Adresse Wassenarseweg 64 2333 AL Leiden Voir sur la carte Coût total Aucune donnée Pushchino branch of Shemyakin and Ovchinnikov Russie Contribution de l’UE Aucune donnée Adresse Institutkaya 6 142292 Pushchino, Moscow Region Voir sur la carte Coût total Aucune donnée Russian Academy of Sciences Russie Contribution de l’UE Aucune donnée Adresse 35 Botanicheskaya 127276 Moscow Voir sur la carte Coût total Aucune donnée Russian Academy of Sciences Russie Contribution de l’UE Aucune donnée Adresse 69 Prospect Oktyabrya 450054 Ufa Voir sur la carte Coût total Aucune donnée