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We consider the check of the involutive basis property in a polynomial context. In order to show that a finite generating set F of a polynomial ideal I is an involutive basis one must confirm two properties. Firstly, the set of leading terms of the elements of F has to be complete. Secondly, one has to prove that F is a Gröbner basis of I. The latter is the… (More)
Systems of polynomial equations often have symmetries. In solving such a system using Buchberger's algorithm, the symmetries are neglected. Incorporating symmetries into the solution process enables us to solve larger problems than with Buchberger's algorithm alone. This paper presents a method that shows how this can be achieved and also gives an algorithm… (More)
The computer algebra software CASA (Computer Algebra Software for Algebraic Geometry), which is based on the computer algebra system Maple, is being developed by the computer algebra group at RISC under the direction of F. Winkler. In this report, CASA is analyzed with respect to its current state and possible improvements. Finally, some improvements and… (More)
The dynamic pattern calculus described in this paper integrates the functional mechanism of the lambda-calculus and the capabilities of pattern matching with hedge variables, i.e., variables that can be instantiated by any finite sequence of terms. We propose a generic confluence proof, where the way pattern abstractions are applied in a non-deterministic… (More)
Preface Many groups around the world conduct research on formal methods for software development, and in most of these groups, some of the effort goes into the problem of reasoning about loops. There is of course a well-known classic way of dealing with loops, namely by having the software developer provide an invariant , which can be shown to be preserved… (More)
We describe the semantics of CLP(H): constraint logic programming over hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms, for hedges, and for function symbols. Constraints involve equations between unranked terms and atoms for regular hedge language membership. We give… (More)
Differential problems are ubiquitous in mathematical modeling of physical and scientific problems. Algebraic analysis of differential systems can help in determining qualitative and quantitative properties of solutions of such systems. In this tutorial paper we describe several algebraic methods for investigating differential systems.