Complete involutive rewriting systems

Involutive Bases of Polynomial Ideals

In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial the self-consistent separation of the whole set of variables into two disjoint subsets. They are cal...

Proving termination using dependent types: the case of XOR-terms

We study a normalization function in an algebra of terms quotiented by an associative, commutative and involutive operator (logical xor). This study is motivated by the formal verification of cryptographic systems, where a normalization function for xor-terms turns out to play a key role. Such a function is easy to define using general recursion. However, as it is to be used in a type theoretic...

Comprehensive Involutive Systems

In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal f...

Complete Growth Series of Coxeter Groups with more than Three Generators

Simplifying Numerical Solution of Constrained Pde Systems through Involutive Completion

When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite genera...