Thomas Decomposition of Algebraic and Differential Systems

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple

On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains

International audienceThis paper provides an algorithm which computes the normal form of a rational differential fraction modulo a regular differential chain if, and only if, this normal form exists. A regularity test for polynomials modulo regular chains is revisited in the nondifferential setting and lifted to differential algebra. A new characterization of regular chains is provided

Determination of set-membership identifiability sets

International audienceThis paper concerns the concept of set-membership identifiability introduced in \cite{jauberthie}. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely {\it mincing}, {\it evaluating} and {\it regularization} (\cite{jaulin2}). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.Comment: 39 page

Constructions of free commutative integro-differential algebras

In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004

Zero estimates on group varieties II

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46615/1/222_2005_Article_BF01388605.pd