Related papers: Involutive Division Technique: Some Generalization…

This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals…

Geometric involutive bases for polynomial systems of equations have their origin in the prolongation and projection methods of the geometers Cartan and Kuranishi for systems of PDE. They are useful for numerical ideal membership testing and…

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…

Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…

In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…

We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural…

We prove that any finite-degree polynomial functor is topologically Noetherian. This theorem is motivated by the recent resolution of Stillman's conjecture and a recent Noetherianity proof for the space of cubics. Via work by…

Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. Once a Groebner basis is certified for the defining ideal I of the…

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory. We show that the sets of partitions ordered with a simple…

In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…

In this paper, we make a contribution to the computation of Gr\"obner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we…

We construct abelian categories of integral Nori motivic sheaves over a scheme of characteristic zero. The first step is to study the presentable derived category of Nori motives over a field. Next we construct an algebra in \'etale motives…

We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can…

We show a new algorithm and its implementation for multiplying bit-polynomials of large degrees. The algorithm is based on evaluating polynomials at a specific set comprising a natural set for evaluation with additive FFT and a high order…

We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…

In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on…

A classification of multiplication modules over multiplication rings with finitely many minimal primes is obtained. A characterisation of multiplication rings with finitely many minimal primes is given via faithful, Noetherian, distributive…