Related papers: A unified framework for the computation of polynom…
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…
We present a framework to decompose real multivariate polynomials while preserving invariance and positivity. This framework has been recently introduced for tensor decompositions, in particular for quantum many-body systems. Here we…
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
It is shown in this paper that non-conforming finite elements on the triangle using $P^{1}$-nonconforming polynomials and $P^{2}$ -conforming polynomials can be easily built and used.They appear as an 'enriched' version of the standard…
The nonvanishing problem asks if a coefficient of a polynomial is nonzero. Many families of polynomials in algebraic combinatorics admit combinatorial counting rules and simultaneously enjoy having saturated Newton polytopes (SNP). Thereby,…
The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is to expand the currently limited range of random polynomials…
It is known a method for converting a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we show a formula for systems of Boolean polynomial equations which is based on the…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
For quadratic spaces which represent 1 there is a characterization of hermitian compositions in the language of algebras-with-involutions using the even Clifford algebra. We extend this notion to define a generalized composition based on…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…
There are two well known tasks, related to Newton polyhedra: to study invariants of singularities in terms of their Newton polyhedra, and to describe Newton polyhedra of resultants and discriminants. We introduce so called resultantal…
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
We give an algorithm to compute weighted Ehrhart functions of lattice polytopes for polynomial weights using Lagrange interpolation. We show how to compute generating functions of polynomials using those of unit cubes and Eulerian numbers,…