Related papers: Roots of unity in orders

Recent work has shown that not only decision trees (DTs) may not be interpretable but also proposed a polynomial-time algorithm for computing one PI-explanation of a DT. This paper shows that for a wide range of classifiers, globally…

A set of Maple V R.3/4 computer algebra routines for the analytical solving of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of commands includes a 1st. order ODE-solver and routines for, among other things: the…

The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\mathbb{Q} G$…

We consider $m \times s$ matrices (with $m\geq s$) in a real affine subspace of dimension $n$. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is…

We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…

We give a separation bound for the complex roots of a trinomial $f \in \mathbb{Z}[X]$. The logarithm of the inverse of our separation bound is polynomial in the size of the sparse encoding of $f$; in particular, it is polynomial in $\log…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

We classify the polynomials with integral coefficients that, when evaluated on a group element of finite order $n$, define a unit in the integral group ring for infinitely many positive integers $n$. We show that this happens if and only if…

We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…

We prove that for any fixed d the generating function of the projection of the set of integer points in a rational d-dimensional polytope can be computed in polynomial time. As a corollary, we deduce that various interesting sets of lattice…

This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability…

We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under…

We present a combination of two algorithms that accurately calculate multiple roots of general polynomials. Algorithm I transforms the singular root-finding into a regular nonlinear least squares problem on a pejorative manifold, and…

We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the…

We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…

We systematically study the computational complexity of a broad class of computational problems in phylogenetic reconstruction. The class contains for example the rooted triple consistency problem, forbidden subtree problems, the quartet…

For certain polynomials we relate the number of roots inside the unit circle with the index of a non-degenerate isolated umbilic point on a real analytic surface in Euclidean 3-space. In particular, for $N>0$ we prove that for a certain…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two-parameter eigenvalue problem. The first determinantal…