Related papers: Computing algebraic numbers of bounded height
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Consider a semi-algebraic set A in R^d constructed from the sets which are determined by inequalities p_i(x)>0, p_i(x)\ge 0, or p_i(x)=0 for a given list of polynomials p_1,...,p_m. We prove several statements that fit into the following…
Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results…
Here we present some revised arguments to a randomized algorithm proposed by Sudan to find the polynomials of bounded degree agreeing on a dense fraction of a set of points in $\mathbb{F}^{2}$ for some field $\mathbb{F}$.
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
We give a partial answer to a question attributed to Chris Miller on algebraic values of certain transcendental functions of order less than one. We obtain C(logH)^n bounds for the number of algebraic points of height at most H on certain…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
We extend coded distributed computing over finite fields to allow the number of workers to be larger than the field size. We give codes that work for fully general matrix multiplication and show that in this case we serendipitously have…
The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on…
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with…
We report on implementations for algorithms treating algebraic and arithmetic properties of hypergeometric functions in the computer algebra system SageMath. We treat hypergeometric series over the rational numbers, over finite fields, and…
We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the…
We provide an algorithmic description of a family of graded decomposition numbers for rational Cherednik algebras.
We present an algorithm which computes the Landau constant up to any given precision.
We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…