Related papers: A Package of Programs for Determination of Some Cl…
We consider Galois/monodromy groups arising in computer vision applications, with a view towards building more efficient polynomial solvers. The Galois/monodromy group allows us to decide when a given problem decomposes into algebraic…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
A spherical three-distance set is a finite collection $X$ of unit vectors in $\mathbb{R}^{n}$ such that for each pair of distinct vectors has three inner product values. We use the semidefinite programming method to improve the upper bounds…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
Three programs in Mathematica are presented, which produce expressions for the lowest order and the higher order corrections of the Phase Integral Approximation. First program is pertinent to one ordinary differential equation of the…
We classify decompositions of simple special finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic zero into the sum of two proper simple subsuperalgebras.
This note explains how to obtain, install, and use the ratpoints program. The program finds rational points up to a specified height on hyperelliptic curves using a highly optimized quadratic sieving algorithm.
This work gives a classification of imprimitive irreducible finite subgroups of the orthogonal group O(7) plus the number of conjugate classes for each group.
Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies the bound $|H|^3 \ge |G|$. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an…
In this paper we survey a new criteria for solvability of finite groups in terms of number of supersolvable (also known as polycyclic) and non-supersolvable subgroups. In particular, we present original examples of supersolvable groups such…
In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential.…
We describe an algorithm which determines whether or not a group which is hyperbolic relative to abelian groups admits a nontrivial splitting over a finite group.
We introduce the class of constant probability (CP) programs and show that classical results from probability theory directly yield a simple decision procedure for (positive) almost sure termination of programs in this class. Moreover,…
We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.
The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to…
With the help of a new program, we do computations concerning the Witten-Reshetikhin-Turaev representations of mapping class groups. In particular we distinguish some mutant fibered knots. The program can be downloaded from…
A computing program in Matlab is given that computes amplitudes in scalar $\phi^3$ theory. The program is partitioned into several parts and a simple guide is given for its use.
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
We give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups.