Related papers: Numerical computation of braid groups
We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm…
We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then…
We present an algorithm for computing the set of torsion points satisfying a given system of multivariate polynomial equations. Its complexity is quasilinear in the logarithm of the degree of the input equations and exponential in their…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
We describe a procedure which verifies that a group given by generators and relators is word-hyperbolic. This procedure always works with a group which is word-hyperbolic, provided there is sufficient memory and time devoted to the problem.…
A hyperplane arrangement in $\mathbb{R}^n$ is a finite collection of affine hyperplanes. The regions are the connected components of the complement of these hyperplanes. By a theorem of Zaslavsky, the number of regions of a hyperplane…
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n^2 \log n)$ algorithm to compute the number of pairs of…
The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some…
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
An algorithm is given to compute a normal form for hyperelliptic curves. The elliptic case has been treated in a previous paper. In this paper the hyperelliptic case is treated.
We present an algorithm that computes the Hasse-Witt matrix of given hyperelliptic curve over Q at all primes of good reduction up to a given bound N. It is simpler and faster than the previous algorithm developed by the authors.
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the…
We propose a method for computing upper bounds for the Heilbronn problem for triangles.
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are introduced and investigated. Furthermore,…
In this paper, we present efficient algorithms for computing the number of points and the order of the Jacobian group of a superelliptic curve over finite fields of prime order p. Our method employs the Hasse-Weil bounds in conjunction with…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…