A Las Vegas algorithm for computing the smith form of a nonsingular integer matrix

2020 ◽  
Author(s):  
Stavros Birmpilis ◽  
George Labahn ◽  
Arne Storjohann
Keyword(s):  
Las Vegas ◽  
Integer Matrix ◽  
Las Vegas Algorithm

Computing Vf modulo p

2011 ◽  
Author(s):  
Jean-Marc Couveignes
Keyword(s):  
Finite Fields ◽  
Algebraic Curves ◽  
Las Vegas ◽  
Jacobian Variety ◽  
Generating Sets ◽  
Monte Carlo Algorithms ◽  
Modulo P ◽  
Curves Over Finite Fields ◽  
Las Vegas Algorithm ◽  
Probabilistic Polynomial Time

This chapter addresses the problem of computing in the group of lsuperscript k-torsion rational points in the Jacobian variety of algebraic curves over finite fields, with an application to computing modular representations. An algorithm in this chapter usually means a probabilistic Las Vegas algorithm. In some places it gives deterministic or probabilistic Monte Carlo algorithms, but this will be stated explicitly. The main reason for using probabilistic Turing machines is that there is a need to construct generating sets for the Picard group of curves over finite fields. Solving such a problem in the deterministic world is out of reach at this time. The unique goal is to prove, as quickly as possible, that the problems studied in this chapter can be solved in probabilistic polynomial time.

scholarly journals A fast las vegas algorithm for triangulating a simple polygon

1989 ◽  
Vol 4 (5) ◽  
pp. 423-432 ◽  
Author(s):  
Kenneth L. Clarkson ◽  
Robert E. Tarjan ◽  
Christopher J. Van Wyk
Keyword(s):  
Las Vegas ◽  
Simple Polygon ◽  
Las Vegas Algorithm

On Random Symmetric Bimatrix Games

2020 ◽  
Vol 22 (03) ◽  
pp. 2050002
Author(s):  
József Abaffy ◽  
Ferenc Forgó
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
High Probability ◽  
Nash Equilibria ◽  
Las Vegas ◽  
Bimatrix Games ◽  
Las Vegas Algorithm

An experiment was conducted on a sample of [Formula: see text] randomly generated symmetric bimatrix games with size [Formula: see text] and [Formula: see text]. Distribution of support sizes and Nash equilibria are used to formulate a conjecture: for finding a symmetric NEP it is enough to check supports up to size [Formula: see text] whereas for nonsymmetric and all NEPs this number is [Formula: see text] and [Formula: see text], respectively. If true, this enables us to use a Las Vegas algorithm that finds a Nash equilibrium in polynomial time with high probability.

scholarly journals A Reduction Algorithm for Large-Base Primitive Permutation Groups

2006 ◽  
Vol 9 ◽  
pp. 159-173 ◽  
Author(s):  
Maska Law ◽  
Alice C. Niemeyer ◽  
Cheryl E. Praeger ◽  
Ákos Seress
Keyword(s):  
Permutation Group ◽  
Las Vegas ◽  
Linear Time ◽  
Symmetric Groups ◽  
Deterministic Algorithm ◽  
Primitive Permutation Group ◽  
Reduction Algorithm ◽  
Product Action ◽  
Speed Up ◽  
Las Vegas Algorithm

AbstractThe authors present a nearly linear-time Las Vegas algorithm that, given a large-base primitive permutation group, constructs its natural imprimitive representation. A large-base primitive permutation group is a subgroup of a wreath product of symmetric groups Sn and Sr in product action on r-tuples of k-element subsets of {1, …, n}, containing Anr. The algorithm is a randomised speed-up of a deterministic algorithm of Babai, Luks, and Seress.

scholarly journals Champ: a Cherednik algebraMagmapackage

2015 ◽  
Vol 18 (1) ◽  
pp. 266-307 ◽  
Author(s):  
U. Thiel
Keyword(s):  
Las Vegas ◽  
Module Structure ◽  
Verma Modules ◽  
Reflection Groups ◽  
Cherednik Algebras ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Rational Cherednik Algebra ◽  
Las Vegas Algorithm ◽  
Rational Cherednik Algebras

We present a computer algebra package based onMagmafor performing computations in rational Cherednik algebras with arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general Las Vegas algorithm for computing the head and the constituents of a module with simple head in characteristic zero, which we develop here theoretically. This algorithm is very successful when applied to Verma modules for restricted rational Cherednik algebras and it allows us to answer several questions posed by Gordon in some specific cases. We can determine the decomposition matrices of the Verma modules, the graded$G$-module structure of the simple modules, and the Calogero–Moser families of the generic restricted rational Cherednik algebra for around half of the exceptional complex reflection groups. In this way we can also confirm Martino’s conjecture for several exceptional complex reflection groups.Supplementary materials are available with this article.

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