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We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron $\mathcal{P}(A,\mathbf{1})=\{x\in\RR^n \mid Ax\geq \b1,~x\geq \b0\}$, when $A$ is a totally unimodular matrix. Our algorithm is based on…
We construct an algorithm for the minimal model program in dimension three over the field of algebraic numbers. As auxiliary results, we also construct algorithms for computing bigraded global Hom modules and for computing Stein…
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…
In this paper we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer assisted analysis of integrability of dynamical systems. We sketch some of the algebraic methods of studying…
We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
We present a deterministic algorithm which, given a graph G with n vertices and an integer 1<m < n, computes in n^{O(ln m)} time the sum of weights w(S) over all m-subsets S of the set of vertices of G, where w(S)=exp{gamma t m +O(1/m)}…
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We…
Weyl groups are ubiquitous, and efficient algorithms for them -- especially for the exceptional algebras -- are clearly desirable. In this paper we provide several of these, addressing practical concerns arising naturally for instance in…
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the…
We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms. The aim of this algorithm is to be fast enough for…
We study a category of Whittaker modules over a complex semisimple Lie algebra by realizing it as a category of twisted D-modules on the associated flag variety using Beilinson-Bernstein localization. The main result of this paper is the…
We present an algorithm to compute values L(s) and derivatives of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Gamma-factor is a product of any number of…
IGraph/M is an efficient general purpose graph theory and network analysis package for Mathematica. IGraph/M serves as the Wolfram Language interfaces to the igraph C library, and also provides several unique pieces of functionality not yet…
Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case…
We present process-algebraic models of multi-writer multi-reader safe, regular and atomic registers. We establish the relationship between our models and alternative versions presented in the literature. We use our models to formally…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…