Related papers: Canonical forms for matrix tuples in polynomial ti…
In the work are defined the concepts semi-canonical and canonical binary matrix. What is described is an algorithm solving the combinatorial problem for finding the semi-canonical matrices in the set \Lambda_n^k consisting of all n\times n…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form.…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
We propose a polynomial time $f$-algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over $\mathbb{F}_q$) for computing an isomorphism (if there is any) of a finite dimensional…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
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…
We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to…
Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical algorithm to test nilpotency of…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We describe a family of new algorithms for finding the canonical image of a set of points under the action of a permutation group. This family of algorithms makes use of the orbit structure of the group, and a chain of subgroups of the…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
The work considers an equivalence relation in the set of all $n\times m$ matrices with entries in the set $[p]=\{ 0,1,\ldots , p-1 \}$. In each element of the factor-set generated by this relation, we define the concept of canonical matrix,…
In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently,…
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…
This paper concerns the enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field. This is the same as the classification of commuting tuples of matrices over a finite field up to…