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We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic…
Parameterized algebraic curves and surfaces are widely used in geometric modeling and their manipulation is an important task in the processing of geometric models. In particular, the determination of the intersection loci between points,…
We explore complex Riemannian geometry and Hermitian metrics on complex algebraic varieties and analytic spaces, respectively. In particular, we introduce Hermitian metrics on holomorphic Lie algebroids and examine the associated…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
The computational complexity of polynomial ideals and Gr\"obner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. Often we have hypergeometric functions with indices linear dependent on a small parameter with respect to which…
We study the set of algebraic numbers of bounded height and bounded degree where an analytic transcendental function takes algebraic values.
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
We survey recent developments on rationality problems for algebraic varieties, with a particular emphasis on cycle-theoretic and combinatorial methods and their applications to hypersurfaces.
We introduce the new sage_acsv package for the SageMath computer algebra system, allowing users to rigorously compute asymptotics for a large variety of multivariate sequences with rational generating functions. Using Sage's support for…
We present `liesuperalg` a SageMath package for representation-theoretic calculations involving Lie superalgebras in Type A. Our package introduces functionality to calculate invariants of weights and produce the associated cup diagrams. We…
We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gr\"obner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders…
Dwork's $p$-adic hypergeometric function is defined to be a ratio ${}_sF_{s-1}(t)/{}_sF_{s-1}(t^p)$ of hypergeometric power series. Dwork showed that it is a uniform limit of rational functions, and hence one can define special values on…
We consider the problem of computing sample points in each connected component of a semi-algebraic set defined by the non-vanishing or the positivity of an n-variate polynomial of degree d, with rational coefficients of bit size bounded by…