相关论文: A Maple Package for Computing Groebner Bases for L…

The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple component choices whereas ensuring a given system reliability level. The obtained model is a nonlinear integer programming…

This paper presents an algorithm for computing Groebner bases based upon labeled polynomials and ideas from the algorithm F5. The main highlights of this algorithm compared with analogues are simplicity both of the algorithm and of the its…

We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis…

The efficiency of Gr\"obner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum of possible monomial orders, most implementations rely on…

We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…

This paper presents a conception for computing gr\"{o}bner basis. We convert some of gr\"{o}bner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem…

In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a…

We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…

We describe the \proglang{R} package \pkg{glmmrBase} and an extension \pkg{glmmrOptim}. \pkg{glmmrBase} provides a flexible approach to specifying, fitting, and analysing generalised linear mixed models. We use an object-orientated class…

We describe Maple packages for the automatic generation of generating functions(and series expansions) for counting lattice animals(fixed polyominoes), in the two-dimensional hexagonal lattice, of bounded but arbitrary width. Our Maple…

We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…

Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis…

Training deep learning (DL) models across Graphics Processing Unit (GPU) clusters is technically challenging. One aspect is that users have to compose command lines to adapt to the heterogeneous launchers, schedulers, affinity options, DL…

Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or…

We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a commutative field K of characteristic zero. In order to reach explicit representatives of some generators of…

Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this by examples coming from actual operator statements and…

Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…

This paper is a sequel of our previous work in which we introduced the MapDE algorithm to determine the existence of analytic invertible mappings of an input (source) differential polynomial system (DPS) to a specific target DPS, and…

The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the…