Investigation of the existence domain for Dyakonov surface waves in the Sage computer algebra system

Surface electromagnetic waves (Dyakonov waves) propagating along a plane interface between an isotropic substance with a constant dielectric constant and an anisotropic crystal, whose dielectric tensor has a symmetry axis directed along the interface, are considered. It is well known that the question of the existence of such surface waves is reduced to the question of the existence of a solution to a certain system of algebraic equations and inequalities. In the present work, this system is investigated in the Sage computer algebra system. The built-in technique of exceptional ideals in Sage made it possible to describe the solution of a system of algebraic equations parametrically using a single parameter, with all the original quantities expressed in terms of this parameter using radicals. The remaining inequalities were only partially investigated analytically. For a complete study of the solvability of the system of equations and inequalities, a symbolic-numerical algorithm is proposed and implemented in Sage, and the results of computer experiments are presented. Based on these results, conclusions were drawn that require further theoretical substantiation.

Mathematical experiment as a tool for modeling the freight transportation process

The process of multimodal freight transportation on a railway loop is investigated, for which a multicriteria optimization model with time indicators is created, which is a nonlinear integer programming problem. The developed approach is based on egalitarian and utilitarian principles in the welfare theory and allows (along with Pareto optimal transportation plans) to find other plans that can be considered rational from the point of view of maintaining the balance of interests of the transportation process participants. A mathematical experiment is an effective heuristic tool in research. The algorithm for solving the optimization problem is implemented in the environment of a computer algebra system and brought to numerical results.

Tonality analysis in Wolfram Mathematica 12 computer algebra system

Sentiment analysis is a class of methods that are used to automatically determine the tonality of statements in the text. There are many solutions and technologies to define of text tonality at the moment and the choice depends on task. With the release of Wolfram Mathematica 12 versions, it became possible to use included nlp methods for determination of text tonality. This article is about definition of text tonality in the wolfram Mathematica 12 using nlp and compare nlp methods with standard definition function.

Mathematical logic: construction of logic circuits from logical elements in Maple

В статье рассматриваются возможности применения библиотеки Logic системы компьютерной алгебры Maple в аспекте компьютерного моделирования логических схем в различных базисах. Смоделированы основные логические элементы в Maple. На конкретном примере детально представлен алгоритм построения логической схемы в различных базисах. The article discusses the possibilities of using the Logic library of the Maple computer algebra system in the aspect of computer modeling of logic circuits in various bases. Basic logic gates are modeled in Maple. On a specific example, an algorithm for constructing a logical circuit in various bases is presented in detail.

ReLie: A Reduce Program for Lie Group Analysis of Differential Equations

Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, along the years many computer algebra packages have been developed to automate the computation. In this paper, we describe the program ReLie, written in the Computer Algebra System Reduce, since 2008 an open source program for all platforms. ReLie is able to perform almost automatically the needed computations for Lie symmetry analysis of differential equations. Its source code is freely available too. The use of the program is illustrated by means of some examples; nevertheless, it is to be underlined that it proves effective also for more complex computations where one has to deal with very large expressions.

Calculus and Digital Natives in Rendezvous: wxMaxima Impact

This article covers how a computer algebra system (CAS) wxMaxima can be explored for teaching single-variable and multivariable calculus to Korean digital natives. We present several examples where wxMaxima can handle calculus problems easily, not straightforwardly but still successfully with some human intervention, and unsuccessfully. By soliciting qualitative feedback on students’ experience in exploiting the CAS, we gathered a mixed reaction. Although some students commented positively, the majority seemed to be resistant to embracing a new technological tool.

FAST NETWORK CODING SIMULATION WITH PARALLELIZATION OF PROCESSES IN THE DTSMS SYSTEM

Изложены принципы быстрого имитационного моделирования процедур сетевого кодирования с распараллеливанием процессов в многоядерных ЭВМ на основе разработанной системы моделирования DTSMS. Представлены способы и схемы взаимодействия элементов модели с реализацией модели сети в соответствии с общепринятой в сетевом кодировании архитектурой «бабочка» для последовательного и асинхронного режимов работы. Выполнена оценка объема выделяемой памяти и времени моделирования для DTSMS в сравнении с реализацией на открытой системе компьютерной алгебры GNU/Octave. The principles of fast network coding simulation with parallelization of processes in multicore computers based on the developed DTSMS simulation system are stated. Methods and schemes of the sequential and asynchronous model elements interaction within the framework of the "butterfly" network model architecture generally accepted in network coding are presented. The allocated memory amount and simulation time for DTSMS are estimated in comparison with the open computer algebra system GNU/Octave.

A Comparative Study of Pricing Option with Efficient Methods

Our main objective of this paper is to introduce four individual techniques of pricing options; the techniques are Binomial method, Trinomial method, Monte Carlo simulation and Black-Scholes-Merton model. Because they play a significant role in option valuation of stock price dynamics, risk managements as well as stock market. In this paper, we briefly discuss all these four methods with their properties and behavior. We also focused on numerical technique for the higher accuracy of option pricing and compare them graphically. We use the Computer Algebra System (CAS) Python (Edition 2019.3.1) for this purpose. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 1-7

Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System

With the help of computer algebra system-Mathematica, this paper considers the weak center problem and local critical periods for bi-center of a [Formula: see text]-equivariant quintic system with eight parameters. The order of weak bi-center is identified and the exact maximum bifurcation number of critical periods generated from the bi-center is given via the combination of symbolic calculation and numerical analysis.