title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð´Ð²ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼ ÑÑÑÐ¾Ð³Ð¸Ñ Ð¸ Ð½ÐµÑÑÑÐ¾Ð³Ð¸Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: The implementation of two algorithms for solving systems of strict and nonstrict linear inequalities
Creators: name: Ð¨Ð¾Ð±ÐµÑÐ³, ÐÐµÐ¾ÑÐ³Ð¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÑÐ¾Ð³Ð¸Ñ Ð¸ Ð½ÐµÑÑÑÐ¾Ð³Ð¸Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²
ÑÐµÑÐµÐ½Ð¸Ðµ ÑÐ¸ÑÑÐµÐ¼ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²
Ð¼ÐµÑÐ¾Ð´ Ð¸ÑÐºÐ»ÑÑÐµÐ½Ð¸Ð¹ Ð¤ÑÑÑÐµ-ÐÐ¾ÑÐºÐ¸Ð½Ð°
systems of strict and nonstrict linear inequalities
solution of systems of linear inequalities
FourierâMotzkin elimination method

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description: The given work is devoted to the implementation of the Fourier-Motzkin elimination method and polynomial algorithm for checking the consistency and solving systems of strict and nonstrict linear inequalities in rational numbers. In the course of this work the following tasks were solved: Â  Â  1. Review the known algorithms for solving this problem and related problems, as well as their implementations. Â  Â  2. Modify Fourier-Motzkin elimination method of exceptions to work with systems of strict and nonstrict linear inequalities and extend it to their solution. Â  Â  3. Identify a polynomial algorithm for checking the consistency of strict and nonstrict linear inequalities and extend it to their solution. Â  Â  4. Implement the selected algorithms. Â  Â  5. Test the implemented algorithms and experimentally compare their performance with other implementations. The paper provides a formal description of the modification of Fourier-Motzkin elimination method to work with systems containing strict inequalities, as well as an extension of this method and polynomial algorithm for checking the consistency of systems of strict and nonstrict linear inequalities to solve such systems. As a result, these algorithms were implemented in Java language, in a form that allows to work with rational numbers of arbitrary precision.