Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2942710.22363/2658-4670-2021-29-4-337-346ArticlesСтатьиResearch ArticleCalculation of integrals in MathPartnerВычисление интегралов в MathPartnerhttps://orcid.org/0000-0002-9698-6374MalaschonokGennadi I.МалашонокГ. И.

Doctor of Physical and Mathematical Sciences, Professor, Department of Informatics

malaschonok@gmail.comhttps://orcid.org/0000-0003-4746-6396SeliverstovAlexandr V.СеливерстовА. В.

Candidate of Physical and Mathematical Sciences, Leading researcher

slvstv@iitp.ruNational University of Kyiv-Mohyla AcademyНациональный университет «Киево-Могилянская академия»Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)Институт проблем передачи информации им. А.А. Харкевича РАН12112021294VOL 29, NO4 (2021)ТОМ 29, №4 (2021)33734612112021Copyright ©; 2021, Malaschonok G.I., Seliverstov A.V.Copyright ©; 2021, Малашонок Г.И., Селиверстов А.В.2021Malaschonok G.I., Seliverstov A.V.Малашонок Г.И., Селиверстов А.В.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/29427

We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for elementary functions. Certain integrals, including improper integrals, can be calculated using numerical algorithms. In this case, every user has the ability to indicate the required accuracy with which he needs to know the numerical value of the integral. We highlight special functions allowing us to calculate complete elliptic integrals. These include functions for calculating the arithmetic-geometric mean and the geometric-harmonic mean, which allow us to calculate the complete elliptic integrals of the first kind. The set also includes the modified arithmetic-geometric mean, proposed by Semjon Adlaj, which allows us to calculate the complete elliptic integrals of the second kind as well as the circumference of an ellipse. The Lagutinski algorithm is of particular interest. For given differentiation in the field of bivariate rational functions, one can decide whether there exists a rational integral. The algorithm is based on calculating the Lagutinski determinant. This year we are celebrating 150th anniversary of Mikhail Lagutinski.

В статье рассмотрены возможности сервиса MathPartner по вычислению определённых и неопределённых интегралов. MathPartner содержит программную реализацию алгоритма Риша и предоставляет пользователям возможность вычислять первообразные для элементарных функций. Некоторые интегралы, в том числе несобственные, можно вычислить с помощью численных алгоритмов. В этом случае каждый пользователь может указать необходимую точность, с которой ему необходимо знать числовое значение интеграла. Отметим специальные функции, которые позволяют вычислять полные эллиптические интегралы. К ним относятся функции для вычисления арифметико-геометрического среднего и геометрическо-гармонического среднего, которые позволяют вычислять полные эллиптические интегралы первого рода. Набор также включает модифицированное арифметико-геометрическое среднее, которое предложил Семён Адлай, что позволяет вычислять полные эллиптические интегралы второго рода и длину (периметр) эллипса. Особый интерес представляет алгоритм Лагутинского. Для данного дифференцирования в поле рациональных функций от двух переменных можно решить, существует ли рациональный интеграл. Алгоритм основан на вычислении определителя Лагутинского. В этом году мы отмечаем 150-летие со дня рождения Михаила Лагутинского.

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