Calculation of integrals in MathPartner

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...

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Autores principales:	Gennadi I. Malaschonok, Alexandr V. Seliverstov
Formato:	article
Lenguaje:	EN
Publicado:	Peoples’ Friendship University of Russia (RUDN University) 2021
Materias:	computer algebra system mathpartner integral arithmetic-geometric mean modified arithmetic-geometric mean lagutinski determinant Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/63c336dee7494afe8bb15dd250bb37dd
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spelling	oai:doaj.org-article:63c336dee7494afe8bb15dd250bb37dd2021-11-12T15:18:25ZCalculation of integrals in MathPartner2658-46702658-714910.22363/2658-4670-2021-29-4-337-346https://doaj.org/article/63c336dee7494afe8bb15dd250bb37dd2021-12-01T00:00:00Zhttp://journals.rudn.ru/miph/article/viewFile/29427/20002https://doaj.org/toc/2658-4670https://doaj.org/toc/2658-7149We 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.Gennadi I. MalaschonokAlexandr V. SeliverstovPeoples’ Friendship University of Russia (RUDN University)articlecomputer algebra systemmathpartnerintegralarithmetic-geometric meanmodified arithmetic-geometric meanlagutinski determinantmathpartnerElectronic computers. Computer scienceQA75.5-76.95ENDiscrete and Continuous Models and Applied Computational Science, Vol 29, Iss 4, Pp 337-346 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	computer algebra system mathpartner integral arithmetic-geometric mean modified arithmetic-geometric mean lagutinski determinant mathpartner Electronic computers. Computer science QA75.5-76.95
spellingShingle	computer algebra system mathpartner integral arithmetic-geometric mean modified arithmetic-geometric mean lagutinski determinant mathpartner Electronic computers. Computer science QA75.5-76.95 Gennadi I. Malaschonok Alexandr V. Seliverstov Calculation of integrals in MathPartner
description	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.
format	article
author	Gennadi I. Malaschonok Alexandr V. Seliverstov
author_facet	Gennadi I. Malaschonok Alexandr V. Seliverstov
author_sort	Gennadi I. Malaschonok
title	Calculation of integrals in MathPartner
title_short	Calculation of integrals in MathPartner
title_full	Calculation of integrals in MathPartner
title_fullStr	Calculation of integrals in MathPartner
title_full_unstemmed	Calculation of integrals in MathPartner
title_sort	calculation of integrals in mathpartner
publisher	Peoples’ Friendship University of Russia (RUDN University)
publishDate	2021
url	https://doaj.org/article/63c336dee7494afe8bb15dd250bb37dd
work_keys_str_mv	AT gennadiimalaschonok calculationofintegralsinmathpartner AT alexandrvseliverstov calculationofintegralsinmathpartner
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Calculation of integrals in MathPartner

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