New Features in MathPartner 2021

Gennadi Malaschonok; Alexandr Seliverstov

doi:10.32603/2071-2340-2021-3-29-40

Gennadi Malaschonok National University of Kyiv-Mohyla Academy, Skovorody vul. 2, Kyiv 04070, Ukraine http://orcid.org/0000-0002-9698-6374
Alexandr Seliverstov Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 19 Bolshoy Karetny pereulok, bild. 1, 127051, Moscow, Russia http://orcid.org/0000-0003-4746-6396

DOI: https://doi.org/10.32603/2071-2340-2021-3-29-40

Keywords: computer algebra, arithmetic-geometric mean, geometric-harmonic mean, complete elliptic integral, pendulum, Sylvester matrix, Bruhat decomposition, LDU decom- position, QR decomposition, Cholesky decomposition, modern teaching technologies.

Abstract

We introduce new features in the MathPartner service that have recently become available to users. We highlight the functions for calculating both arithmetic-geometric mean and geometric-harmonic mean. They allow calculating complete elliptic integrals of the first kind. They are useful for solving many physics problems, for example, one can calculate the period of a simple pendulum. Next, one can calculate the modified arithmetic-geometric mean proposed by Semjon Adlaj. Consequently, one can calculate the complete elliptic integrals of the second kind as well as the circumference of an ellipse. Furthermore, one
can also calculate the Sylvester matrices of the first and the second kind. Thus, by means of a few strings, one can calculate the resultant of two polynomials as well as the discriminant of a binary form. Some new matrix functions are also added. So, today the list of matrix functions includes the transpose, adjugate, conjugate, inverse, generalized inverse, and pseudo inverse of a matrix, the matrix determinant, the kernel, the echelon form, the characteristic polynomial, the Bruhat decomposition, the triangular LDU decomposition, which is an exact block recursive LU decomposition, the QR block recursive decomposition, and the singular value decomposition. In addition, two block-recursive functions have been implemented for calculating the Cholesky decomposition of symmetric positive-definite matrices: one function for sparse matrices with the standard multiplication algorithm and another function for dense matrices with multiplication according to the Winograd–Strassen algorithm. The linear programming problems can be solved too. So, the MathPartner service has become better and handy. It is freely available at http://mathpar.ukma.edu.ua/ as well as at http://mathpar.com/

Author Biographies

Gennadi Malaschonok, National University of Kyiv-Mohyla Academy, Skovorody vul. 2, Kyiv 04070, Ukraine

Doctor of Physical and Mathematical Sciences professor, Department of Informatics, National University of Kyiv-Mohyla Academy (NaUKMA) https://orcid.org/0000-0002-9698-6374 E-mail: malaschonok@gmail.com

Alexandr Seliverstov, Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 19 Bolshoy Karetny pereulok, bild. 1, 127051, Moscow, Russia

PhD, Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), slvstv@iitp.ru

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