COMPUTING UNIMODULAR MATRICES OF POWER TRANSFORMATIONS

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Resumo

An algorithm for solving the following problem is described. Let m < n integer vectors in the n-dimensional real space be given. Their linear span forms a linear subspace L in R. It is required to find a unimodular matrix such that the linear transformation defined by it takes the subspace L into a coordinate subspace. Computer programs implementing the proposed algorithms and the power transforms for which they are designed are described.

Sobre autores

A. BRUNO

Institute of Applied Mathematics, Russian Academy of Sciences

Email: abruno@keldysh.ru
Moscow, Russia

A. AZIMOV

Samarkand State University

Autor responsável pela correspondência
Email: Azimov_Alijon_Akhmadovich@mail.ru
Samarkand, Uzbekistan

Bibliografia

  1. Хинчин А.Я. Цепные дроби. М.: Физматгиз, 1961.
  2. Euler L. De relatione inter ternas pluresve quantitates instituenda // 1785, All Works 591.
  3. Брюно А.Д. Локальный метод нелинейного анализа дифференциальных уравнений. М.: Наука, 1979. 252 с.
  4. Брюно А.Д. Вычисление основных единиц числовых колец с помощью обобщенной цепной дроби // Программирование. 2019. № 2. С. 17–31. https://doi.org/10.1134/S0132347419020055
  5. Thompson I. Understanding Maple. Cambridge University Press, 2016. 228 p.
  6. The Sage Developers. SageMath, the Sage Mathematics Software System (Version 9.1.1). 2020. https://doi.org/10.5281/zenodo. 4066866. https://www.sagemath.org.
  7. Meurer A., Smith C.P., [et al.]. SymPy: symbolic computing in Python // PeerJ Computer Science. 2017. V. 3. e103. ISSN 2376–5992. DOI: . URL: https://doi.org/10.7717/ peerj-cs.103.
  8. Брюно А.Д. Степенная геометрия в алгебраических и дифференциальных уравнениях. М.: Физматлит, 1998. 288 с.
  9. Брюно А.Д., Батхин А.Б. Разрешение алгебраической сингулярности алгоритмами степенной геометрии // Программирование. 2012. № 2. С. 11–28.

Declaração de direitos autorais © А.Д. Брюно, А.А. Азимов, 2023

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