Affiliation:
1. Keldysh Institute of Applied Mathematics
Abstract
We propose a method for computing the position of all level lines of a real polynomial in the real plane. To do this, it is necessary to compute its critical points and critical curves, and then to compute critical values of the polynomial (there are finite number of them). Now finite number of critical levels and one representative of noncritical level corresponding to a value between two neighboring critical ones enough to compute. We propose a scheme for computing level lines based on polynomial computer algebra algorithms: Gröbner bases, primary ideal decomposition. Software for these computations are pointed out. Nontrivial examples are considered.
Publisher
Keldysh Institute of Applied Mathematics
Reference19 articles.
1. Брюно А. Д., Батхин А. Б. Введение в нелинейный анализ алгебраических уравнений // Препринты ИПМ им. М. В. Келдыша. 2020. № 87. DOI: 10.20948/prepr-2020-87.
2. Брюно А. Д. Локальный метод нелинейного анализа дифференциальных уравнений. М.: Наука, 1979. 252 с.
3. Kollár J. Lectures on Resolution of Singularities. Princeton, Oxford: Princeton University Press, 2007.
4. Kollár J. Resolution of Singularities – Seattle Lecture. 2007. arXiv: math /0508332v3 [math.AG].
5. Милнор Д. Теория Морса: Пер. с англ. Изд. 3-е. М.: Издательство ЛКИ, 2011. 184 с.
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2 articles.
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