Parametric Expansions of an Algebraic Variety Near Its Singularities II

The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. Axioms 2023, 5, 469, where we calculated parametric expansions of the three-dimensional algebraic manifold Ω, which appeared in theoretical physics,...

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Bibliographic Details
Published in:Axioms Vol. 13; no. 2; p. 106
Main Authors: Bruno, Alexander D., Azimov, Alijon A.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2024
Subjects:
Algebra
algebraic variety
Algorithms
Analysis
Axioms
Functions, Algebraic
Infinity
local parametrization
Mathematical analysis
Nonlinear analysis
Parametric equations
Polynomials
power geometry
singular point
Singularities
Singularities (Mathematics)
Theoretical physics
Russia
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. Axioms 2023, 5, 469, where we calculated parametric expansions of the three-dimensional algebraic manifold Ω, which appeared in theoretical physics, near its 3 singular points and near its one line of singular points. For that we used algorithms of Nonlinear Analysis: extraction of truncated polynomials, using the Newton polyhedron, their power transformations and Formal Generalized Implicit Function Theorem. Here we calculate parametric expansions of the manifold Ω near its one more singular point, near two curves of singular points and near infinity. Here we use 3 new things: (1) computation in algebraic extension of the field of rational numbers, (2) expansions near a curve of singular points and (3) calculation of branches near infinity.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13020106