TOPOLOGY OF FAMILIES OF ALGEBRAIC CURVES CONTINUOUSLY DEPENDING ON A PARAMETER, AND APPLICATIONS

DOI10.1142/S0218196713500380zbMath1348.14137OpenAlexW2015050869MaRDI QIDQ5746934

Juan Gerardo Alcázar

Publication date: 11 February 2014

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196713500380

zbMATH Keywords

analytic dependencetopology of real algebraic curvesalgebraic curves depending on parametersalgebraic surface singularitiesPfaffian chains

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Pfaffian systems (58A17) Topology of real algebraic varieties (14P25) Computational aspects in algebraic geometry (14Q99)

Cites Work

• Computing the shapes arising in a family of space rational curves depending on one parameter
• A generic and flexible framework for the geometrical and topological analysis of (algebraic) surfaces
• On the different shapes arising in a family of plane rational curves depending on a parameter
• Real root isolation for exp-log-arctan functions
• Isotopic triangulation of a real algebraic surface
• An efficient method for analyzing the topology of plane real algebraic curves.
• Multiplicities of Pfaffian intersections, and the Łojasiewicz inequality
• Efficient topology determination of implicitly defined algebraic plane curves.
• Polynomial algorithms in computer algebra
• A delineability-based method for computing critical sets of algebraic surfaces
• On the number of homotopy types of fibres of a definable map

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