Certifying reality of projection

Dataset

Description

Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton’s method is locally quadratically convergent near each nonsingular solution. In such cases, Smale’s alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding solution when the polynomial system is real. Using the theory of Newton-invariant sets, we certifiably decide the reality of projections of solutions. We apply this method to certifiably count the number of real and totally real tritangent hyperplanes for instances of curves of genus 4.

Attributes

Attribute NameValues
Creator
  • Samantha Sherman

  • Jonathan Hauenstein

Contributor
  • Avinash Kulkarni

  • Emre Sertoz

Publisher
  • Samantha Sherman

  • Jonathan Hauenstein

Departments and Units
Record Visibility and Access Public
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R0DB7ZW2

This DOI is the best way to cite this dataset.


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