Estimating the number of solutions equation of N-point gravitational lens algebraic geometry methods

TL;DR

This paper discusses algebraic geometry methods to estimate the number of solutions in polynomial systems arising from N-point gravitational lens equations, aiding in understanding the solution space without explicit solving.

Contribution

It introduces algebraic geometry techniques to estimate solutions of gravitational lens equations, addressing the challenge of solving polynomial systems without explicit algorithms.

Findings

Provides a framework for solution count estimation

Enhances understanding of gravitational lens equations

Supports numerical solution approaches

Abstract

One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns. The difficulty lies in the fact that, in general, is not known constructive or analytical algorithm for solving systems of polynomial equations In this connection, use numerical methods like the method of tracing. For the N-point gravitational lenses have a system of polynomial equations. Systems Research is advisable to start with an assessment of the number of solutions. This can be done by methods of algebraic geometry.