Effective approximation of the solutions of algebraic equations

TL;DR

This paper introduces an algorithm for locally approximating solutions to algebraic equations using Nash maps, ensuring the approximations satisfy the same polynomial relations as the original holomorphic map.

Contribution

The paper presents a novel algorithm for constructing Nash maps that approximate holomorphic solutions of algebraic equations while preserving their polynomial relations.

Findings

Algorithm successfully constructs Nash maps approximating holomorphic solutions.

Approximations maintain the polynomial relations of the original map.

Method enhances computational approaches for algebraic equations.

Abstract

Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy the same relations.