Monday, November 14, 2016

Home




A website about algebraic functions

This web site is about a particular class of multi-valued functions and is currently under construction. When completed, it will give readers a practical guide to understanding what algebraic functions are, how to plot, illustrate and analyze contour integrations over them, explain how to compute power expansions of these functions, explain, implement and code the Newton Polygon algorithm, and show how the entire foundation of Complex Analysis for single valued functions is applicable to algebraic functions. For example, how does one apply Laurent's Theorem to algebraic functions? How can a (convergent) power expansion of an algebraic function extend across multiple singular points? The following sections answer these questions. The reader is advised to read the sections in sequential order as each section builds and makes frequent reference to previous sections.

The software used in this web site is Mathematica.

Choose pages in menu above:

  • Section 1: Introduction
  • Section 2: Applying Laurent's Theorem to algebraic functions
  • Section 3: Applying the Residue Theorem to algebraic functions
  • Section 4: Puiseux Series and the Newton Polygon Algorithm, Part 1: Background and basic concepts
  • Section 5: Puiseux Series and the Newton Polygon Algorithm, Part 2: Examples
  • Section 6: Designing doPuiseux
  • Section 7: Riemann Surfaces

The Mathematica Code page will contain the complete code to implement the Newton Polygon Application and other concepts reviewed.

Blog Archive