Arithmetic with algebraic numbers (Part I) --- CAG L17

We "solve" any given polynomial by creating an abstract root that arithmetically behaves like a root. We then begin to study the properties of this abstract root. More precisely, we study the abstract number field determined by an irreducible polynomial. In this first part, we study a single root and in the following part we will study multiple roots possibly coming from different polynomials.

0:00 Setting up the problem
3:28 Field extensions
5:10 Main lemma
12:54 Actual roots
15:16 Embeddings
21:21 Summary

== Relevant resources ==

Website for this lecture:

== General description ==

This video is part of my "Computational Algebraic Geometry" lecture series taking place in Leibniz University Hannover (Germany).

Videos will be uploaded weekly on Monday and Wednesday afternoons during lecture times of the Winter Semester 2021/2022.