# roots

Published articles for roots.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Testing Polynomial Equality

DevFeed: [Testing Polynomial Equality](<https://devfeed.tech/articles/testing-polynomial-equality-40409.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2017/04/24/testing-polynomial-equality/>)

Published: 2017-04-24T09:00:14Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Testing](<https://devfeed.tech/topics/testing.md>), [function](<https://devfeed.tech/topics/function.md>)

Tags: [field](<https://devfeed.tech/tags/field.md>), [function](<https://devfeed.tech/tags/function.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>), [random](<https://devfeed.tech/tags/random.md>), [roots](<https://devfeed.tech/tags/roots.md>), [testing](<https://devfeed.tech/tags/testing.md>), [variables](<https://devfeed.tech/tags/variables.md>)

### AI overview

The article explains how to test whether two multivariable polynomial expressions represent the same function. It presents randomized evaluation over a finite subset of a field and uses the Schwartz-Zippel lemma to bound the probability of an incorrect equality judgment.

### Source excerpt

Problem: Determine if two polynomial expressions represent the same function. Specifically, if $ p(x_1, x_2, \dots, x_n)$ and $ q(x_1, x_2, \dots, x_n)$ are a polynomial with inputs, outputs and coefficients in a field $ F$, where $ |F|$ is sufficiently large, then the problem is to determine if $ p(\mathbf{x}) = q(\mathbf{x})$ for every $ x \in F$, in time polynomial in the number of bits required to write down $ p$ and $ q$.

## Battle Language à la Marmite

DevFeed: [Battle Language à la Marmite](<https://devfeed.tech/articles/battle-language-a-la-marmite-34463.md>)

Original publisher: [Read original article](<https://tapoueh.org/blog/2012/03/battle-language-%C3%A0-la-marmite/>)

Author: Dimitri Fontaine PostgreSQL Major Contributor; Author

Published: 2012-03-01T13:49:00Z

Content type: opinion

Language: fr

Sources: [Dimitri Fontaine](<https://devfeed.tech/sources/dimitri-fontaine.md>)

Topics: [Lisp](<https://devfeed.tech/topics/lisp.md>), [Emacs](<https://devfeed.tech/topics/emacs.md>), [Common Lisp](<https://devfeed.tech/topics/common-lisp.md>), [Erlang](<https://devfeed.tech/topics/erlang.md>), [Haskell](<https://devfeed.tech/topics/haskell.md>), [Ruby](<https://devfeed.tech/topics/ruby.md>)

Tags: [article](<https://devfeed.tech/tags/article.md>), [code](<https://devfeed.tech/tags/code.md>), [emacs](<https://devfeed.tech/tags/emacs.md>), [emacs-lisp](<https://devfeed.tech/tags/emacs-lisp.md>), [erlang](<https://devfeed.tech/tags/erlang.md>), [haskell](<https://devfeed.tech/tags/haskell.md>), [language](<https://devfeed.tech/tags/language.md>), [languages](<https://devfeed.tech/tags/languages.md>), [lisp](<https://devfeed.tech/tags/lisp.md>), [roots](<https://devfeed.tech/tags/roots.md>), [ruby](<https://devfeed.tech/tags/ruby.md>)

### AI overview

The author recounts participating in the Battle Language event at La Marmite, where they presented Emacs Lisp as part of the broader Lisp family. The presentation briefly covered John McCarthy's axiomatic approach and referenced Paul Graham's The Roots of Lisp and its Common Lisp implementation. The event also included discussion of functional and object-oriented languages, including Erlang, Haskell, and Ruby.

### Source excerpt

J'ai eu la chance hier soir de participer à la Battle Language à la Marmite, où j'avais proposé de parler de Emacs Lisp, proposition qui s'est transformée en porte-étendard de la grande famille Lisp. J'ai utilisé avec plaisir certains contenu de Lisperati dans ma présentation et je vous recommande le détour sur ce site ! J'ai dans cette présentation très rapide (5 minutes seulement) mentionné l'approche axiomatique de John McCarthy lorsqu'il a découvert le language, on peut en lire un peu plus sur le site de Paul Graham et son article The Roots of Lisp et le code associé, une implémentation du LISP de McCarthy en common lisp.

## The Fundamental Theorem of Algebra (with Galois Theory)

DevFeed: [The Fundamental Theorem of Algebra (with Galois Theory)](<https://devfeed.tech/articles/the-fundamental-theorem-of-algebra-with-galois-theory-40259.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/02/the-fundamental-theorem-of-algebra-galois-theory/>)

Published: 2012-02-02T22:42:11Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [field](<https://devfeed.tech/tags/field.md>), [fundamental-theorem-of-algebra](<https://devfeed.tech/tags/fundamental-theorem-of-algebra.md>), [galois-theory](<https://devfeed.tech/tags/galois-theory.md>), [group-theory](<https://devfeed.tech/tags/group-theory.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>), [roots](<https://devfeed.tech/tags/roots.md>)

### AI overview

This mathematics post presents a Galois-theoretic proof strategy for the fundamental theorem of algebra. It assumes familiarity with field extensions, Galois theory, and group theory, and develops the argument using splitting fields, an intermediate extension of degree 2, Sylow subgroups, and the Galois correspondence.

### Source excerpt

This post assumes familiarity with some basic concepts in abstract algebra, specifically the terminology of field extensions, and the classical results in Galois theory and group theory. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem, and in re-proving an established theorem we introduce new concepts and strategies.