Hacker News
- Is the largest root of a random real polynomial more likely real than complex? https://mathoverflow.net/questions/470951/is-the-largest-root-of-a-random-polynomial-more-likely-to-be-real-than-complex 121 comments
- Polynomial Root-finding with the Jenkins-Traub Algorithm http://math-blog.com/2008/03/06/polynomial-root-finding-with-the-jenkins-traub-algorithm/ 10 comments programming
- "The Beauty Of Roots", by John C. Baez, J. Daniel Christensen and Sam Derbyshire. "The set of all complex roots of all Littlewood polynomials exhibits many complicated, beautiful and fascinating patterns." [abstract + link to PDF, 3pp] https://arxiv.org/abs/2310.00326 2 comments math
- Transformers can be trained to compute the roots of polynomials https://f-charton.github.io/polynomial-roots/ 6 comments programming
- What's the best way to find the roots of an arbitrary polynomial over the complex numbers? https://en.wikipedia.org/wiki/Cantor%E2%80%93Zassenhaus_algorithm 7 comments math
- A degree 10 polynomial with 256 roots. I don't know if this is the optimal degree. https://onecompiler.com/c/3xqucku9q 10 comments math
- Using polynomial commitments to replace state roots - ethrear.ch/Cryptography [vbuterin] https://ethresear.ch/t/using-polynomial-commitments-to-replace-state-roots/7095 10 comments ethereum
- Find the largest root of a polynomial with a neural network https://codegolf.stackexchange.com/questions/193728/find-the-largest-root-of-a-polynomial-with-a-neural-network 3 comments math
- Complex polynomial roots toy (really wicked) https://duetosymmetry.com/tool/polynomial-roots-toy/ 24 comments math
- What is the relationship between permutations and roots of a polynomial? https://www.reddit.com/r/math/comments/8v8gjw/what_is_the_relationship_between_permutations_and/ 9 comments math
- Cool tool to see the behavior of the complex roots of polynomials as you vary the coefficients. Try tracking how the roots permute as you move a coefficient around in a closed loop. https://duetosymmetry.com/tool/polynomial-roots-toy/ 11 comments math
- A water-based mechanism to calculate the positive roots (if existent) of polynomial equations https://sinews.siam.org/details-page/a-water-based-solution-of-polynomial-equations 11 comments math
- Interactive polynomial roots toy https://duetosymmetry.com/tool/polynomial-roots-toy/ 3 comments math
- Conditioning of roots of orthogonal polynomials https://www.reddit.com/r/math/comments/77pno7/conditioning_of_roots_of_orthogonal_polynomials/ 4 comments math
- A visual method of finding the real roots of polynomials of any degree. https://en.wikipedia.org/wiki/lill%27s_method 22 comments math
- Complex roots of all 3rd degree polynomials whose non-constant coefficients are 6th roots of unity. The animation shows what happens as the constant term, e^itheta, goes around the unit circle. https://i.redd.it/t003thzro9yy.gif 66 comments math
- Density plot in the complex plane of the set of roots of monic degree 19 polynomials with coefficients +/- 1 https://s3-us-west-2.amazonaws.com/steventhornton.ca/bohemian_eigenvalues/figure2_original.png 54 comments math
- Can I find the common roots of two polynomials by dividing them and forcing the remainder to be zero? https://www.reddit.com/r/math/comments/4yjjlh/can_i_find_the_common_roots_of_two_polynomials_by/ 19 comments math
- What additional tools do we need, besides arithmetic and radicals, to find the roots of higher degree polynomials in terms of their coefficients? https://www.reddit.com/r/math/comments/4y5cnu/what_additional_tools_do_we_need_besides/ 17 comments math
- Showing both roots of a symbolic polynomial https://www.reddit.com/r/matlab/comments/4hy1xx/showing_both_roots_of_a_symbolic_polynomial/ 3 comments matlab
- Why do roots of polynomials tend to have absolute value close to 1? [Mathoverflow] http://mathoverflow.net/questions/182412/why-do-roots-of-polynomials-tend-to-have-absolute-value-close-to-1 6 comments math
- Proving the fundamental theorem of algebra (all polynomials have a root in the complex plane) by coloring the complex plane http://www.cs.amherst.edu/~djv/ftap.pdf 10 comments math
- Why do roots of polynomials tend to have absolute value 1? http://mathoverflow.net/questions/182412/why-do-roots-of-polynomials-tend-to-have-absolute-value-1 17 comments math
- Cool pictures and questions involving the roots of nth order polynomials with coefficients {-1, 0, 1} http://math.ucr.edu/home/baez/roots/ 26 comments math
- DDogleg is a new Java numerics library for optimization, robust model fitting, polynomial root finding, and more. http://ddogleg.org 9 comments java
- [Pyhton 2.5.4] TypeError: Polynomials, Derivatives, and finding Roots... http://en.wikipedia.org/wiki/Newton's_method 6 comments learnprogramming
- “The Egg:” Bizarre behavior of the roots of a family of polynomials. http://math.stackexchange.com/questions/206890/the-egg-bizarre-behavior-of-the-roots-of-a-family-of-polynomials 3 comments math
- Visualisation of the algebraic numbers in the complex plane: colors indicate degree of the polynomial the number is a root of, points becomes smaller as integer polynomial coefficients increase http://upload.wikimedia.org/wikipedia/en/d/d1/algebraicszoom.png 3 comments math
- Roots of Polynomials mod p http://en.wikipedia.org/wiki/Chevalley-Warning_theorem 12 comments math
- What the set of roots of polynomials with degree 6 and small integer coefficients looks like http://jdc.math.uwo.ca/roots/ 13 comments math
- Roots of Taylor polynomials for the exponential function [pics] http://www.mai.liu.se/~halun/complex/taylor/ 9 comments math
- Beautiful plots of roots of polynomials http://math.ucr.edu/home/baez/week285.html 8 comments math
- Beautiful plots of roots of polynomials http://math.ucr.edu/home/baez/week285.html 26 comments reddit.com
- Why does R[x]/(x^2+1) have all roots to every polynomial in R[x], when in general K[x]/(p(x)) is only guaranteed to have just a single root of p(x)? https://www.reddit.com/r/math/comments/5x3iwt/why_does_rxx21_have_all_roots_to_every_polynomial/ 18 comments math
- Can you construct a power series with rational coefficients so that each nth partial sum is a polynomial with n distinct roots? http://math.stackexchange.com/q/492326/51970 3 comments math
- I just learned for an nth order polynomial how to calculate the sum of its roots, sum of the square of it roots and product of its roots directly from its coefficients. What other useful facts about polynomials don't I know? http://www.khanacademy.org/test-prep/competition-math/v/sum-of-squares-of-polynomial-roots 20 comments math
- Conway's constant is the unique positive real root of the following polynomial (WTF) http://en.wikipedia.org/wiki/conway%27s_constant 9 comments math
- Question: Is there any formula like the quadratic formula for degrees of the polynomial greater than 2, or is the RRT (Rational Root Theorem) only used? https://www.reddit.com/r/math/comments/6uo2pm/question_is_there_any_formula_like_the_quadratic/ 4 comments math
- New Proof Reveals the Hidden Structure of Common Equations | Quanta Magazine | Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another. https://www.quantamagazine.org/new-proof-reveals-the-hidden-structure-of-common-equations-20220421/ 6 comments math
- What's the most reliable way in Python to run a partial fraction expansion on a rational polynomial function, reliable meaning it handles repeated complex roots correctly https://www.reddit.com/r/math/comments/abwpdn/whats_the_most_reliable_way_in_python_to_run_a/ 8 comments math
