My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

LinkBack Thread Tools Display Modes
September 6th, 2012, 05:11 PM   #101
Math Team
agentredlum's Avatar
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Solvable Quintics

Originally Posted by mathbalarka
I want to share something about solving general quintic and the Kiepert's algorithm, are you interested?
most definitely yes.
agentredlum is offline  
September 6th, 2012, 10:03 PM   #102
Math Team
mathbalarka's Avatar
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Solvable Quintics

The most useful algorithmic process of solving a general quintic is Kiepert's algorithm. Here's the flow chart for it :

Whereas, another algorithm is :

But the part where we convert the principal quintic in the Bring-Jerrard form, we use a quartic Tschrinhausen transformation which is rather harder than just transforming Principal form into the Brioschi normal form.

The next stage of the Kiepert algorithm transforms the Brioschi normal form into the Jacobi sextic form. This can be very beneficial, since a sextic has 6 roots. Hence now we have the same group with a permutation of six elements. Now O. Perron shows that all the roots can be derived in terms of elliptic curves. Now appropriate trivial transformations gives back the original general quintic with the 5 roots (6-th root has been discarded).


mathbalarka is offline  

  My Math Forum > High School Math Forum > Algebra

quintics, solvable

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Tschirnhaus transformation and quintics Surgborg Abstract Algebra 28 August 4th, 2013 06:40 AM
Advanced Analysis of Quintics mathbalarka Algebra 6 March 29th, 2013 01:00 PM
Quintics : Easy! mathbalarka Algebra 6 January 24th, 2013 12:03 AM
Quintics mathbalarka Algebra 8 September 29th, 2012 07:19 AM
Algorithmic Process For Solving Quintics? mathbalarka Algebra 6 September 2nd, 2012 11:05 AM

Copyright © 2018 My Math Forum. All rights reserved.