Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 1 of 1
  1. MHB Journeyman
    MHB Math Helper
    mathbalarka's Avatar
    Status
    Offline
    Join Date
    Mar 2013
    Location
    West Bengal, India
    Posts
    573
    Thanks
    699 times
    Thanked
    1,378 time
    Thank/Post
    2.405
    Trophies
    8 Highscores
    Awards
    Graduate POTW Award (Jul-Dec 2013)
    #1
    This is a graph containing the main Tschirnhausen transformations of a general quintic and the algorithms to solve them. The methods would be explicitly described most probably elsewhere in this forum



    • The lower-most nodes are the elementariest functions to which the root of a general quintic can be extracted.
    • In any sub-graph of the above, the lowermost elements are the form reduced from the topmost elements via Tschirnhausen transformations.
    • Deeper colors indicates the effectiveness of the algorithm in computational research, as well as popularity.
    • Dotted lines indicates a reduction that is non-obvious although not a part of the interest, in most cases.
    • Black lines indicates a transformation that is not part of the algorithm.
    • The red arrows indicate the Kiepert algorithm, which I like to call Kiepert-Perron algorithm.
    • The green arrows indicate Glasser's derivation.
    • The magenta-like colors indicate Hasner's method and Kronecker-Brioschi derivation respectively.


    Any comment/question regarding this thread should be posted in http://mathhelpboards.com/commentary...tics-8210.html
    Last edited by mathbalarka; December 19th, 2013 at 15:45.

Similar Threads

  1. Field Theory - Basic Theory - D&F Section 13.1
    By Peter in forum Linear and Abstract Algebra
    Replies: 2
    Last Post: October 2nd, 2013, 00:31
  2. Self-introduction
    By DeusAbscondus in forum Introductions
    Replies: 3
    Last Post: July 2nd, 2012, 08:54
  3. Introduction
    By anky2930 in forum Introductions
    Replies: 1
    Last Post: April 13th, 2012, 15:10
  4. Introduction
    By Jameson in forum Introductions
    Replies: 1
    Last Post: March 26th, 2012, 20:42
  5. Introduction
    By dwsmith in forum Introductions
    Replies: 3
    Last Post: March 25th, 2012, 17:37

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards