Talk:Quintic equation

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This page is kind of messy. Eyu100

I agree. In my opinion an encyclopedia article should not contain a cartoon, especially one that is only loosely connected with the subject. Thinking that something is funny is POV anyway. Also I am disturbed by the repeated mentioning of computer algebra systems. I know they are powerful. I know they may very well be mentioned somewhere in the article. But the way they are in right now simply breaks the flow of the text and obscures the core idea I wish to learn from the article. Pure mathematics and practical applications should really be in separate sections. — Pt _(T) 22:13, 20 Apr 2005 (UTC)

I disagree with the statement that an encyclopedia article shouldn't contain a cartoon. In some cases, and not just those about humor or cartoonists, a cartoon is very appropriate. I do agree though that this particular cartoon is only loosely connected with the subject (as a pun, of course, the joke has no substantive contribution to the content of the article). As the contributor of the cartoon, however, I would like to note that this type of cartoon might be seen in a techincal (even encyclopedic) article in certain types of mathematical, scientific, and engineering magazines, and even serious academia need not be completely humorless. Perhaps very few people besides me find the cartoon appropriate (or funny for that matter), in which case it should go, but if this is an issue, there should be some discussion to determine if this is the case. CyborgTosser (Only half the battle) 16:32, 30 May 2005 (UTC)

The cartoon is great. It actually serves as a pedagogical tool. I'm thinking about even putting it on my door so students passing by can look at it. --C S (Talk) 17:54, 19 November 2005 (UTC)

did you actually make that cartoon? i just cant get over it (no im serious) good work :)

btw is this the easiest approach? im finding the reduction a bit difficult

Is it true that Galois was the one who proved insolvability for equations of degree higher than 5? I think I saw somewhere that Abel's proof was valid for n>5 too.

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I'd dispute that the Brin Radical solution counts as an Algebraic solution. The formula for a Brin Radical includes an infinite sum, and hence is not strictly speeking algebraic (although I'd prefer someone with a bit more knowledge on this to verify this).

From Galois Theory 2nd Edition, I Stewart, Chapman and Hall, ISBN 0-412-34550-1 Therorem 15.7 (p144) If K is a Field of characteristic zero and n >= 5, then the general polynomial of degree n over K is not soluble by radicals. --Pfafrich 18:59, 18 November 2005 (UTC)

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I've split the Brin Radical material into a seperate page. I think the previous treatment gave too much emphesis to the Brin Radicals, and downplayed the insovability by radicals which is a very deep and beautiful result, which gavce rise to the foundations of much of modern group theory. --Pfafrich 20:57, 18 November 2005 (UTC)

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Shouldn't the general formula be more like:

ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0

instead of:

ax⁵ + bx⁴ + cx³ + dx + e = 0

Or is this a different type of quintic than the article is talking about? --Psiphiorg 21:07, 18 November 2005 (GMT)

I think it's the same thing, ie. you get rid of the quadratic term with a substitution of variables like the one for the cubic. Phr 11:52, 25 February 2006 (UTC)

I think this was my mistake when originally typing in. ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0 is the general form. Phr may be correct in that it can be simplified, but I've not checked this. --Salix alba (talk) 15:47, 25 February 2006 (UTC)

Contents 1 the degree after a quintic equation... 2 The caption in the image is truncated and therefore misleading. 3 David Dummit,Sigeru Kobayashi and Hiroshi Nakagawa 4 <math> Tags 5 Requested Move 6 Linear algebraic methods

[edit] the degree after a quintic equation...

What comes after a quintic equation? How do you solve and graph it? And what comes after that? How do you solve polynomials where the highest degree is over 1 million, or progressive? I have been looking around and it seems that every one likes to say they cannot be solved.

For polynomial equation of degree >4, there does not exist a general solution. It is not a case of "they haven't found it yet!". A "formula" giving the solutions has been proven not to exist. --Veddan (talk) 19:50, 15 May 2008 (UTC)

[edit] The caption in the image is truncated and therefore misleading.

The caption of the image "Polynomialdeg5.png" appears in my browser as:

 Polynomial of degree 5: f(x) = (x+4)(x+2)(x+1)(x-1)(x-3)/20

without the final "+2".

Can the size of the image be adjusted to account for the size of the caption? Or perhaps the caption can be shrunk to fit? —Preceding unsigned comment added by Ndokos (talk • contribs) 13:38, November 22, 2006

I have added spaces between the factors and around the plus sign so that the caption can word wrap. How does it look now in your browser?

--Psiphiorg 00:39, 23 November 2006 (UTC)

Looks good! Thanks.

--Ndokos 21:18, 30 November 2006 (UTC)

"this is known as the Abel-Ruffini theorem, first published in 1824, which was one of the first applications of group theory in algebra"

This is untrue, due to a confusion between Abels work which has no mention of groups, with the slightly later work of Galois, who developed finite group theory to prove the inslovability (by the way Galois proof reads more like a sketch of a proof, rather than a proof itself)

Galois didn't have too much time to write, because of the duel, isn't it? Albmont 17:29, 28 February 2007 (UTC)

[edit] David Dummit,Sigeru Kobayashi and Hiroshi Nakagawa

The Quintic is solvable by radicals,it was demonstrated by David Dummit and (independently), Sigeru Kobayashi and Hiroshi Nakagawa in 1991-92.How was it done?.Is Abel-Ruffini Theorem fallacious? Is Galois' great theorem fallacious?

(http://library.wolfram.com/examples/quintic/timeline.html#20)

Arkapravo Bhaumik 06:23, 25 January 2007 (UTC)

I tried some research, but much of it is over my head. I'm pretty sure that Kobayashi and Dummit just demonstrated that some quintics are solvable by radicals, not all of them, though (note "David Dummit and (independently) Sigeru Kobayashi and Hiroshi Nakagawa give methods for finding the roots of a general solvable quintic in radicals."). I tried solving a quintic with radicals in Mathematica, and got [1] as the solution; therefore I think that it might be a little complex for this article :-). —Mets501 (talk) 15:13, 25 January 2007 (UTC)

I liked that huge expression; I think it deserves a page. Something like "Examples of Solvable Quintics". I will show it to my daughters to scare them off the computer late at night <evil grin>. Albmont 17:32, 28 February 2007 (UTC)

We ought to have a page on the "Solution Of the Qunitic by David Dummit,Sigeru Kobayashi and Hiroshi Nakagawa" this would deal with elliptic functions and help us to structure the solution. Arkapravo Bhaumik 05:59, 8 February 2007 (UTC)

[edit] <math> Tags

I switched almost all the equations and variable mentions to use <math> formatting. This eliminated the mixed appearance of variables forced to italics using double apostrophes and superscripts done via sup tags, and the formatting produced by putting everything between the math tags. I did not touch the image caption that gave trouble earlier.

I did this most immediately because of the poor result of using ''t''<sup>5</sup> (namely, t⁵). The spacing is off such that the t leans forward into the superscript 5, which left me guessing at whether I was staring at some rendering error, a t⁶, an l⁵, or even an I⁵, before settling on t⁵, and thank goodness for context. The spacing is also off enough with commas and periods that immediately follow double-apostrophe italicized variables to make the page unsightly without use of the math tag (though if it's any more difficult to read, it's only because the spacing isn't what I'd expect after too much time with TeX output).

If I've unknowingly committed some great faux pas, please inform me: I'm new here.

—Jay Uv. 02:29, 26 January 2007 (UTC)

[edit] Requested Move

[edit] Linear algebraic methods

hi, im currently in year twelve studying maths b and c. and i have come across the need to find an exact value for a quintic 64x^5 + 16x^3 + x - 4. i read this sentence "The quintic equation can be solved by creating a companion matrix of the quintic equation and calculating the eigenvalues of said matrix." and thought - yippee i can solve it as i have a good knowledge of matrices and eigenvalues, but i did it and the result was not equal to what three computed answers gave me, so I'm thinking this statement is untrue. can someone confirm this for me?

cheers