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August 31st, 2012, 08:32 PM   #21
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Re: Solvable Quintics

[attachment=0:3juv0j7f]Quintic function - Wikipedia, the free encyclopedia.png[/attachment:3juv0j7f]

I found the skipjack problem!

the excerpt above is from this wiki link

http://en.m.wikipedia.org/wiki/Quintic_equation

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September 1st, 2012, 12:51 AM   #22
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Re: Solvable Quintics

Quote:
Originally Posted by agentredlum
I found the skipjack problem!
Yes! Nice!

But as you see, it's actually an enormous solution and the derivation of the solution is not so elegant

@skipjack : How many terms there are inside the fifth-root symbol ?

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September 1st, 2012, 02:33 AM   #23
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Re: Solvable Quintics

Consider about the general Bring-Jerrard quintic

Set

The equation becomes

dependent on a single constant a. This is the Bring-Jerrard normal form.

Bring introduces a function, namely which is the root of the above equation. (the root is )

This is called the Bring-radical or the hyper root.

This is a transcendental function. We can easily get an expansion of it by the Taylor series of the reverse function of :



Feel free to ask anything,

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September 1st, 2012, 03:16 AM   #24
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Re: Solvable Quintics

Quote:
Originally Posted by agentredlum
I found the skipjack problem!
I think a simpler method is possible using Spearman-Williams parametrization of the given Bring-quintic.
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September 1st, 2012, 03:28 AM   #25
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Quote:
Originally Posted by mathbalarka
I could just send you the paper by Dummit.
It's available online (search for "Solving Solvable Quintics") for free.
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September 1st, 2012, 03:35 AM   #26
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Re: Solvable Quintics

Quote:
Originally Posted by skipjack
It's available online (search for "Solving Solvable Quintics") for free.
Well, guess I didn't knew that!
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September 1st, 2012, 03:53 AM   #27
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The 1994 paper by Speaman and Williams (and a later paper by the same authors) are also available online for free.
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September 2nd, 2012, 07:14 PM   #28
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Re: Solvable Quintics

Quote:
Originally Posted by mathbalarka
Consider about the general Bring-Jerrard quintic

Set

The equation becomes

.
How did you get this?
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September 2nd, 2012, 07:22 PM   #29
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Re: Solvable Quintics

Quote:
Originally Posted by agentredlum

How did you get this?
Sorry, I made a mistake while writing the transformation. I meant .
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September 2nd, 2012, 07:32 PM   #30
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Re: Solvable Quintics

Quote:
Originally Posted by mathbalarka
Consider about the general Bring-Jerrard quintic

Set

The equation becomes

dependent on a single constant a. This is the Bring-Jerrard normal form.

Feel free to ask anything,

Balarka

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All right, suppose a = 1, please show me the calculation of the Bring hyper radical.

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