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 February 25th, 2010, 08:28 AM #1 Newbie   Joined: Feb 2010 Posts: 6 Thanks: 0 Solving real roots polynomial equation I have shown some more methods which is much quicker than previous ones for solving real roots polynomial equations. These examples are from’ Solving Real Roots Polynomial Equations’(New And Simple Methods Of Solving Real Roots Polynomial Equations Part-2). Try it to see whether it works well. Click here. http://www.rkmath.yolasite.com
 February 25th, 2010, 09:41 AM #2 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 Re: Solving real roots polynomial equation I've looked briefly through the first paper. I haven't looked close enough to say much about the methods or the novelty of the results, but a few things: I see no reference to other mathematicians here. Have you built on on (or even examined) work that's been done in the last century on roots of polynomial equations? How does your method depart from these methods and why? This is always a useful thing to see when someone claims their result is new-- it provides motivation and shows that this isn't just some guy who has "discovered" some nonsense, or something that's already well-known. It's shocking (and suspicious) to see a "new" result in the solution to polynomial equations which does not rely on any methods from higher algebra. Can you provide any insight on how you've proven something new with elementary methods? Also, how do you know your results are new? You really need to work on the formatting: it's difficult to follow what's going on. In particular: * departing form standard notation makes it difficult for mathematicians to read. (e.g. $a_nx^n+a_{n-1}x^{n-1}+\ldots + a_1x+a_0$ is much clearer notation than $AX^n+BX^{n-1}-------------YX+Z$. Also, your equations are difficult to distinguish from text; you should really be making use of a different font or style (e.g. math is always in italics, text is never in italics.) * If you insist on using word (instead of typesetting it in LaTeX), use a different font than calibri. Preferably one which is standard in mathematical papers (Latin Modern, Garamond, etc.) It looks nicer, and is much easier to take seriously (I'm not joking here.) * It is traditional to provide proofs immediately after first introducing a theorem; perhaps a quick remark, or an example beforehand is illuminating, but I shouldn't have to go to the end of the paper to read a proof of a statement on page one. * Your results are completely unmotivated; prose helps make math papers clearer. Especially, I don't get any sense of why I should care about what you have to say. I may have time to take a look at this in more detail this weekend.
February 27th, 2010, 07:45 AM   #3
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Re: Solving real roots polynomial equation

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 "cknapp"
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 I see no reference to other mathematicians here.
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All are my own ideas. I didn’t take anything from anywhere. This is only a draft. I like to add many things including a few references?, general proofs, some more examples, explanations and good formatting( all in good English), Only if my works are appreciated
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 Have you built on on (or even examined) work that's been done in the last century on roots of polynomial equations?
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I saw them, only after writing these  papers. Because I didn’t study any degree.
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 How does your method depart from these methods and why?
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All are simple formulas.
Easy and suitable to school students.

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 This is always a useful thing to see when someone claims their result is new-- it provides motivation and shows that this isn't just some guy who has "discovered" some nonsense, or something that's already well-known. It's shocking (and suspicious) to see a "new" result in the solution to polynomial equations which does not rely on any methods from higher algebra.
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Please note that these formulas are only for real roots polynomial equations.
After seeing many math websites in net, I satisfied myself that no one discovered it before. I have shown that my method works well.Perhaps I may be wrong. You  (mathematicians and scholars) will decide.
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 Can you provide any insight on how you've proven something new with elementary methods?
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All are based on simple facts , already known by all.
I think differently.
See the proofs, especially theorem 6. It does not need any proof. Theorem 1 is another form of theorem 6. My works all are mainly based  on theorem 1. I will try to give you a detailed notes.
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 Also, how do you know your results are new?
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After seeing many math websites in net, I satisfied myself that no one discovered it before. Perhaps I may be wrong. You  (mathematicians and scholars) will decide.
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 it's difficult to follow what's going on
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I have poor English knowledge. I can’t explain accurately in English as I think. That is why I wrote main points only. I didn’t explain any thing.
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 You really need to work on the formatting: In particular: * departing form standard notation makes it difficult for mathematicians to read. (e.g. $a_nx^n+a_{n-1}x^{n-1}+\ldots + a_1x+a_0$ is much clearer notation than $AX^n+BX^{n-1}-------------YX+Z$. Also, your equations are difficult to distinguish from text; you should really be making use of a different font or style (e.g. math is always in italics, text is never in italics.) * If you insist on using word (instead of typesetting it in LaTeX), use a different font than calibri. Preferably one which is standard in mathematical papers (Latin Modern, Garamond, etc.) It looks nicer, and is much easier to take seriously (I'm not joking here.) * It is traditional to provide proofs immediately after first introducing a theorem; perhaps a quick remark, or an example beforehand is illuminating, but I shouldn't have to go to the end of the paper to read a proof of a statement on page one.
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You are correct. Your suggestion all are accepted. Thank you.
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 * Your results are completely unmotivated; prose helps make math papers clearer. Especially, I don't get any sense of why I should care about what you have to say.
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It is only a request.
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 I may have time to take a look at this in more detail this weekend
.

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Thanks.
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By the by, Part-1 is posted in net a year back. So far no one told ‘ it is not new ’ , ‘ theory is wrong ‘,’ it is useless and difficult ‘.
Second one – ‘ it is not a breakthrough ’.
third – ‘ I think its an amazing discovery. a powerful and unique method. awesome work on the whole.’
Fourth one – ‘ is it a joke ? ‘
So,  You  (mathematicians and scholars) will give the verdict that ‘ it is a breakthrough or not’, ‘it is a new method or not’, ‘it is simple or not’, ‘it is useful or not’ and ‘appreciate it or not’.
Thank you.

February 27th, 2010, 04:39 PM   #4
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Re: Solving real roots polynomial equation

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 Originally Posted by RKJCHENNAI All are my own ideas. I didn’t take anything from anywhere. This is only a draft. I like to add many things including a few references?, general proofs, some more examples, explanations and good formatting( all in good English), Only if my works are appreciated
Unfortunately, it's unlikely that an amateur working alone will discover something new that mathematicians find of any interest. Of course, it is possible. More likely than not, though, your results (even if new) will be of little interest to the mathematical community.

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 I think differently.
A bold statement in mathematics.

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 See the proofs, especially theorem 6. It does not need any proof.
A dangerous statement in mathematics.

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 I have poor English knowledge. I can’t explain accurately in English as I think. That is why I wrote main points only. I didn’t explain any thing.
Fair enough.

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 [quote:26nofcko]* Your results are completely unmotivated; prose helps make math papers clearer. Especially, I don't get any sense of why I should care about what you have to say.
It is only a request.[/quote:26nofcko]
I had mostly meant that there is little explanation. You explained why above.

The statement of theorem 1 needs to be refined: if k=0, then it is vacuous-- all polynomials with a 0-valued constant have 0 as a root.
Also, if n=1, then the two statements ($rs>k/z$ and $rs\leq nk/z$) are contradictory.

Your proof does not give anything unless n=3. You need to show that it holds for all polynomials that you are interested in.

n=3 has been "solved"-- we can very easily find all roots of a degree 3 polynomial. For n>4 polynomials are not necessarily solvable, so methods for approximating roots are certainly useful; unfortunately, a lot of work has gone into these, and I fail to see anything terribly original in your ideas.

I hope that's not too blunt...

March 1st, 2010, 10:58 PM   #5
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Re: Solving real roots polynomial equation

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 Unfortunately, it's unlikely that an amateur working alone will discover something new that mathematicians find of any interest. Of course, it is possible. More likely than not, though, your results (even if new) will be of little interest to the mathematical community.
okay.

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 See the proofs, especially theorem 6. It does not need any proof.
I didn’t mean it. Actual(indirect) meaning is that the proof is very, very simple. Any one can prove it. Because it is obvious.

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 I had mostly meant that there is little explanation. You explained why above..
Misunderstanding.
Sorry.

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 The statement of theorem 1 needs to be refined: if k=0, then it is vacuous-- all polynomials with a 0-valued constant have 0 as a root.
X is not equal to 0 (to be included)

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 Also, if n=1, then the two statements ( and ) are contradictory.
n > 1 (it is already told)

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 Your proof does not give anything unless n=3. You need to show that it holds for all polynomials that you are interested in.
Yes. I have general proofs.

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 n=3 has been "solved"-- we can very easily find all roots of a degree 3 polynomial. For n>4 polynomials are not necessarily solvable, so methods for approximating roots are certainly useful; unfortunately, a lot of work has gone into these, and I fail to see anything terribly original in your ideas. I hope that's not too blunt...
I am disappointed.

 March 5th, 2010, 04:12 PM #6 Senior Member   Joined: Apr 2008 Posts: 435 Thanks: 0 Re: Solving real roots polynomial equation Disappointing you or not, I agree with cknapp. Having skimmed through your papers, the first thing that strikes me is the new format. It is far more difficult to read through notations atypical of established papers than those I am accustomed to reading. It was an interesting challenge to read through your work. Perhaps the general proofs for cases when n is not equal to 3 would add validity to your claims, but these claims do not seem to substantiate a new development in math. I'm sorry.

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