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/sci/ - Science & Math

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10273451 No.10273451 [Reply] [Original]

I've been working on a program to solve for all the zeros of any polynomial equation. I figured out how to solve for the real portion using the Rational Root Theorem. I am stuck on solving for the complex roots. I was told to look into Eigen values but I don't understand them. Any suggestions?

>> No.10273460

Bump for time

>> No.10273469

>>10273451
bug bump tump

>> No.10273480

>>10273451
Literally impossible
https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

>> No.10273504

You can find the roots numerically/approximately using a normal root finding algorithm. Finding them exactly for higher-order polynomials will be quite difficult and in some sense impossible (see above).

>> No.10273553

>>10273480
>links theorem he/she doesn't understand

>> No.10273569

>>10273553
>projecting

>> No.10273575

>>10273451
>Any suggestions?
wikipedia, a calculus textbook, linear algebra textbook, differential equations textbook
Pretty much any of those will describe to you the basics of eigenvalues.

>> No.10273615

>>10273569
explain how abel-ruffini implies there exists a polynomial whose roots can't be solved for

>> No.10273628

>>10273451
https://www.youtube.com/watch?v=b7FxPsqfkOY

https://en.wikipedia.org/wiki/Bairstow%27s_method

https://en.wikipedia.org/wiki/Sturm%27s_theorem

https://en.wikipedia.org/wiki/Budan%27s_theorem

https://en.wikipedia.org/wiki/Lagrange_inversion_theorem#Example

>> No.10273690

>>10273569
>The theorem does not assert that some higher-degree polynomial equations have no solution.

Literally the start of the second paragraph, you active moron.

>> No.10273707

>>10273690
I don't think you know what the word solution means. The fundamental theorem of algebra gardeners all polynomials have a solution.

>>10273451
Easiest way: Just set x = a +ib, multiply it out, factor out i, set real and imaginary parts to 0 and sold both equations with your algorithm for real values.

>> No.10273718

>>10273707
>gardeners

>> No.10273745

>>10273707
A solution in this context is a root for the polynomial. OP’s looking for all solutions. >>10273480 and >>10273569 are trying to say that Abel-Ruffini implies that this is impossible. Just as you say, FToA says it’s not. Abel-Ruffini only says the roots can’t be expressed algebraically in terms of the coefficients for every polynomial of degree 5+.

>> No.10273836
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10273836

You guys are being FUCKING autistic, as usual. Of course the solutions exist. However, finding them exactly with a computer will be prohibitively expensive for large-degree polynomials, precisely because of Ruffini etc., since your computerised symbolic algebra or whatever will have to grow in size exponentially as the degree of the polynomial increases. Obviously, finding them approximately numerically is trivial.

>> No.10273845 [DELETED] 

Are people here trolling or retarded? Three of the polynomials can be simply plugged in the quadratic formula and the other two in the cubic formula.

>> No.10273847

>>10273836
You are being fucking retarded, it won't just grow exponentially, there are polynomials you won't find solutions for at all except numerically.

>>10273845
What even is this post.

>> No.10273848

>>10273845
>Are people here trolling or retarded? Three of the polynomials can be simply plugged in the quadratic formula and the other two in the cubic formula.
What is reading comprehension