TI-BD Teasers #3: Polynomial zeroes

Re: TI-BD Teasers #3: Polynomial zeroes

Thu, 01 Oct 2015 05:10:48 +0000

I know irr( can be used to find some, but it's limited to roots above 1. Maybe we could use that, with checks to mame sure those roots exist first?

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Wed, 30 Sep 2015 06:05:34 +0000

I'm pretty sure Muller's method can be used to approximate complex roots, though I'm not sure how exactly to implement it.

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Tue, 29 Sep 2015 22:12:43 +0000

Just to be clear, I want you to generate the COMPLEX roots, as well. Muller's method, as far as I know, only calculates real roots.

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Tue, 29 Sep 2015 22:09:03 +0000

Here's my solution, using the Durand-Kerner method:

Prompt L1 L1/L1(1 -> L1 (.4+.9i)^(-1+cumSum(1 or deltalist(cumSum(L1 -> L2 dim(L1)-cumSum(1 or L1 -> L4 Repeat max(abs(L2-L3))≤e~10 L2 -> L3 For(A,1,dim(L2 L2(A Ans-sum(L1 Ans^L4)/prod(Ans-L2+(0i=Ans-L2 ->L2(A End Disp max(abs(L2-L3 End L2

This should give you an idea of where to go.

Re: TI-BD Teasers #3: Polynomial zeroes

Tue, 29 Sep 2015 20:58:01 +0000

This will be very difficult. Good thing I took Numerical Analysis at university and learned about Muller's Method.

Are we allowed to use solve(? nDeriv(? Do we need to handle multiple roots (and if so how should we output them)? Can we assume the coefficients are real? Are there bounds on the coefficients? To what accuracy must we find the roots?

TI-BD Teasers #3: Polynomial zeroes

Tue, 29 Sep 2015 18:11:43 +0000

Challenge: Create a program that finds all the roots, real and complex, of a given polynomial of any degree.
Restrictions: None. Create your best program!

Input: A list containing the coefficients.
Output: A complex list containing the roots.

lirtosiast: For you, I have an extra challenge: Your program must take its input as a string containing the actual polynomial, eg. "3X^3-X^2+X-3", instead.