Problem 42775. Raise a polynomial to a power

Created by William

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>In Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

120 Solutions
55 Solvers

Last Solution submitted on Apr 15, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Jess Stuart on 6 Feb 2017

Thought of another way to do this...
q=poly(kron(roots(p),ones(N,1)));

One-liner with size 21, but fails because of trivial roundoff error :(

Lateef Adewale Kareem on 7 Apr 2017

This isnt a particularly difficult problem

you can call this function powerpoly

function ppower = powerpoly(p,n)
ppower = p;
i = 1
while i < n
ppower = conv(ppower,p);
i = i + 1;
end

Solution Comments

Solution 1114065

3 Comments

3 Comments

Jess Stuart on 2 Feb 2017

This is a numerical algorithm and is not exact, but very accurate. I'm failing the test because the output for p=1:5; N=3 is off by this amount...

-3.4972e-14 8.8818e-15 3.5527e-14 0.0000e+00 0.0000e+00 -2.8422e-14
Columns 7 through 12:
0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 -5.6843e-14
Column 13:
0.0000e+00

COMPLETELY RIDICULOUS!!!!. Using isequal() is a poor choice for evaluating numerical algorithms.

Jess Stuart on 2 Feb 2017

Here is my algorithm that "failed" the isequal test by -5e-14 on a few values. I thought I would actually try to write a somewhat fast algorithm instead of just a for loop calling conv() repeatedly and reallocating memory each time.

function q = polypow(p,N)
q=ifft((fft([p zeros(1,(N-1)*(length(p)-1))])).^N);
end

Peng Liu on 3 Feb 2017

Given you comments above, you might be interested in solving my convolution series at http://www.mathworks.com/matlabcentral/cody/?term=Fast+1-D+Convolution

Problem Recent Solvers55

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42775. Raise a polynomial to a power

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers55

Suggested Problems

More from this Author2

Problem Tags

Community Treasure Hunt

Problem 42775. Raise a polynomial to a power

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers55

Suggested Problems

More from this Author2

Problem Tags

Community Treasure Hunt

Players