Raise Binomials to integer powers

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Ilya
Ilya 2014 年 6 月 13 日
編集済み: Ilya 2014 年 6 月 17 日
It's needed to raise first-degree binomials (ax+b) (i.e. polynomial vectors [a b]) to integer powers. Is there any fast solution? Polynomial multiplication with convolutions is not fast if the required degree is high..
I know about the Pascal triangle, but I don't know/have an algorithm.

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Matt J
Matt J 2014 年 6 月 13 日
編集済み: Matt J 2014 年 6 月 13 日
Polynomial multiplication with convolutions is not fast if the required degree is high.
What about with FFTs, e.g.,
n=3;
p=[1,1];
p_to_the_n = real(ifft(fft(p,n+1).^n))
p_to_the_n =
1 3 3 1
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Ilya
Ilya 2014 年 6 月 17 日
That's a valuable remark! I suspected this, but didn't know exactly that it might be so bad even with integers!

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