Questions tagged [polynomials]
128 questions
3
votes
1 answer
Polylogarithm growth rate proof using Polynomial growth equation
In the CLRS, there's this part, where it's shown that $$\lim_{n\to\infty}\frac{(n^b)}{(a^n)} = 0$$ In the same chapter, it uses the aforementioned equation to prove that any polylogarithm function grows slower than any polynomial one, thus,…
chakmeshma
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2
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0 answers
Polynomials and NSA
I'm looking for some applications of criteria of irreducibility of integer polynomials inside and outside mathematics.
I was reading the of CV Filaseta, a great researcher in this area and he has gained some grants from NSA. Then this makes me…
user17640
- 129
- 2
2
votes
1 answer
Do you know of a brute-force algorithm for optimizing polynomial expressions?
For instance, given the polynomial expression $xy + x + y + 1$ it will output $(x+1)(y+1)$.
Thanks!
Daniel Donnelly
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1
vote
1 answer
What is the use of Horner's Method?
Here is Wikipedia's explanation of Horner's Method:
Given the polynomial
$$
p(x) = \sum_{i=0}^n a_i x^i = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots + a_n x^n,
$$
where $a_0, \ldots, a_n$ are real numbers, we wish to evaluate the polynomial at a…
PP121
- 53
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1
vote
1 answer
Proof of Minsky Papert Symmetrization technique
I frequently hear about the Minsky-Papert Symmetrization technique in many papers with a reference to the book of Minsky. I could not locate the book online. Could someone supply me a proof of the symmetrization technique?
For instance, it is used…
Turbo
- 2,891
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Binomial basis and the usual basis of polynomial algebra $\mathbb C(X)$
Consider the polynomial algebra $\mathbb C[X]$. Then the set $\{1, X, X^2,\dots,\}$ forms a vector space basis for this algebra. In general, we know that the set $\{P_n(X) \in \mathbb C[X]: n \ge 0 \text{ and degree}(P_n) = n\}$ forms a basis. We…
GA316
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