Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Gathen, Joachim von zur"'
The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two polynomials of deg
Externí odkaz:
http://arxiv.org/abs/2103.15926
The functional (de)composition of polynomials is a topic in pure and computer algebra with many applications. The structure of decompositions of (suitably normalized) polynomials f(x) = g(h(x)) in F[x] over a field F is well understood in many cases,
Externí odkaz:
http://arxiv.org/abs/1912.00212
In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for Newton's r
Externí odkaz:
http://arxiv.org/abs/1812.07020
Autor:
Gathen, Joachim von zur
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to \log_2(n) mi
Externí odkaz:
http://arxiv.org/abs/1712.01407
In the ElGamal signature and encryption schemes, an element $x$ of the underlying group $G = \mathbb{Z}_p^\times = \{1, \ldots, p-1 \}$ for a prime $p$ is also considered as an exponent, for example in $g^x$, where $g$ is a generator of G. This ElGam
Externí odkaz:
http://arxiv.org/abs/1708.04395
This paper deals with properties of the algebraic variety defined as the set of zeros of a "typical" sequence of polynomials. We consider various types of "nice" varieties: set-theoretic and ideal-theoretic complete intersections, absolutely irreduci
Externí odkaz:
http://arxiv.org/abs/1512.05598
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more variables,
Externí odkaz:
http://arxiv.org/abs/1407.2970
We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/1407.0906