منابع مشابه
Splitting of Quartic Polynomials
For integers r, s, t, u define the recursion A(n + 4) = rA(n + 3) sA(n + 2) + tA(n + 1) uA(n) where the initial conditions are set up in such a way that A(n) = a" + ß" + y" + S" where a, ß, y, S are the roots of the associated polynomial f(x) = x* rxi + sx2 tx + u. In this paper a detailed deterministic procedure using the A(n) for finding how f(x) splits modulo a prime integerp is given. This ...
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We investigate the parameter plane of the Newton’s method applied to the family of quartic polynomials pa,b(z) = z 4 +az + bz +az+ 1, where a and b are real parameters. We divide the parameter plane (a, b) ∈ R into twelve open and connected regions where p, p′ and p′′ have simple roots. In each of these regions we focus on the study of the Newton’s operator acting on the Riemann sphere.
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We present two splitting formulas for calculating the Tutte polynomial of a matroid. The rst one is for a generalized parallel connection across a 3-point line of two matroids and the second one is applicable to a 3-sum of two matroids. An important tool used is the bipointed Tutte polynomial of a matroid, an extension of the pointed Tutte polynomial introduced by Thomas Brylawski in Bry71].
متن کاملThe Connected Isentropes Conjecture in a Space of Quartic Polynomials
This note is a shortened version of my dissertation thesis, defended at Stony Brook University in December 2004. It illustrates how dynamic complexity of a system evolves under deformations. The objects I considered are quartic polynomial maps of the interval that are compositions of two logistic maps. In the parameter space P of such maps, I considered the algebraic curves corresponding to the...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1984
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1984-0744941-3