Indecomposability of Polynomials via Jacobian Matrix
نویسنده
چکیده
Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives sharp bounds for the indecomposability problem.
منابع مشابه
Indecomposable Polynomials and Their Spectrum
We address some questions concerning indecomposable polynomials and their spectrum. How does the spectrum behave via reduction or specialisation, or via a more general ring morphism? Are the indecomposability properties equivalent over a field and over its algebraic closure? How many polynomials are decomposable over a finite field?
متن کاملNumerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials
In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...
متن کاملIndecomposability of polynomials and related Diophantine equations
We present a new criterion for indecomposability of polynomials over Z. Using the criterion we obtain general finiteness result on polynomial Diophantine equation f(x) = g(y).
متن کاملOn the indecomposability of polynomials
Applying a combinatorial lemma a new sufficient condition for the indecomposability of integer polynomials is established.
متن کاملThe Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials
In this paper, we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays. Constant or pantograph delays may appear in state-control or both. We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then, these are utilized to reduce the solution of optimal control with constant...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010