RATIONAL SOLUTIONS OF POLYNOMIAL-EXPONENTIAL EQUATIONS
نویسندگان
چکیده
منابع مشابه
Rational Solutions of Underdetermined Polynomial Equations
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our work provides a method to compute rational solutions of single polynomial equations that are typically large with 10 . . . 10 terms and that are heavily und...
متن کاملCertifying solutions to square systems of polynomial-exponential equations
Smale’s α-theory certifies that Newton iterations will converge quadratically to a solution of a square system of analytic functions based on the Newton residual and all higher order derivatives at the given point. Shub and Smale presented a bound for the higher order derivatives of a system of polynomial equations based in part on the degrees of the equations. For a given system of polynomial-...
متن کاملMonochromatic Solutions of Exponential Equations
We show that for every 2-coloring of N and every k 2 N, there are infinitely many monochromatic solutions of the system of k2 equations zij = x yj i , 1 i, j k, where x1, . . . , xk, y1, . . . , yk are distinct positive integers greater than 1. We give similar, but somewhat weaker, results for more than two colors. – Dedicated to the memory of Paul Erdős.
متن کاملPolynomial solutions of differential equations
A new approach for investigating polynomial solutions of differential equations is proposed. It is based on elementary linear algebra. Any differential operator of the form L(y) = k=N ∑ k=0 ak(x)y, where ak is a polynomial of degree ≤ k, over an infinite ground field F has all eigenvalues in F in the space of polynomials of degree at most n, for all n. If these eigenvalues are distinct, then th...
متن کاملPolynomial and Rational Solutions of Holonomic Systems
Polynomial and rational solutions for linear ordinary differential equations can be obtained by algorithmic methods. For instance, the maple package DEtools provides efficient functions polysols and ratsols to find polynomial and rational solutions for a given linear ordinary differential equation with rational function coefficients. A natural analogue of the notion of linear ordinary different...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112500820