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Displaying 301 – 320 of 2843

An improvement of Euclid's algorithm

Zítko, Jan, Kuřátko, Jan (2010)

Programs and Algorithms of Numerical Mathematics

The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using $c$ - $s$ transformation and $Q R$ -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.

An inequality for Hilbert series of graded algebras.

Ralf Fröberg (1985)

Mathematica Scandinavica

An iterative construction of bases for finitely generated modules over principal ideal domains

Alexander Abian, Paula Kemp, Sergi Sverchkov (1993)

Czechoslovak Mathematical Journal

An $ℓ$ -algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem

Stuart A. Steinberg (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.

An overview of some recent developments on integer-valued polynomials: Answers and Questions

Jean-Luc Chabert (2010)

Actes des rencontres du CIRM

The purpose of my talk is to give an overview of some more or less recent developments on integer-valued polynomials and, doing so, to emphasize that integer-valued polynomials really occur in different areas: combinatorics, arithmetic, number theory, commutative and non-commutative algebra, topology, ultrametric analysis, and dynamics. I will show that several answers were given to open problems, and I will raise also some new questions.