Search for dissertations about: "Algebraic number"

Showing result 1 - 5 of 97 swedish dissertations containing the words Algebraic number.

  1. 1. Canonical Bases for Algebraic Computations

    Author : Patrik Nordbeck; Algebra; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; gruppteori; algebra; algebraisk geometri; fältteori; Talteori; group theory; algebraic geometry; field theory; Matematik; Number Theory; regular languages; Mathematics; composition of polynomials; factor algebras; Gröbner bases; SAGBI bases;

    Abstract : This thesis deals with computational methods in algebra, mainly focusing on the concept of Gröbner and SAGBI bases in non-commutative algebras. The material has a natural division into two parts. The first part is a rather extensive treatment of the basic theory of Gröbner bases and SAGBI bases in the non-commutative polynomial ring. READ MORE

  2. 2. Quaternion Orders and Ternary Quadratic Forms Orders of Class Number One and Representations of Algebraic Integers by Quadratic Forms

    Author : Elise Björkholdt; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Keywords : quaternion order; ternary quadratic form; class number; even Clifford algebra; quaternion algebra; embedding number; 11E12; 16H05; 11E20; 11E25; 11E88; even Clifford algebra;

    Abstract : Let R be the ring of integers in a totally real quadratic field K. The purpose of the thesis is to study totally definite quaternion R-orders and representations of elements in R by totally positive definite integral ternary quadratic forms. The thesis consists of three papers. READ MORE

  3. 3. Algebraic Dynamical Systems, Analytical Results and Numerical Simulations

    Author : Robert Nyqvist; Andrei Khrennikov; Vladimir Anashin; Växjö universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; discrete dynamical systems; p-adic numbers; finite fields; number of periodic points; Chebotarev s Density Theorem; computational number theory; MATHEMATICS; MATEMATIK; algebraic dynamical systems;

    Abstract : In this thesis we study discrete dynamical system, given by a polynomial, over both finite extension of the fields of p-adic numbers and over finite fields. Especially in the p-adic case, we study fixed points of dynamical systems, and which elements that are attracted to them. We show with different examples how complex these dynamics are. READ MORE

  4. 4. Constructive Newton–Puiseux Theorem, Sheaf Model of the Separable Closure and Dynamic Evaluation

    Author : Bassel Mannaa; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Newton–Puiseux; Algebraic curve; Sheaf model; Dynamic evaluation; Algebraic number; Grothendieck topos; Grothendieck topos;

    Abstract : Computing the Puiseux expansions of a plane algebraic curve defined by an affine equation over an algebraically closed field is a an important algorithm in algebraic geometry. This is the so-called Newton–Puiseux Theorem. The termination of this algorithm, however, is usually justified by non-constructive means. READ MORE

  5. 5. Quasi-Lie Algebras and Quasi-Deformations. Algebraic Structures Associated with Twisted Derivations

    Author : Daniel Larsson; Matematik LTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Talteori; fältteori; algebraisk geometri; algebra; gruppteori; Lie Algebras; Quasi-Deformations; Number Theory; field theory; algebraic geometry; group theory; Quasi-Lie Algebras;

    Abstract : This thesis introduces a new deformation scheme for Lie algebras, which we refer to as ?quasi-deformations? to clearly distinguish it from the classical Grothendieck-Schlessinger and Gers-tenhaber deformation schemes. The main difference is that quasi-deformations are not in gene-ral category-preserving, i.e. READ MORE