Sökning: "Gröbner basis"

Visar resultat 6 - 10 av 10 avhandlingar innehållade orden Gröbner basis.

  1. 6. Canonical Bases for Algebraic Computations

    Författare :Patrik Nordbeck; Algebra; []
    Nyckelord :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;

    Sammanfattning : 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. LÄS MER

  3. 7. Formal Languages and Automata in Computational Algebra

    Författare :Jonas Månsson; Algebra; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; control; Datalogi; Talteori; algebraisk geometri; algebra; gruppteori; Computer science; numerical analysis; systems; group theory; field theory; algebraic geometry; finite automata; Number Theory; Gröbner bases; SAGBI bases; numerisk analys; system; kontroll; fältteori;

    Sammanfattning : This thesis is a collection of six papers in computational algebra. In particular, we study noncommutative Gröb- ner bases, SAGBI bases and similar algebraic objects which can be represented as a graph or an automaton. LÄS MER

  4. 8. New Results on Triangulation, Polynomial Equation Solving and Their Application in Global Localization

    Författare :Klas Josephson; Matematik LTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES;

    Sammanfattning : This thesis addresses the problem of global localization from images. The overall goal is to find the location and the direction of a camera given an image taken with the camera relative a 3D world model. In order to solve the problem several subproblems have to be handled. LÄS MER

  5. 9. Algebraic Methods for Verification and Control of Discrete Event Dynamic Systems

    Författare :Jonas Plantin; Linköpings universitet; []
    Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY;

    Sammanfattning : Discrete event dynamic systems (DEDS) have become increasingly important in industry and there is a need for structured methods applicable to the design process of DEDS. In this thesis we consider algebraic methods for verification and control of DEDS.To model DEDS we use polynomials in a quotient ring. LÄS MER

  7. 10. Topological and geometrical methods in data analysis

    Författare :Oliver Gäfvert; Sandra di Rocco; Henry Schenck; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; multiparameter persistent homology; computational algebraic geometry; algorithms; complexity; Mathematics; Matematik;

    Sammanfattning : This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. LÄS MER