Essays about: "SAGBI basis"

Found 4 essays containing the words SAGBI basis.

  1. 1. Classification of almost monomial subalgebras of small codimension

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Ludvig Sundell; [2023]
    Keywords : Algebra; Subalgebra; Polynomial; SAGBI basis; LAGBI basis; Lower semigroup; Mathematics and Statistics;

    Abstract : In this text, we study almost monomial subalgebras using LAGBI bases. We introduce the concept of a LAGBI base and present an algorithm for computing them. We then use this algorithm to find, and present in a table, all polynomial subalgebras with Frobenius number smaller than or equal to ten. READ MORE

  3. 2. Describing Finite Codimensional Polynomial Subalgebras Using Partial Derivatives

    University essay from Lunds universitet/Matematik LTH

    Author : Erik Leffler; [2022]
    Keywords : Algebra Polynomial Derivations alpha-Derivations SAGBI Basis; Mathematics and Statistics;

    Abstract : In this text we continue the work of describing subalgebras of K[x] of finite codimension that was started in Describing subalgebras of K[x] using derivatives. In the referenced paper, the authors present how univariate subalgebras can be described by conditions based on evaluations in certain scalars, and proceed to develop a large theoretical framework to understand the nature of such conditions. READ MORE

  4. 3. Derivations in Univariate Polynomial Subalgebras of Finite Codimension

    University essay from Lunds universitet/Matematik LTH

    Author : Erik Leffler; [2021]
    Keywords : Algebra; Polynomials; SAGBI-basis; derivations; alpha-derivations; Subalgebra conditions.; Mathematics and Statistics;

    Abstract : In this text we continue the work of describing subalgebras of K[x] of finite codimension that was started in “Describing subalgebras of K[x] using derivatives” [2]. In the referenced paper, the authors present how such subalgebras can be described by conditions on the values in certain points and proceed to develop a large theoretical framework to under-stand the nature of such conditions. READ MORE

  5. 4. Conditions for Univariate SAGBI Bases

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Rode Grönkvist; [2020]
    Keywords : SAGBI; SAGBI bases; univariate SAGBI bases; resultant; polynomial algebra; Mathematics and Statistics;

    Abstract : This thesis describes the fundaments of SAGBI theory, including definitions, subduction, SAGBI basis verification and construction. A resultant identity is then used to demonstrate some conditions on univariate SAGBI bases for subalgebras generated by two polynomials... READ MORE