Essays about: "Polynomial Bases"

Found 5 essays containing the words Polynomial Bases.

  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. 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

  4. 3. Bilinear Gaussian Radial Basis Function Networks for classification of repeated measurements

    University essay from Linköpings universitet/Matematisk statistik; Linköpings universitet/Tekniska fakulteten

    Author : Andreas Sjödin Hällstrand; [2020]
    Keywords : Bilinear Regression; Classification; Supervised Learning; High Dimensional Statistics; Growth Curve Model; Regularization; Radial Basis;

    Abstract : The Growth Curve Model is a bilinear statistical model which can be used to analyse several groups of repeated measurements. Normally the Growth Curve Model is defined in such a way that the permitted sampling frequency of the repeated measurement is limited by the number of observed individuals in the data set. READ MORE

  5. 4. A Gröbner basis algorithm for fast encoding of Reed-Müller codes

    University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : Olle Abrahamsson; [2016]
    Keywords : Gröbner basis; error correcting codes; coding theory; algebra; Reed-Müller; Gröbnerbas; felrättande koder; kodningsteori; algebra; Reed-Müller;

    Abstract : In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. READ MORE

  6. 5. Computational Complexity of Finite Field Multiplication

    University essay from Institutionen för systemteknik

    Author : Nils-Hassan Quttineh; [2003]
    Keywords : Datorteknik; Finite Field; Multiplication; Complexity; Polynomial Bases; Normal Bases; Triangular Bases; Multiples.; Datorteknik;

    Abstract : The subject for this thesis is to find a basis which minimizes the number of bit operations involved in a finite field multiplication. The number of bases of a finite field increases quickly with the extension degree, and it is therefore important to find efficient search algorithms. Only fields of characteristic two are considered. READ MORE