I Algebraic Concepts. - 1 Introduction. - 2 Groups Rings Integral Domains and Fields. - 3 Power Series and Polynomials. - 4 Chinese Remainder Theorem and Interpolation. - 5 Polynomials in Several Variables. - II Polynomial MatrixEvaluation Interpolation Inversion. - 1 Introduction. - 2 Results from Matrix Theory. - 3 Matrix MethodEvaluation and Interpolation of Single Variable Polynomials. - 4 Tensor Product MethodEvaluation and Interpolation of Multi-variable Polynomials. - III Fourier Evaluation and Interpolation. - 1 Introduction. - 2 Discrete Fourier Transform over a Ring. - 3 Convolution. - 4 Error-Free DFT. - 5 Polynomial EvaluationInterpolationMultiplication. - 6 Multivariable Polynomial Interpolation. - IV Polynomial Hensel Codes. - 1 Introduction. - 2 Hensel Fields. - 3 Isomorphic Algebras. - 4 Hensel Codes for Rational Polynomials. - 5 Arithmetic of Hensel Codes. - 6 Forward and Inverse Mapping Algorithms. - 7 Direct Solution of Linear Systems and Matrix Inversion. - 8 HenselNewtonSchultz Iterative Matrix Inversion. - V Matrix ComputationsEuclidean and Non-Euclidean Domains. - 1 Introduction. - 2 Matrices over Euclidean Domains. - 3 Matrices over Non-Euclidean Domains. - 4 Multivariable Polynomial Hensel Codes. Language: English