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[null,"1.","Record Nr.",null,"UNINA9910616204903321"]
[null,null,"Autore",null,"Edwards Harold M."]
[null,null,"Titolo",null,"Essays in constructive mathematics / / Harold M. Edwards"]
[null,null,"Pubbl/distr/stampa",null,"Cham, Switzerland : , : Springer, , [2022]"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"3-030-98558-X"]
[null,null,"Edizione",null,"[Second edition.]"]
[null,null,"Descrizione fisica",null,"1 online resource (325 pages)"]
[null,null,"Disciplina",null,"511.3"]
[null,null,"Soggetti",null,"Constructive mathematics"]
[{"$nulls":4},"Matemàtica constructiva"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Intro -- To the Reader -- Contents -- Part I The Original Essays -- 1 A Fundamental Theorem -- Essay  1.1 General Arithmetic -- Essay  1.2 A Fundamental Theorem -- Essay  1.3 Root Fields (Simple Algebraic Extensions) -- Essay  1.4 Factorization of Polynomials with Integer Coefficients -- Essay  1.5 A Factorization Algorithm -- Essay  1.6 Validation of the Factorization Algorithm -- Essay  1.7 About the Factorization Algorithm -- Essay  1.8 Proof of the Fundamental Theorem -- Essay  1.9 Minimal Splitting Polynomials -- 2 Topics in Algebra -- Essay  2.1  Galois's Fundamental Theorem -- Essay  2.2 Algebraic Quantities -- Essay  2.3 Adjunctions and the Factorization of Polynomials -- Essay  2.4 The Splitting Field of xⁿ + c₁xⁿ⁻¹ + c₂xⁿ⁻² + · · · + cₙ -- Essay  2.5 A Fundamental Theorem of Divisor Theory -- 3 Some Quadratic Problems -- Essay  3.1  The Problem A□ + B = □ and \"Hypernumbers -- Essay  3.2  Modules -- Essay  3.3  The Class Semigroup. Solution of  A□ + B = □ -- Essay  3.4  Multiplication of Modules and Module Classes -- Essay  3.5  Is A a Square Mod p? -- Essay  3.6  Gauss's Composition of Forms -- Essay  3.7  The Construction of Compositions -- 4 The Genus of an Algebraic Curve -- Essay  4.1 Abel's Memoir -- Essay  4.2 Euler's Addition Formula -- Essay  4.3 An Algebraic Definition of the Genus -- Essay  4.4 Newton's Polygon -- Essay  4.5 Determination of the Genus -- Essay  4.6 Holomorphic Differentials -- Essay  4.7 The Riemann-Roch Theorem -- Essay  4.8 The Genus Is a Birational Invariant -- 5 Miscellany -- Essay  5.1  On the So-Called Fundamental Theorem of Algebra -- Essay  5.2  "]
[{"$nulls":4},"Proof by Contradiction and the Sylow Theorems -- Essay  5.3  Overview of ``Linear Algebra'' -- Essay  5.4  The Spectral Theorem -- Essay  5.5  Kronecker as One of E. T. Bell's ``Men of Mathematics'' -- Part II Three Topics in Rational Arithmetic."]
[{"$nulls":4},"6 Constructive Algebra -- Essay  6.1  Fields -- Essay  6.2  Factorization -- Essay  6.3  Algorithms -- Endnotes to Chapter 6 -- 7 The Algorithmic Foundations of Galois's Theory -- Essay  7.1 What Are the Roots of a Polynomial? -- Essay  7.2 Galois's Overlooked Construction -- Essay  7.3 The Idea of Galois's Construction -- Essay  7.4 Galois's Determination of the Roots of f(x) in Q(V) -- Essay  7.5 The Galois Group and Galois's Proposition 1 -- Essay  7.6 The Foundation -- Essay  7.7 Extension of the Notion of the Galois Group of a  Polynomial -- Essay  7.8 The Solution of Cubic Polynomials -- Essay  7.9 Galois's Proposition 2 -- Essay  7.10 Galois's Proposition 3 -- Essay  7.11 Solvability by Radicals -- Essay  7.12 The Simplest Case -- Essay  7.13 Solvability by Radicals Implies Solvability of the Galois Group -- Essay  7.14 Roots of Unity -- Essay  7.15 Solvability of the Galois Group implies Solvability by Radicals -- Essay  7.16 The Explicit Solution of Cubics by Radicals -- 8 A Constructive Definition of Points on an Algebraic Curve -- Essay  8.1 The Points on an Algebraic Curve -- Essay  8.2 Curve Fields That Contain Indeterminates -- Essay  8.3 Points of Curve Fields of the Form A(x) -- Essay  8.4 Expansions at a Point Where x Is a Local Parameter -- Essay  8.5 Augmentation and the Newton Diagram -- Essay  8.6 Stub Solutions and Ambiguities -- Essay  8.7 The Algorithm of Essay 8.6 Must Terminate -- Essay  8.8 Expansion Rules -- Essay  8.9 Points -- Essay  8.10 Points Are Intrinsic to K -- Essay  8.11 Quantities Integral Over x -- Essay  8.12 Points as Divisors -- 9 Abel's Theorem -- Essay  9.1  What Was Abel's Theorem? -- Essay  9.2  Normal Bases -- Essay  9.3  The Field of Constants -- Essay  9.4  Differentials and Holomorphic Differentials -- Essay  9.5  The Construction of Holomorphic Differentials."]
[{"$nulls":4},"Essay  9.6  Parametric Points Constructed Using a Normal Basis -- Essay  9.7  The Theorem of Abel's Last Paper -- Essay  9.8  A Theorem About Holomorphic Differentials -- Essay  9.9  A Change of Parameters -- Essay  9.10  Abel's Addition Theorems -- Essay  9.11  Addition on an Elliptic Curve -- Endnotes to Chapter 9 -- Postscript -- References -- Index."]