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A first course in computational algebraic geometry /
A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2013.
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| Colección: | AIMS library series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; Preface; Prologue: General Remarks on Computer Algebra Systems; 1 The Geometry-Algebra Dictionary; 1.1 Affine Algebraic Geometry; 1.1.1 Ideals in Polynomial Rings; 1.1.2 Affine Algebraic Sets; 1.1.3 Hilbert's Nullstellensatz; 1.1.4 Irreducible Algebraic Sets; 1.1.5 Removing Algebraic Sets; 1.1.6 Polynomial Maps; 1.1.7 The Geometry of Elimination; 1.1.8 Noether Normalization and Dimension; 1.1.9 Local Studies; 1.2 Projective Algebraic Geometry; 1.2.1 The Projective Space; 1.2.2 Projective Algebraic Sets; 1.2.3 Affine Charts and the Projective Closure
- 1.2.4 The Hilbert Polynomial2 Computing; 2.1 Standard Bases and Singular; 2.2 Applications; 2.2.1 Ideal Membership; 2.2.2 Elimination; 2.2.3 Radical Membership; 2.2.4 Ideal Intersections; 2.2.5 Ideal Quotients; 2.2.6 Kernel of a Ring Map; 2.2.7 Integrality Criterion; 2.2.8 Noether Normalization; 2.2.9 Subalgebra Membership; 2.2.10 Homogenization; 2.3 Dimension and the Hilbert Function; 2.4 Primary Decomposition and Radicals; 2.5 Buchberger's Algorithm and Field Extensions; 3 Sudoku; 4 A Problem in Group Theory Solved by Computer Algebra; 4.1 Finite Groups and Thompson's Theorem
- 4.2 Characterization of Finite Solvable GroupsBibliography; Index