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A first course in computational algebraic geometry / Wolfram Decker and Gerhard Pfister.

By: Contributor(s): Material type: TextTextSeries: AIMS library seriesPublication details: Cambridge ; New York : Cambridge University Press, 2013.Description: 1 online resource (viii, 118 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781107314795
  • 1107314798
  • 110730704X
  • 9781107307049
  • 9781139565769
  • 1139565761
  • 9781299006355
  • 1299006353
  • 9781107301955
  • 1107301955
  • 1107238641
  • 9781107238640
  • 1107255880
  • 9781107255883
  • 1107312590
  • 9781107312593
Subject(s): Additional physical formats: Print version:: First Course in Computational Algebraic Geometry.DDC classification:
  • 516.35 23
LOC classification:
  • QA564
Online resources:
Contents:
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
Summary: A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library EBSCO Mathematics Available
Total holds: 0

Includes bibliographical references and index.

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

Print version record.

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

English.

Added to collection customer.56279.3

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