Discovering Mathematics with Magma [electronic resource] : Reducing the Abstract to the Concrete / edited by Wieb Bosma, John Cannon.

Contributor(s): Bosma, Wieb [editor.] | Cannon, John [editor.] | SpringerLink (Online service)
Material type: TextTextSeries: Algorithms and Computation in Mathematics: 19Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XXIV, 364 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540376347Subject(s): Mathematics | Computer science -- Mathematics | Algebra | Algorithms | Computer software | Mathematics | Mathematical Software | Algebra | Algorithms | Symbolic and Algebraic ManipulationAdditional physical formats: Printed edition:: No titleDDC classification: 004 LOC classification: QA76.75-76.765Online resources: Click here to access online
Contents:
Some computational experiments in number theory -- Applications of the class field theory of global fields -- Some ternary Diophantine equations of signature (n, n, 2) -- Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma -- Computing with the analytic Jacobian of a genus 2 curve -- Graded rings and special K3 surfaces -- Constructing the split octonions -- Support varieties for modules -- When is projectivity detected on subalgebras? -- Cohomology and group extensions in Magma -- Computing the primitive permutation groups of degree less than 1000 -- Computer aided discovery of a fast algorithm for testing conjugacy in braid groups -- Searching for linear codes with large minimum distance -- Colouring planar graphs -- Appendix: The Magma language.
In: Springer eBooksSummary: This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the reader to the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning new theoretical results. The authors of the chapters were chosen both for their expertise in the particular field and for their innovative use of Magma. Although by no means exhaustive, the topics range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.
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Some computational experiments in number theory -- Applications of the class field theory of global fields -- Some ternary Diophantine equations of signature (n, n, 2) -- Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma -- Computing with the analytic Jacobian of a genus 2 curve -- Graded rings and special K3 surfaces -- Constructing the split octonions -- Support varieties for modules -- When is projectivity detected on subalgebras? -- Cohomology and group extensions in Magma -- Computing the primitive permutation groups of degree less than 1000 -- Computer aided discovery of a fast algorithm for testing conjugacy in braid groups -- Searching for linear codes with large minimum distance -- Colouring planar graphs -- Appendix: The Magma language.

This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the reader to the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning new theoretical results. The authors of the chapters were chosen both for their expertise in the particular field and for their innovative use of Magma. Although by no means exhaustive, the topics range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.

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