Ebook: Computational Algebra and Number Theory

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few.
Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed.
Audience: Students, experts, and those performing current research in any of the topics mentioned above.

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Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few.
Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed.
Audience: Students, experts, and those performing current research in any of the topics mentioned above.

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Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few.
Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed.
Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Content:
Front Matter....Pages i-xiv
Calculating Growth Functions for Groups Using Automata....Pages 1-18
The Minimal Faithful Degree of a Finite Commutative Inverse Semigroup....Pages 19-27
Generalisations of the Todd-Coxeter Algorithm....Pages 29-51
Computing Left Kan Extensions Using the Todd-Coxeter Procedure....Pages 53-73
Computing Finite Soluble Quotients....Pages 75-82
Computing Automorphism Groups of p-Groups....Pages 83-90
The Art and Science of Computing in Large Groups....Pages 91-109
Does the Set of Points of an Elliptic Curve Determine the Group?....Pages 111-118
An Implementation of the Elliptic Curve Integer Factorization Method....Pages 119-136
Continued Fractions of Algebraic Numbers....Pages 137-152
Bounds for Class Numbers of Quadratic Orders....Pages 153-158
Short Representation of Quadratic Integers....Pages 159-185
A Density Conjecture for the Negative Pell Equation....Pages 187-200
Computing Aurifeuillian Factors....Pages 201-212
Computation of Cyclotomic Polynomials with Magma....Pages 213-225
On Some Characteristics of Uniformity of Distribution and Their Applications....Pages 227-241
Recent Progress on Consistency Testing for Polynomial Systems....Pages 243-253
A New Generalisation of the Kummer Congruence....Pages 255-265
Series Expansions of Algebraic Functions....Pages 267-277
Generation of Cocyclic Hadamard Matrices....Pages 279-290
Large Cayley Graphs and Digraphs with Small Degree and Diameter....Pages 291-302
Hyperbolic Pyritohedra Constructed from the Coxeter Group [4,3,5]....Pages 303-321

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Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few.
Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed.
Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Content:
Front Matter....Pages i-xiv
Calculating Growth Functions for Groups Using Automata....Pages 1-18
The Minimal Faithful Degree of a Finite Commutative Inverse Semigroup....Pages 19-27
Generalisations of the Todd-Coxeter Algorithm....Pages 29-51
Computing Left Kan Extensions Using the Todd-Coxeter Procedure....Pages 53-73
Computing Finite Soluble Quotients....Pages 75-82
Computing Automorphism Groups of p-Groups....Pages 83-90
The Art and Science of Computing in Large Groups....Pages 91-109
Does the Set of Points of an Elliptic Curve Determine the Group?....Pages 111-118
An Implementation of the Elliptic Curve Integer Factorization Method....Pages 119-136
Continued Fractions of Algebraic Numbers....Pages 137-152
Bounds for Class Numbers of Quadratic Orders....Pages 153-158
Short Representation of Quadratic Integers....Pages 159-185
A Density Conjecture for the Negative Pell Equation....Pages 187-200
Computing Aurifeuillian Factors....Pages 201-212
Computation of Cyclotomic Polynomials with Magma....Pages 213-225
On Some Characteristics of Uniformity of Distribution and Their Applications....Pages 227-241
Recent Progress on Consistency Testing for Polynomial Systems....Pages 243-253
A New Generalisation of the Kummer Congruence....Pages 255-265
Series Expansions of Algebraic Functions....Pages 267-277
Generation of Cocyclic Hadamard Matrices....Pages 279-290
Large Cayley Graphs and Digraphs with Small Degree and Diameter....Pages 291-302
Hyperbolic Pyritohedra Constructed from the Coxeter Group [4,3,5]....Pages 303-321
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