Ebook: Algorithmic Algebra and Number Theory: Selected Papers From a Conference Held at the University of Heidelberg in October 1997

This book contains 22 lectures presented at the final conference of the German research program "Algorithmic Number Theory and Algebra 1991-1997", sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research program and the meeting was to bring together developers of computer algebra software and researchers using computational methods to gain insight into experimental problems and theoretical questions in algebra and number theory. The book gives an overview on algorithmic methods and results obtained during this period mainly in algebraic number theory, commutative algebra and algebraic geometry, and group and representation theory. Some of the articles illustrate the current state of the computer algebra systems developed with support from the research program, for example KANT and LiDIA for algebraic number theory, SINGULAR, REDLOG and INVAR for commutative algebra and invariant theory respectively, and GAP, SYSYPHOS and CHEVIE for group and representation theory.

---

This book contains 22 lectures presented at the final conference of the German research program "Algorithmic Number Theory and Algebra 1991-1997", sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research program and the meeting was to bring together developers of computer algebra software and researchers using computational methods to gain insight into experimental problems and theoretical questions in algebra and number theory. The book gives an overview on algorithmic methods and results obtained during this period mainly in algebraic number theory, commutative algebra and algebraic geometry, and group and representation theory. Some of the articles illustrate the current state of the computer algebra systems developed with support from the research program, for example KANT and LiDIA for algebraic number theory, SINGULAR, REDLOG and INVAR for commutative algebra and invariant theory respectively, and GAP, SYSYPHOS and CHEVIE for group and representation theory.

---

This book contains 22 lectures presented at the final conference of the German research program "Algorithmic Number Theory and Algebra 1991-1997", sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research program and the meeting was to bring together developers of computer algebra software and researchers using computational methods to gain insight into experimental problems and theoretical questions in algebra and number theory. The book gives an overview on algorithmic methods and results obtained during this period mainly in algebraic number theory, commutative algebra and algebraic geometry, and group and representation theory. Some of the articles illustrate the current state of the computer algebra systems developed with support from the research program, for example KANT and LiDIA for algebraic number theory, SINGULAR, REDLOG and INVAR for commutative algebra and invariant theory respectively, and GAP, SYSYPHOS and CHEVIE for group and representation theory.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Sieving Methods for Class Group Computation....Pages 3-10
Arithmetic of Modular Curves and Applications....Pages 11-48
Local and Global Ramification Properties of Elliptic Curves....Pages 49-64
Techniques for the Computation of Galois Groups....Pages 65-77
Fortschritte in der inversen Galoistheorie....Pages 79-102
From Class Groups to Class Fields....Pages 103-119
A Gross-Zagier Formula for Function Fields....Pages 121-137
Extremal Lattices....Pages 139-170
Front Matter....Pages 171-171
On the Real Nullstellensatz....Pages 173-185
Primary Decomposition: Algorithms and Comparisons....Pages 187-220
Real Quantifier Elimination in Practice....Pages 221-247
Hilbert Series and Degree Bounds in Invariant Theory....Pages 249-263
Invariant Rings and Fields of Finite Groups....Pages 265-281
Computing Versal Deformations with Singular....Pages 283-293
Algorithms for the Computation of Free Resolutions....Pages 295-310
Front Matter....Pages 311-311
Computational Aspects of the Isomorphism Problem....Pages 313-329
Representations of Heeke Algebras and Finite Groups of Lie Type....Pages 331-378
The Groups of Order 512....Pages 379-380
Computational Aspects of Representation Theory of Finite Groups II....Pages 381-397
High Performance Computations in Group Representation Theory....Pages 399-415
Front Matter....Pages 311-311
The Structure of Maximal Finite Primitive Matrix Groups....Pages 417-422
Presentations and Representations of Groups....Pages 423-434
Back Matter....Pages 435-437

---

This book contains 22 lectures presented at the final conference of the German research program "Algorithmic Number Theory and Algebra 1991-1997", sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research program and the meeting was to bring together developers of computer algebra software and researchers using computational methods to gain insight into experimental problems and theoretical questions in algebra and number theory. The book gives an overview on algorithmic methods and results obtained during this period mainly in algebraic number theory, commutative algebra and algebraic geometry, and group and representation theory. Some of the articles illustrate the current state of the computer algebra systems developed with support from the research program, for example KANT and LiDIA for algebraic number theory, SINGULAR, REDLOG and INVAR for commutative algebra and invariant theory respectively, and GAP, SYSYPHOS and CHEVIE for group and representation theory.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Sieving Methods for Class Group Computation....Pages 3-10
Arithmetic of Modular Curves and Applications....Pages 11-48
Local and Global Ramification Properties of Elliptic Curves....Pages 49-64
Techniques for the Computation of Galois Groups....Pages 65-77
Fortschritte in der inversen Galoistheorie....Pages 79-102
From Class Groups to Class Fields....Pages 103-119
A Gross-Zagier Formula for Function Fields....Pages 121-137
Extremal Lattices....Pages 139-170
Front Matter....Pages 171-171
On the Real Nullstellensatz....Pages 173-185
Primary Decomposition: Algorithms and Comparisons....Pages 187-220
Real Quantifier Elimination in Practice....Pages 221-247
Hilbert Series and Degree Bounds in Invariant Theory....Pages 249-263
Invariant Rings and Fields of Finite Groups....Pages 265-281
Computing Versal Deformations with Singular....Pages 283-293
Algorithms for the Computation of Free Resolutions....Pages 295-310
Front Matter....Pages 311-311
Computational Aspects of the Isomorphism Problem....Pages 313-329
Representations of Heeke Algebras and Finite Groups of Lie Type....Pages 331-378
The Groups of Order 512....Pages 379-380
Computational Aspects of Representation Theory of Finite Groups II....Pages 381-397
High Performance Computations in Group Representation Theory....Pages 399-415
Front Matter....Pages 311-311
The Structure of Maximal Finite Primitive Matrix Groups....Pages 417-422
Presentations and Representations of Groups....Pages 423-434
Back Matter....Pages 435-437
....