***************************************************************** * Second Magma Conference on Computational Algebra * * Marquette University, Milwaukee, May 12--16, 1996 * ***************************************************************** An interdisciplinary conference on computational algebra and number theory, computer algebra and their applications will be held from May 12--16, 1996 at Marquette University, Milwaukee, Wisconsin, USA. The purpose of this conference is to bring to- gether mathematicians and software developers to present recent developments in cognate areas of computational algebra and number theory, to inform theoreticians about available computational tools and provide an opportunity to become familiar with their use, to identify desirable directions for theoretical research and practical development, and to promote the use of advanced tools in applied areas. In the past few years a number of very significant advances have taken place in several different branches of computational alge- bra and number theory. The organizers of this Conference per- ceive a need to bring together theoretical mathematicians and developers of algorithms and software tools to consider ways of overcoming the compartmentalized nature of computational algebra in the context of the increasing tendency for sophisticated ap- plications to draw on computational techniques from several quite different areas. Conference Site ############### The Department of Mathematics, Statistics and Computer Science at Marquette University will host the meeting. Since January 1994, the Department has been located in Katharine Reed Cudahy Hall, in the center of the Marquette campus. Marquette University, located on an 80-acre urban campus near downtown Milwaukee, Wisconsin, is an independent, coeducational institution founded in 1881. Lectures will be held in the main lecture auditorium which seats 140 people and features network connections and video projection equipment. A discussion area outside the lecture hall, at the foot of the atrium, will be available for morning and afternoon teas. Extensive computing facilities will be available for conference delegates, including Internet services. Proceedings ########### A proceedings of the Conference will appear as a special issue of the Journal of Symbolic Computation. Conference Program ################## Sunday, May 12 12:45 -- 13:00 Official Welcome and Opening Remarks 13:00 -- 14:30 Number Theory 13:00 -- 13:50 Invited Lecture Computational Class Field Theory Henri Cohen, Bordeaux 14:00 -- 14:25 Contributed Talk Computations in Kummer Extensions Mario Daberkow, TU-Berlin Coffee Break 15:00 -- 16:30 Module Theory and Homological Algebra 15:00 -- 15:50 Invited Lecture Computing Canonical Presentations for Z-modules George Havas, Queensland 16:00 -- 16:25 Contributed Talk Sheafhom: Programs for Homological Algebra and Algebraic Topology Mark McConnell, Oklahoma State 16:30 -- 18:30 Magma Workshop An Overview of Magma John Cannon, Sydney Getting Started with Magma Wieb Bosma, Sydney Laboratory Session 18:30 -- 19:30 Informal Reception (Drinks and Nibbles Provided) Monday, May 13 09:00 -- 10:25 Commutative Algebra 09:00 -- 09:55 Invited Lecture Factoring High-Degree Polynomials over Finite Fields: New Theory, Faster Practice Erich Kaltofen, North Carolina 10:00 -- 10:25 Contributed Talk A New Approach to Primary Decomposition Alain Sausse, INRIA-Sophia Antipolis Coffee Break 11:00 -- 12:00 Group Theory 11:00 -- 12:00 Contributed Talks Verification of Strong Generating Set Constructions Akos Seress, Ohio State A New Existence Proof for Ly, the Sporadic Simple Group of R. Lyons Holger Gollan, Essen 12:00 -- 13:00 System Presentation Pari Henri Cohen, Bordeaux Lunch 14:00 -- 16:00 Representation Theory 14:00 -- 14:55 Invited Lecture Parallel Linear Algebra and Computational Representation Theory Gerhard Michler, Essen 15:00 -- 16:00 Contributed Talks The Use of Peakwords and Condensation in Computational Modular Representation Theory Klaus Lux, Aachen Interface between DTP and Magma Jacques Calmet and Karsten Homann, Karlsruhe Coffee Break 16:30 -- 18:30 Magma Workshop Commutative Algebra John Cannon (with Allan Steel), Sydney Field Theory Wieb Bosma, Sydney Laboratory Session Tuesday, May 14 09:00 -- 09:55 Algebraic Geometry 09:00 -- 09:55 Invited Lecture Computational Aspects of Curves of Genus at least 2 Bjorn Poonen, Princeton 10:00 -- 10:25 Contributed Talk Irregular Primes to Eight Million J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. A. Shokrollahi Coffee Break 11:00 -- 12:00 Group Theory 11:00 -- 12:00 Contributed Talks Computing in the Monster Simon Norton, Cambridge Embeddings of PSL_2(q) in E_8(C) Alex Ryba, Marquette 12:00 -- 13:00 System Presentation Macauley 2 Dan Grayson, UIC Lunch and Poster Session 14:00 -- 15:25 Module Theory 14:00 -- 14:55 Invited Lecture Computer Calculations of Modules and Cohomology Jon Carlson, Athens 15:00 -- 16:00 Contributed Talks The Cohomology of Augmented Algebras Robert Bruner, Wayne State On the Cohomology of Split Extensions of Elementary Abelian 2-groups Stephen Siegel, Northwestern Coffee Break 16:30 -- 18:30 Magma Workshop Module Theory Jon Carlson, Athens Permutation and Matrix Groups Bruce Cox, Sydney Laboratory Session Wednesday, May 15 09:00 -- 10:30 Number Theory 09:00 -- 09:55 Invited Lecture Classical Invariant Theory and Elliptic Curves John Cremona, Exeter 10:00 -- 10:25 Contributed Talk Computations with Brauer's Class Number Relations Wieb Bosma (Sydney) and Bart de Smit (Amsterdam) Coffee Break 11:00 -- 13:00 Semigroups 11:00 -- 12:00 Contributed Talks An Optimal Algorithm for Constructing the Reduced Groebner Basis of Binomial Ideals and Applications to Commutative Semigroups Ulla Koppenhagen and Ernst Mayr, Munchen Idempotent Algebras Associated with Periodic Semigroups Francis Pastijn, Marquette 12:00 -- 13:00 Invited Lecture and System Presentation Computational Automata and Semigroup Theory: The Automate System Stuart Margolis, Bar Ilan Lunch 14:00 -- 15:30 Finite Geometry and Codes 14:00 -- 14:55 Invited Lecture Applications of Magma in Designs and Codes Jenny Key, Clemson 15:00 -- 15:25 Contributed Talk Constructing Non-Linear Trellis Codes James Sarvis, MIT Coffee Break 16:00 -- 17:15 Magma Workshop Designs, Codes and Planes Jenny Key, Clemson Finitely Presented Groups George Havas, Queensland 18:00 -- 21:00 Conference Dinner Thursday, May 16 09:00 -- 10:30 Group Theory 09:00 -- 09:55 Invited Lecture Partitions, Normalizers, and Subgroup Conjugacy Jeff Leon, UICC 10:00 -- 10:25 Contributed Talk Algorithms for Soluble Groups: Past, Present and Future Mike Slattery, Marquette Coffee Break 11:00 -- 12:00 Rings and Fields 11:00 -- 12:00 Invited Talk Noncommutative Groebner Bases: Theory and Applications Ed Green, Virginia Tech 12:00 -- 13:00 System Presentation KANT 4 Mario Daberkow and Claus Fieker, TU-Berlin Lunch 14:00 -- 15:30 Group Theory 14:00 -- 14:55 Invited Lecture Recognizing Matrix Groups Charles Leedham-Green, QMW 15:00 -- 15:25 Contributed Talk Nine New Algorithms for Permutation Groups John Cannon, Sydney Coffee and Conference End Poster Presentations Computational Techniques for Investigating Polygons of Finite Groups Paul Brown, Berkeley Weak Parameters for the SL_2 Hash Function Chris Charnes (with Josef Pieprzyk), Wollongong Factoring Polynomials over Large Finite Fields and Hadamard Designs Shuhong Gao, Clemson Experiments with Algorithms and Orders in the Computation of Noncommutative Groebner Bases Ben Keller, Virginia Tech The Category of Abstract Interpretations with Magma Kaninda Musumbu, Bordeaux Ideals in Monoidal Rings and 16th Hilbert Problem Valery Romanovskii, Minsk The Magma Groebner Walk Allan Steel, Sydney Polynomials taking many Values over Finite Fields Michael Zieve, Berkeley