COMPUTERS IN ALGEBRA: NEW ANSWERS, NEW QUESTIONS

  • Praeger, Cheryl E. (Department of Mathematics and Statistics, University of Western Australia)
  • 발행 : 2001.07.01

초록

The use and development of of computer technology by algebraists over the last forty years has revolutionised the way in which algebraists think about algebra, and the way they teach it and conduct their research. This paper is a personal reflection on these changes by a somewhat unwilling computer user.

키워드

참고문헌

  1. Proceedings of the International Congress of Mathematics v.Ⅰ;Ⅱ Computational complexity in finite groups L. Babai
  2. Theory of Computing Local expansion of vertex-transitive graphs and random generation in finite groups
  3. Groups and computation v.Ⅱ Randomization in group algorithms: conceptual questions
  4. J. Comput. System Sci. v.50 no.2 Fast Monte Carlo algorithms for permutation groups L. Babai;G. Cooperman;L. Finkelstein;E. M. Luks;A. Seress
  5. Proc. of International Symposium on Symbolicand Algrebraic Computation ISSAC '91 Nearly linear time algorithms for permutation groups with a small base L. Babai;G. Cooperman;L. Finkelstein;A. Seress
  6. Proc. 24th FOCS Computational complexity and the classification of finite simple groups L. Babai;W. M. Kantor;E. M. Luks
  7. SIAM J. Comput v.26 Fast management of permutation groups Ⅰ L. Babai;E. M. Luks;A. Seress
  8. Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithm Strong bias of group generators: an obstacle to the "product replacement algorithm" L. Babai;I. Pak
  9. Preparation Measuring the performnce of random element generators in large algebraic structures A. Baddeley;C. R. Leedham-Green;A. C. Niemeyer;M. Firth
  10. Groups and Computation v.Ⅱ Experimenting and computing with infinite groups G. Baumslag;C. F. Miller,Ⅲ
  11. Proc. Second Internat. Conf. Theory of Groups of Lecture Notes in Math v.372 Computation in nilpotent group(application) A. J. Bayes;J. Kautsky;J. W. Wamsley
  12. Handbook of Magma functions W. Bosma;J. Cannon
  13. Wiley Monographs in Crystallography Crystallographic groups of four-dimensional space Wiley-Interscience H. Brown;R. Bulow;J. Neubuser;H. Wondratschek;H. Zassenhaus
  14. Quart. J. Pure Appl. Math v.33 On an unsettled question in the theory of discontinuous groups W. Burnside
  15. Lecture Notes in Comput. Sci. v.559 Fundamental algorithms for permutation groups G. Butler
  16. Proc. Rutgers Group Theory Year A computational toolkit for finite permutation groups J. Cannon
  17. Comm. Algebra v.23 Generating random elements of a finite group F. Celler;C. R. Leedham-Green;S. H. Murray;A. C. Niemeyer;E. A. O'Brien
  18. Ann. Probab. v.21 Comparison techniques for random walk on finite groups P. Diaconis;L. Saloff-Coste
  19. Geom. Funct. Anal. v.4 Moderate growth and random walk on finite groups
  20. Probab. Theory Related Fields v.105 Walks on generating sets of abelian groups
  21. Pacific J. Math. v.13 Solvability of groups of odd order W. Feit;J. G. Thompson
  22. 21st Annual Symposium on foundations of Computer Science Polynomial-time algorithmsfor permutation groups M. Furst;J. Hopcroft;E. Luks
  23. Appl. Algebra Engrg. Comm. Comput. v.7 no.3 CHEVIE-a system for computing and processing generic character tables M. Geck;G. Hiss;F. Lubeck;G. Malle;G. Pfeiffer
  24. The Theory of Groups M. Hall Jr.
  25. Burnside Groups v.806 Application of computers to questions like those of burnside G. Havas;M. F. Newman
  26. J. Symbolic Comput v.9 A nilpotent quotient algorithm for graded lie rings G. Havas;M. F. Newman;M. R. Vaughan-Lee
  27. Perfect Groups D. F. Holt;W. Plesken
  28. J. Experimental Math. v.1 An implementation of the Newmann-Praeger algorithm for the recognition of special linear groups D. F. Holt;S. Rees
  29. Groups and Computation v.DIMACS Series 11 A graphics system for displaying finite quotients of finitely presented groups
  30. J. Algebra v.20 A characterization of the Mclaughlin's simple group Z. Janko;S. K. Wong
  31. J. Comput System. Sci. v.30 Sylow's theorem in polynomial time W. M. Kantor
  32. Computational Group Theory Algorithms for finite soluble groups and the SOGOS system R. Laue;J. Neubuser;U. Schoenwaelder
  33. Computer, Algebra, Foundation, Applications, Systems(to appear) Recognising matrix groups over finite fields C. R. Leedham-Green;A. C. Niemeyer;E. A. O'Brien;C. E. Praeger;V. Weispfenning(ed.);J. Grabmeier(ed.);E. Kaltofen(ed.)
  34. J. Symbolic Comput. v.12 Computing with group homomorphisms C. R. Leedham-Green;C. E. Praeger;L. H. Soicher
  35. Math. Comp v.20 On an algorithm for finding a base and strong generating set for a group given by generating permutations J. S. Leon
  36. J. Comput System Sci. v.25 Isomorphism of graphs of bounded valance can be tested in polynomial time E. M. Luks
  37. Groups and Computation v.DIMACS Series 11 Permutation groups and polynomial-time computation
  38. J. Algebra v.20 Evidence for a new finite simple group R. Lyons
  39. J. Austral. Math. Soc. Ser. v.A 17 A Computer application to finite p-groups I. D. Macdonald
  40. Ars Combin v.16B Cayley properties of vertex symmetric graphs D. Marusic
  41. Technical Report, Dept. Comp. Sci. Nauty users guide(version 1.5) B. McKay
  42. J. Algebraic Combin v.3 no.1 Non-Cayley nertex-transitive graphs of order twice the product of two odd primes A. A. Miller;C. E. Praeger
  43. Groups'93-Galway/St. Andrews of London Math. Soc. Lecture Note Ser. v.212 An Invitation to computational group theory J. Neubuser;C. M. Campbell(ed.);T. C. Hurley(ed.);E. F. Robertson(ed.);S. J. Tobin(ed.);J. J. Ward(ed.)
  44. Computational Group Theory CAS; design and use of a system for the handling of characters of finite groups J. Neubuser;H. Pahlings;W. Plesken
  45. Proc. London Math. Soc. v.65 no.3 A recognition algorithm for special linear groups P. M. Neumann;C. E. Praeger
  46. Group Theory of Lecture Notes in Math v.573 Determination of groups of prime-power order M. F. Newman
  47. Mathmatics Research Reports A still unsettled question
  48. Group Theory A CAYLEY library for the groups of order dividing 128 M. F. Newman;E. A. O'Brien
  49. J. Symbolic Comput v.9 The p-group generation algorithm E. A. O'Brien
  50. J. Algebra v.143 no.1 The groups of order 256
  51. Electron. J. Probab. v.4 no.1 Random walks on finite groups with few random generators I. Park
  52. Computational Group Theory The computer calculation of modular characters(the Meat-Axe) R. A. Parker;M. D. Atkinson(ed.)
  53. DIMACS Series v.DIMACS 11 Computation with matrix groups over finite fields C. E. Praeger
  54. Lehrstuhl D Fur Mathematik(5th ed.) GAP-Groups, Algirithms and Programming M. Schonert(et al.)
  55. Computational problems in abstract algebra Computational methods in the study of permutation groups C. C. Sims
  56. Finite Groups '72 The existence and uniqueness T. Hagen(ed.);M. P. Hale(ed.);E. E. Shult(ed.)
  57. Proceedings International Conference of Mathematicians Group theoretic algorithms, a survey
  58. Group and Computation GRAPE: A system for computing with graphs and groups L. H. Sochier
  59. London Math. Soc. Monogr.(N.S.) v.5 The Restricted burnside Problem M. R. Vaughan-Lee