COMPUTERS IN ALGEBRA: NEW ANSWERS, NEW QUESTIONS

  • Praeger, Cheryl E.
  • Published : 2001.07.01

Abstract

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.

Keywords

computational algebra;computational group theory

References

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