2005

1. Nils Bruin, The primitive solutions to x³+y⁹=z², J. Number Theory 111 (2005), no. 1, 179–189.^[MR]
2. Nils Bruin and E. Victor Flynn, Towers of 2-covers of hyperelliptic curves, Trans. Amer. Math. Soc. 357 (2005), no. 11, 4329–4347 (electronic).^[MR]
3. John J. Cannon, Derek F. Holt, Michael Slattery, and Allan K. Steel, Computing subgroups of bounded index in a finite group, J. Symbolic Comput. 40 (2005), no. 2, 1013–1022.^[MR]
4. Francisco Diaz y Diaz, Jean-François Jaulent, Sebastian Pauli, Michael Pohst, and Florence Soriano-Gafiuk, A new algorithm for the computation of logarithmic l-class groups of number fields, Experiment. Math. 14 (2005), no. 1, 65–74.^[MR]
5. Volker Gebhardt, A new approach to the conjugacy problem in Garside groups, J. Algebra 292 (2005), no. 1, 282–302.^[MR]
6. W. A. de Graaf, M. Harrison, J. Píniková, and J. Schicho, A Lie algebra method for rational parametrization of Severi-Brauer surfaces (extended abstract), Proc. MEGA 2005, Univ. Pisa, 2005.
7. Willem A. de Graaf, Classification of solvable Lie algebras, Experiment. Math. 14 (2005), no. 1, 15–25.^[MR]
8. Markus Grassl and Greg White, New codes from chains of quasi-cyclic codes, in IEEE International Symposium on Information Theory (ISIT), Adelaide, 2005.
9. George Havas and M. R. Vaughan-Lee, 4-Engel groups are locally nilpotent, Internat. J. Algebra Comput. 15 (2005), no. 4, 649–682.^[MR]
10. Derek F. Holt and Colva M. Roney-Dougal, Constructing maximal subgroups of classical groups, LMS J. Comput. Math. 8 (2005), 46–79 (electronic).^[MR]
11. Jürgen Klüners and Sebastian Pauli, Computing residue class rings and Picard groups of orders, J. Algebra 292 (2005), no. 1, 47–64.^[MR]
12. Phong Q. Nguyen and Damien Stehlé, Floating-point LLL revisited, Advances in cryptology—EUROCRYPT 2005, Lecture Notes in Comput. Sci., vol. 3494, Springer, Berlin, 2005, pp. 215–233.^[MR]
13. Miles Reid, Constructing algebraic varieties via commutative algebra, European Congress of Mathematics, Eur. Math. Soc., Zürich, 2005, pp. 655–667.^[MR]
14. Colva M. Roney-Dougal, The primitive permutation groups of degree less than 2500, J. Algebra 292 (2005), no. 1, 154–183.^[MR]
15. Allan Steel, Conquering inseparability: Primary decomposition and multivariate factorization over algebraic function fields of positive characteristic, J. Symbolic Comput. 40 (2005), no. 3, 1053–1075.^[MR]

2006

1. Geoff Bailey, The Magma language, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 331–356.
2. M. A. Bennett, N. Bruin, K. Győry, and L. Hajdu, Powers from products of consecutive terms in arithmetic progression, Proc. London Math. Soc. (3) 92 (2006), no. 2, 273–306.^[MR]
3. Wieb Bosma and John Cannon (eds.), Discovering Mathematics with Magma, Algorithms and Computation in Mathematics, vol. 19, Springer-Verlag, Berlin, 2006, pp. xxiv+374.^[MR]
4. Martin Bright, Brauer groups of diagonal quartic surfaces, J. Symbolic Comput. 41 (2006), no. 5, 544–558.^[MR]
5. Gavin Brown, Graded rings and special K3 surfaces, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 137–159.^[MR]
6. N. Bruin, K. Győry, L. Hajdu, and Sz. Tengely, Arithmetic progressions consisting of unlike powers, Indag. Math. (N.S.) 17 (2006), no. 4, 539–555.^[MR/doi]
7. Nils Bruin, Some ternary Diophantine equations of signature (n,n,2), Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 63–91.^[MR]
8. John J. Cannon and Derek F. Holt, Computing conjugacy class representatives in permutation groups, J. Algebra 300 (2006), no. 1, 213–222.^[MR]
9. Claus Fieker, Applications of the class field theory of global fields, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 31–62.^[MR]
10. Claus Fieker and Michael E. Pohst, Dependency of units in number fields, Math. Comp. 75 (2006), no. 255, 1507–1518 (electronic).^[MR]
11. Volker Gebhardt, Computer aided discovery of a fast algorithm for testing conjugacy in braid groups, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 261–285.^[MR/doi]
12. Willem A. de Graaf, Michael Harrison, Jana Pílniková, and Josef Schicho, A Lie algebra method for rational parametrization of Severi-Brauer surfaces, J. Algebra 303 (2006), no. 2, 514–529.^[MR]
13. Markus Grassl, Searching for linear codes with large minimum distance, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 287–313.^[MR/doi]
14. Michael Harrison and Josef Schicho, Rational parametrisation for degree 6 Del Pezzo surfaces using Lie algebras, ISSAC 2006, ACM, New York, 2006, pp. 132–137.^[MR]
15. Derek F. Holt, Cohomology and group extensions in Magma, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 221–241.^[MR]
16. Derek F. Holt and E. A. O'Brien, A computer-assisted analysis of some matrix groups, J. Algebra 300 (2006), no. 1, 199–212.^[MR]
17. Alexander M. Kasprzyk, Toric Fano three-folds with terminal singularities, Tohoku Math. J. (2) 58 (2006), no. 1, 101–121.^{[MR/doi/arXiv]}
18. Paulette Lieby, Colouring planar graphs, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 315–330.^[MR/doi]
19. Phil Martin and Mark Watkins, Symmetric powers of elliptic curve L-functions, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 377–392.^[MR]
20. Phong Q. Nguyen and Damien Stehlé, LLL on the average, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 238–256.^[MR]
21. Sebastian Pauli, Constructing class fields over local fields, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 627–652.^[MR]
22. Colva M. Roney-Dougal and William R. Unger, Computing the primitive permutation groups of degree less than 1000, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 243–260.^[MR]
23. Josef Schicho, The parametric degree of a rational surface, Math. Z. 254 (2006), no. 1, 185–198.^[MR]
24. Donald E. Taylor, Constructing the split octonions, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 161–185.^[MR/doi]
25. W. R. Unger, Computing the character table of a finite group, J. Symbolic Comput. 41 (2006), no. 8, 847–862.^[MR]
26. W. R. Unger, Computing the soluble radical of a permutation group, J. Algebra 300 (2006), no. 1, 305–315.^[MR]
27. Mark Watkins, A note on integral points on elliptic curves, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 707–720.^[MR]

2007

1. David Abelson, Seok-Hee Hong, and D. E. Taylor, Geometric automorphism groups of graphs, Discrete Appl. Math. 155 (2007), no. 17, 2211–2226.^[MR/doi]
2. Baur Bektemirov, Barry Mazur, William Stein, and Mark Watkins, Average ranks of elliptic curves: tension between data and conjecture, Bull. Amer. Math. Soc. (N.S.) 44 (2007), no. 2, 233–254 (electronic).^[MR]
3. R. P. Brent, Some long-period random number generators using shifts and xors, ANZIAM Journal 48 (2007), C188–C202.
4. M. J. Bright, N. Bruin, E. V. Flynn, and A. Logan, The Brauer-Manin obstruction and Sh[2], LMS J. Comput. Math. 10 (2007), 354–377 (electronic).^[MR]
5. Gavin Brown, A database of polarized K3 surfaces, Experiment. Math. 16 (2007), no. 1, 7–20.^[MR]
6. Gavin Brown and Kaori Suzuki, Computing certain Fano 3-folds, Japan J. Indust. Appl. Math. 24 (2007), no. 3, 241–250.^[MR/link]
7. Gavin Brown and Kaori Suzuki, Fano 3-folds with divisible anticanonical class, Manuscripta Math. 123 (2007), no. 1, 37–51.^[MR]
8. Arjeh M. Cohen and D. E. Taylor, On a certain Lie algebra defined by a finite group, Amer. Math. Monthly 114 (2007), no. 7, 633–639.^[MR]
9. Claus Fieker, Sparse representation for cyclotomic fields, Experiment. Math. 16 (2007), no. 4, 493–500.^[MR]
10. Claus Fieker and Willem A. de Graaf, Finding integral linear dependencies of algebraic numbers and algebraic Lie algebras, LMS J. Comput. Math. 10 (2007), 271–287 (electronic).^[MR]
11. Robert Fraatz, On the computation of integral closures of cyclic extensions of function fields, LMS J. Comput. Math. 10 (2007), 141–160 (electronic).^[MR]
12. Steven D. Galbraith, Florian Hess, and Frederik Vercauteren, Hyperelliptic pairings, Pairing-based cryptography—Pairing 2007, Lecture Notes in Comput. Sci., vol. 4575, Springer, Berlin, 2007, pp. 108–131.^[MR]
13. Willem A. de Graaf, Classification of 6-dimensional nilpotent lie algebras over fields of characteristic not 2, J. Algebra 309 (2007), no. 2, 640–653.^[MR]
14. R. Granger, F. Hess, R. Oyono, N. Thériault, and F. Vercauteren, Ate pairing on hyperelliptic curves, Advances in cryptology—EUROCRYPT 2007, Lecture Notes in Comput. Sci., vol. 4515, Springer, Berlin, 2007, pp. 430–447.^[MR]
15. Guillaume Hanrot and Damien Stehlé, Improved analysis of Kannan's shortest lattice vector algorithm (extended abstract), Advances in cryptology—CRYPTO 2007, Lecture Notes in Comput. Sci., vol. 4622, Springer, Berlin, 2007, pp. 170–186.^[MR]
16. Scott H. Murray, Representations of parabolic and Borel subgroups, Comm. Algebra 35 (2007), no. 2, 455–459.^[MR]
17. John Voight, Quadratic forms that represent almost the same primes, Math. Comp. 76 (2007), no. 259, 1589–1617 (electronic).^[MR/arXiv]
18. Gregory White, Enumeration-based Algorithms in Coding Theory, PhD Thesis, University of Sydney, 2007.

2008

1. Ali Akhavi and Damien Stehlé, Speeding-up lattice reduction with random projections (extended abstract), LATIN 2008: Theoretical informatics, Lecture Notes in Comput. Sci., vol. 4957, Springer, Berlin, 2008, pp. 293–305.^[MR]
2. Jianbei An, John J. Cannon, E. A. O'Brien, and W. R. Unger, The Alperin weight conjecture and Dade's conjecture for the simple group Fi₂₄', LMS J. Comput. Math. 11 (2008), 100–145.^[MR]
3. Tobias Beck and Josef Schicho, Adjoint computation for hypersurfaces using formal desingularizations, J. Algebra 320 (2008), no. 11, 3984–3996.^[MR]
4. Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé, and Paul Zimmermann, Faster multiplication in GF(2)[x], Algorithmic number theory, Lecture Notes in Computer Science, vol. 5011, Springer, Berlin, 2008, pp. 153–166.^[MR/doi]
5. Richard P. Brent and Paul Zimmermann, A multi-level blocking distinct-degree factorization algorithm, Finite fields and applications, Contemp. Math., vol. 461, Amer. Math. Soc., Providence, RI, 2008, pp. 47–58.^[MR]
6. Nils Bruin, The arithmetic of Prym varieties in genus 3, Compos. Math. 144 (2008), no. 2, 317–338.^[MR/link]
7. Nils Bruin and Michael Stoll, Deciding existence of rational points on curves: an experiment, Experiment. Math. 17 (2008), no. 2, 181–189.^[MR/arXiv]
8. John J. Cannon and Derek F. Holt, The transitive permutation groups of degree 32, Experiment. Math. 17 (2008), no. 3, 307–314.^[MR]
9. Arjeh M. Cohen, Sergei Haller, and Scott H. Murray, Computing in unipotent and reductive algebraic groups, LMS J. Comput. Math. 11 (2008), 343–366.^[MR/arXiv]
10. Arjeh M. Cohen, Jan Willem Knopper, and Scott H. Murray, Automatic proof of graph nonisomorphism, Math. Comput. Sci. 2 (2008), no. 2, 211–229.^[MR]
11. J. E. Cremona, T. A. Fisher, C. O'Neil, D. Simon, and M. Stoll, Explicit n-descent on elliptic curves. I. Algebra, J. Reine Angew. Math. 615 (2008), 121–155.^[MR]
12. Lassina Dembélé and Steve Donnelly, Computing Hilbert modular forms over fields with nontrivial class group, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, Berlin/Heidelberg, 2008, pp. 371–386.
13. Tim Dokchitser and Vladimir Dokchitser, Root numbers of elliptic curves in residue characteristic 2, Bull. Lond. Math. Soc. 40 (2008), no. 3, 516–524.^[MR]
14. Claus Fieker and Michael E. Pohst, A lower regulator bound for number fields, J. Number Theory 128 (2008), no. 10, 2767–2775.^[MR]
15. Matthew H. J. Fiset and Alexander M. Kasprzyk, A note on palindromic δ-vectors for certain rational polytopes, Electron. J. Combin. 15 (2008), no. 1, Note 18, 4.^[MR/link]
16. Tom Fisher, Finding rational points on elliptic curves using 6-descent and 12-descent, J. Algebra 320 (2008), no. 2, 853–884.^[MR]
17. Tom Fisher, The invariants of a genus one curve, Proc. Lond. Math. Soc. (3) 97 (2008), no. 3, 753–782.^[MR/arXiv]
18. S. D. Galbraith, F. Hess, and F. Vercauteren, Aspects of pairing inversion, IEEE Transactions on Information Theory 54 (2008), no. 12, 5719–5728.
19. Steven D. Galbraith, Michael Harrison, and David J. Mireles Morales, Efficient hyperelliptic arithmetic using balanced representation for divisors, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, 2008, pp. 342-356.^[eprint]
20. Derek F. Holt and Mark J. Stather, Computing a chief series and the soluble radical of a matrix group over a finite field, LMS J. Comput. Math. 11 (2008), 223–251.^[MR]
21. Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, and Florence Soriano-Gafiuk, Computation of 2-groups of positive classes of exceptional number fields, J. Théor. Nombres Bordeaux 20 (2008), no. 3, 715–732.^[MR]
22. Muraleedaran Krishnasamy and D. E. Taylor, Embeddings of complex line systems and finite reflection groups, J. Aust. Math. Soc. 85 (2008), no. 2, 211–228.^[MR/doi]
23. John Voight, The Gauss higher relative class number problem, Ann. Sci. Math. Québec 32 (2008), no. 2, 221–232.^[MR/arXiv]
24. Mark Watkins, On elliptic curves and random matrix theory, J. Théor. Nombres Bordeaux 20 (2008), no. 3, 829–845.^[MR]
25. Mark Watkins, Some heuristics about elliptic curves, Experiment. Math. 17 (2008), no. 1, 105–125.^[MR/arXiv]

2009

1. Karim Belabas, Mark van Hoeij, J. Klüners, and Allan Steel, Factoring polynomials over global fields, J. Théor. Nombres Bordeaux 21 (2009), 15–39.^[doi]
2. Richard P. Brent and Paul Zimmermann, Ten new primitive binary trinomials, Math. Comp. 78 (2009), no. 266, 1197–1199.^[MR/doi]
3. Gavin Brown, Alexander M. Kasprzyk, and Daniel Ryder, Computational birational geometry of minimal rational surfaces, preprint (2009).^[arXiv]
4. Nils Bruin and Michael Stoll, Two-cover descent on hyperelliptic curves, Math. Comp. 78 (2009), no. 268, 2347–2370.^[MR/doi]
5. Dietrich Burde, Bettina Eick, and Willem de Graaf, Computing faithful representations for nilpotent Lie algebras, J. Algebra 322 (2009), no. 3, 602–612.^[MR/doi]
6. Serena Cicalò and Willem A. de Graaf, Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition. II, J. Symbolic Comput. 44 (2009), no. 7, 786–800.^[MR/doi]
7. Arjeh M. Cohen and Scott H. Murray, An algorithm for Lang's Theorem, J. Algebra 322 (2009), no. 3, 675–702.^[MR/doi]
8. Arjeh M. Cohen and Dan Roozemond, Computing Chevalley bases in small characteristics, J. Algebra 322 (2009), no. 3, 703–721.^[doi]
9. John Cremona, Tom Fisher, Cathy O'Neil, Denis Simon, and Michael Stoll, Explicit n-descent on elliptic curves II: Geometry, Journal für die Reine und Angewandte Mathematik. [Crelle's Journal] 632 (2009), 63–84 pages.^[doi]
10. Lassina Dembélé, A non-solvable Galois extension of Q ramified at 2 only, C. R. Math. Acad. Sci. Paris 347 (2009), no. 3-4, 111–116.^[MR/arXiv]
11. Tim Dokchitser and Vladimir Dokchitser, Elliptic curves with all quadratic twists of positive rank, Acta Arith. 137 (2009), no. 2, 193–197.^[MR/link]
12. Tim Dokchitser and Vladimir Dokchitser, Regulator constants and the parity conjecture, Invent. Math. 178 (2009), no. 1, 23–71.^[doi]
13. N. Dummigan, P. Martin, and M. Watkins, Euler factors and local root numbers for symmetric powers of elliptic curves, Pure and Appl. Math. Qu. 5 (2009), no. 4, 1311–1341.^[doi]
14. Neil Dummigan and Mark Watkins, Critical values of symmetric power L-functions, Pure Appl. Math. Q. 5 (2009), no. 1, part 2, 127–161.^[MR/doi]
15. Claus Fieker, Minimizing representations over number fields ii: computations in the Brauer group, J. Algebra 322 (2009), no. 3, 752–765.^[doi]
16. Steven D. Galbraith, Jordi Pujolàs, Christophe Ritzenthaler, and Benjamin Smith, Distortion maps for supersingular genus two curves, J. Math. Cryptol. 3 (2009), no. 1, 1–18.^[MR/doi]
17. Willem A. de Graaf, Constructing algebraic groups from their Lie algebras, J. Symbolic Comput. 44 (2009), no. 9, 1223–1233.^[MR/doi]
18. Willem A. de Graaf and Andrea Pavan, Constructing arithmetic subgroups of unipotent groups, J. Algebra 322 (2009), no. 11, 3950–3970.^[MR/doi]
19. Willem A. de Graaf, Jana Pílniková, and Josef Schicho, Parametrizing del Pezzo surfaces of degree 8 using Lie algebras, J. Symbolic Comput. 44 (2009), no. 1, 1–14.^[MR/doi]
20. Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, and Florence Soriano-Gafiuk, Computation of 2-groups of narrow logarithmic divisor classes of number fields, J. Symbolic Comput. 44 (2009), no. 7, 852–863.^[MR/doi]
21. Alexander M. Kasprzyk, Bounds on fake weighted projective space, Kodai Math. J. 32 (2009), no. 2, 197–208.^{[MR/doi/arXiv]}
22. Gustav I. Lehrer and Donald E. Taylor, Unitary reflection groups, Australian Mathematical Society Lecture Series, vol. 20, Cambridge University Press, Cambridge, 2009, pp. viii+294.^[MR]
23. Ivan Morel, Damien Stehlé, and Gilles Villard, H-LLL: using Householder inside LLL, ISSAC '09: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2009, pp. 271–278.^[doi]
24. J. -M. Muller, N. Brisebarre, F. de Dinechin, C. -P. Jeannerod, L. Vincent, G. Melquiond, N. Revol, D. Stehlé, and S. Torres, Handbook of floating-point arithmetic., Birkhäuser, Boston, MA, 2009, pp. 660.
25. Gabriele Nebe, Finite Weil-representations and associated Hecke-algebras, J. Number Theory 129 (2009), no. 3, 588–603.^[MR/doi]
26. Gabriele Nebe and Allan Steel, Recognition of division algebras, J. Algebra 322 (2009), no. 3, 903–909.^[doi]
27. Phong Q. Nguyen and Damien Stehlé, An LLL algorithm with quadratic complexity, SIAM Journal on Computing 39 (2009), no. 3, 874–903.^[doi]
28. Phong Q. Nguyen and Damien Stehlé, Low-dimensional lattice basis reduction revisited, ACM Transactions on Algorithms 5 (2009), no. 4.^[doi]
29. Xavier Pujol and Damien Stehlé, Solving the shortest lattice vector problem in time 2^2.465n, (2009).^[link]
30. Damien Stehlé, The LLL algorithm, survey and applications, Nguyen, Phong Q. and Vallée, Brigitte (Eds.) Floating-point LLL: Theoretical and Practical Aspects, Information Security and Cryptography, Springer, Berlin, 2009.
31. Damien Stehlé, Ron Steinfeld, Keisuke Tanaka, and Keita Xagawa, Efficient public-key encryption based on ideal lattices (extended abstract), Advances in Cryptology - ASIACRYPT 2008, Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008, Lecture Notes in Comput. Sci., vol. 5912, Springer, Berlin, 2009, pp. 617–635.
32. John Voight, Computing fundamental domains for Fuchsian groups, J. Théor. Nombres Bordeaux 21 (2009), no. 2, 469–491.^[MR/link]
33. John Voight, Shimura curves of genus at most two, Math. Comp. 78 (2009), no. 266, 1155–1172.^[MR/link]
34. M. Watkins, On the extremality of an 80-dimensional lattice, in Explicit Methods in Number Theory, European Mathematical Society Publishing House, Zürich, 2009, pp. 1886–1889.^[doi]
35. Robert A. Wilson, The Finite Simple Groups, Graduate Texts in Mathematics, vol. 251, Springer-Verlag London Ltd., London, 2009, pp. xvi+298.^[MR]