Commutative Algebra

  1. I. Abdeljaouad-Tej, S. Orange, G. Renault, and A. Valibouze, Computation of the decomposition group of a triangular ideal, Appl. Algebra Engrg. Comm. Comput. 15 (2004), no. 3-4, 279–294.[MR]
  2. Fatima Abu Salem, Shuhong Gao, and Alan G. B. Lauder, Factoring polynomials via polytopes, ISSAC 2004, ACM, New York, 2004, pp. 4–11.[MR]
  3. Selma Altınok, Gavin Brown, and Miles Reid, Fano 3-folds, K3 surfaces and graded rings, Topology and Geometry: Commemorating SISTAG, Contemp. Math., vol. 314, Amer. Math. Soc., Providence, RI, 2002, pp. 25–53.[MR]
  4. David F. Anderson, Andrea Frazier, Aaron Lauve, and Philip S. Livingston, The zero-divisor graph of a commutative ring: II, Ideal Theoretic Methods in Commutative Algebra (Columbia, MO, 1999), Lecture Notes in Pure and Appl. Math., vol. 220, Dekker, New York, 2001, pp. 61–72.[MR]
  5. David F. Anderson and Philip S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434–447.[MR]
  6. Gwénolé Ars, Jean-Charles Faugère, Hideki Imai, Mitsuru Kawazoe, and Makoto Sugita, Comparison between XL and Gröbner basis algorithms, Advances in Cryptology—Asiacrypt 2004, Lecture Notes in Comput. Sci., vol. 3329, Springer, Berlin, 2004, pp. 338–353.[MR]
  7. Philippe Aubry and Marc Moreno Maza, Triangular sets for solving polynomial systems: A comparative implementation of four methods, J. Symbolic Comput. 28 (1999), no. 1-2, 125–154.[MR]
  8. Mohamed Ayad and Peter Fleischmann, On the decomposition of rational functions, J. Symbolic Comput. 43 (2008), no. 4, 259–274.[MR]
  9. Bernd Bank, Marc Giusti, Joos Heintz, Mohab Safey El Din, and Eric Schost, On the geometry of polar varieties, Appl. Algebra Engrg. Comm. Comput. 21 (2010), no. 1, 33–83.[MR/doi]
  10. Aurélie Bauer and Antoine Joux, Toward a rigorous variation of Coppersmith's algorithm on three variables, Advances in cryptology—EUROCRYPT 2007, Lecture Notes in Comput. Sci., vol. 4515, Springer, Berlin, 2007, pp. 361–378.[MR]
  11. Thomas Bayer, An algorithm for computing invariants of linear actions of algebraic groups up to a given degree, J. Symbolic Comput. 35 (2003), no. 4, 441–449.[MR]
  12. Karim. Belabas, Mark van Hoeij, J. Klüners, and Allan Steel, Factoring polynomials over global fields, Journal de Théorie des Nombres de Bordeaux (2009), no. 21, 15–39.
  13. Dave Benson, Dickson invariants, regularity and computation in group cohomology, Illinois J. Math. 48 (2004), no. 1, 171–197.[MR/link]
  14. Thomas Beth, Jörn Müller-Quade, and Rainer Steinwandt, Computing restrictions of ideals in finitely generated k-algebras by means of Buchberger's algorithm, J. Symbolic Comput. 41 (2006), no. 3-4, 372–380.[MR]
  15. Alin Bostan, Frédéric Chyzak, and Nicolas Le Roux, Products of ordinary differential operators by evaluation and interpolation, in ISSAC '08: International Symposium on Symbolic and Algebraic Computation, ACM, New York, NY, USA, 2008, pp. 23–30.[doi/arXiv]
  16. Alin Bostan, Frédéric Chyzak, Bruno Salvy, Grégoire Lecerf, and Éric Schost, Differential equations for algebraic functions, ISSAC 2007, ACM, New York, 2007, pp. 25–32.[MR/arXiv]
  17. Alin Bostan, Thomas Cluzeau, and Bruno Salvy, Fast algorithms for polynomial solutions of linear differential equations, ISSAC'05: Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2005, pp. 45–52 (electronic).[MR]
  18. Alin Bostan, Bruno Salvy, and Éric Schost, Fast algorithms for zero-dimensional polynomial systems using duality, Appl. Algebra Engrg. Comm. Comput. 14 (2003), no. 4, 239–272.[MR]
  19. Hoans-Christian Graf von Bothmer, Oliver Labs, Josef Schicho, and Christiaan van de Woestijne, The Casas-Alvero conjecture for infinitely many degrees, J. Algebra 316 (2007), no. 1, 224–230.[MR/link]
  20. Mireille Boutin and Gregor Kemper, On reconstructing n-point configurations from the distribution of distances or areas, Adv. in Appl. Math. 32 (2004), no. 4, 709–735.[MR]
  21. Mireille Boutin and Gregor Kemper, On reconstructing configurations of points in P2 from a joint distribution of invariants, Appl. Algebra Engrg. Comm. Comput. 15 (2005), no. 6, 361–391.[MR]
  22. Richard Brent and Paul Zimmermann, A multi-level blocking distinct degree factorization algorithm, Finite Fields and Applications, Contemporary Mathematics, vol. 461, 2008, 47–58 pages.
  23. Michael Brickenstein and Alexander Dreyer, PolyBoRi: a framework for Gröbner-basis computations with Boolean polynomials, J. Symbolic Comp. 44 (2009), no. 9, 1326–1345.
  24. Michael Brickenstein, Alexander Dreyer, Gert-Martin Greuel, Markus Wedler, and Oliver Wienand, New developments in the theory of Gröbner bases and applications to formal verification, J. Pure Appl. Algebra 213 (2009), no. 8, 1612–1635.[MR]
  25. Abraham Broer, On Chevalley-Shephard-Todd's theorem in positive characteristic, Symmetry and Spaces, Progress in Mathematics, Birkhäuser Boston, 2010, pp. 21–34.[doi]
  26. Gavin Brown, Graded rings and special K3 surfaces, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 137–159.[MR]
  27. Stanislav Bulygin and Ruud Pellikaan, Bounded distance decoding of linear error-correcting codes with Gröbner bases, J. Symb. Comput. 44 (2009), no. 12, 1626–1643.
  28. Laurent Busé and Jean-Pierre Jouanolou, On the closed image of a rational map and the implicitization problem, J. Algebra 265 (2003), no. 1, 312–357.[MR]
  29. Daniel Cabarcas, An Implementation of Faugère's F4 Algorithm for Computing Gröbner Bases, Master's Thesis, University of Cincinnati, 2010.[link]
  30. H. E. A. Campbell, B. Fodden, and David L. Wehlau, Invariants of the diagonal Cp-action on V3, J. Algebra 303 (2006), no. 2, 501–513.[MR]
  31. H. E. A. Campbell, I. P. Hughes, G. Kemper, R. J. Shank, and D. L. Wehlau, Depth of modular invariant rings, Transform. Groups 5 (2000), no. 1, 21–34.[MR]
  32. H. E. A. Campbell, R. J. Shank, and D. L. Wehlau, Vector invariants for the two dimensional modular representation of a cyclic group of prime order, Advances in Mathematics 225 (2010), no. 2, 1069–1094.[doi]
  33. Jon F. Carlson, Cohomology, computations, and commutative algebra, Notices Amer. Math. Soc. 52 (2005), no. 4, 426–434.[MR]
  34. Chris Charnes, Martin Rötteler, and Thomas Beth, On homogeneous bent functions, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (Melbourne, 2001), Lecture Notes in Comput. Sci., vol. 2227, Springer, Berlin, 2001, pp. 249–259.[MR]
  35. Chris Charnes, Martin Rötteler, and Thomas Beth, Homogeneous bent functions, invariants, and designs, Des. Codes Cryptogr. 26 (2002), no. 1-3, 139–154.[MR]
  36. G. Chèze and S. Najib, Indecomposability of polynomials via Jacobian matrix, J. Algebra 324 (2010), no. 1, 1–11.[MR/doi]
  37. Mihai Cipu, Gröbner bases and Diophantine analysis, J. Symbolic Comput. 43 (2008), no. 10, 681–687.[MR]
  38. Olivier Cormier, On Liouvillian solutions of linear differential equations of order 4 and 5, in ISSAC '01: Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2001, pp. 93–100 (electronic).[MR]
  39. Olivier Cormier, Michael F. Singer, and Felix Ulmer, Computing the Galois group of a polynomial using linear differential equations, in Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews), ACM, New York, 2000, pp. 78–85 (electronic).[MR]
  40. Robert S. Coulter, George Havas, and Marie Henderson, On decomposition of sub-linearised polynomials, J. Aust. Math. Soc. 76 (2004), no. 3, 317–328.[MR/doi]
  41. David A. Cox, John Little, and Donal O'Shea, Using Algebraic Geometry, Graduate Texts in Mathematics, vol. 185, Springer, New York, 2005, pp. xii+572.[MR]
  42. Wolfram Decker and Theo de Jong, Gröbner bases and invariant theory, Gröbner bases and applications (Linz, 1998), London Math. Soc. Lecture Note Ser., vol. 251, Cambridge Univ. Press, Cambridge, 1998, pp. 61–89.[MR]
  43. Harm Derksen, Computation of invariants for reductive groups, Adv. Math. 141 (1999), no. 2, 366–384.[MR]
  44. Harm Derksen and Gregor Kemper, Computational Invariant Theory, Invariant Theory and Algebraic Transformation Groups, I, Springer-Verlag, Berlin, 2002, pp. x+268.[MR]
  45. Jan Draisma, Gregor Kemper, and David Wehlau, Polarization of separating invariants, Canad. J. Math. 60 (2008), no. 3, 556–571.[MR]
  46. Emilie Dufresne, Jonathan Elmer, and Martin Kohls, The Cohen-Macaulay property of separating invariants of finite groups, Transform. Groups 14 (2009), no. 4, 771–785.[MR/doi]
  47. Alexander Duncan, Michael LeBlanc, and David L. Wehlau, A SAGBI basis for F[V2⊕V2⊕V3]C p, Canad. Math. Bull. 52 (2009), no. 1, 72–83.[MR]
  48. Clémence Durvye and Grégoire Lecerf, A concise proof of the Kronecker polynomial system solver from scratch, Expo. Math. 26 (2008), no. 2, 101–139.[MR]
  49. Tobias Eibach, Enrico Pilz, and Gunnar Völkel, Attacking Bivium using SAT solvers, Theory and Applications of Satisfiability Testing, SAT 2008, Lecture Notes in Computer Science, vol. 4996, Springer, Berlin, 2008, pp. 63–76.
  50. Tobias Eibach, Gunnar Völkel, and Enrico Pilz, Optimising Gröbner bases on Bivium, Math. Comput. Sci. 3 (2010), no. 2, 159–172.[doi]
  51. Jonathan Elmer, Depth and detection in modular invariant theory, J. Algebra 322 (2009), no. 5, 1653–1666.[MR/doi]
  52. Jonathan Elmer and Peter Fleischmann, On the depth of modular invariant rings for the groups Cp×Cp, Symmetry and Spaces, Progr. Math., vol. 278, Birkhäuser Boston Inc., Boston, MA, 2010, pp. 45–61.[MR/doi]
  53. Nicholas Eriksson, Toric ideals of homogeneous phylogenetic models, ISSAC 2004, ACM, New York, 2004, pp. 149–154.[MR/arXiv]
  54. Arno van den Essen, Andrzej Nowicki, and Andrzej Tyc, Generalizations of a lemma of Freudenburg, J. Pure Appl. Algebra 177 (2003), no. 1, 43–47.[MR]
  55. Jeffrey B. Farr and Shuhong Gao, Computing Gröbner bases for vanishing ideals of finite sets of points, Applied Algebra, Algebraic Algorithms and Error-correcting Codes, Lecture Notes in Comput. Sci., vol. 3857, Springer, Berlin, 2006, pp. 118–127.[MR]
  56. Jeffrey B. Farr and Shuhong Gao, Gröbner bases and generalized Padé approximation, Math. Comp. 75 (2006), no. 253, 461–473 (electronic).[MR]
  57. Jean-Charles Faugère, Guillaume Moroz, Fabrice Rouillier, and Mohab Safey El Din, Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities, in ISSAC '08: International Symposium on Symbolic and Algebraic Computation, ACM, New York, NY, USA, 2008, pp. 79–86.[doi]
  58. Boris Feigin and Boris Shoikhet, On [A,A]/[A, [A,A]] and on a Wn-action on the consecutive commutators of free associative algebra, Math. Res. Lett. 14 (2007), no. 5, 781–795.[MR/arXiv]
  59. Akpodigha Filatei, Implementation of fast polynomial arithmentic in Aldor, Master's Thesis, University of Western Ontario, 2006.
  60. Tom Fisher, The Hessian of a genus one curve, preprint (2006), 28 pages.[arXiv]
  61. P. Fleischmann, M. Sezer, R. J. Shank, and C. F. Woodcock, The Noether numbers for cyclic groups of prime order, Adv. Math. 207 (2006), no. 1, 149–155.[MR]
  62. Shuhong Gao, Daqing Wan, and Mingsheng Wang, Primary decomposition of zero-dimensional ideals over finite fields, Math. Comp. 78 (2009), no. 265, 509–521.[MR/link]
  63. Karin Gatermann, Computer algebra methods for equivariant dynamical systems, Lecture Notes in Mathematics, vol. 1728, Springer-Verlag, Berlin, 2000, pp. xvi+153.[MR]
  64. Karin Gatermann and Frédéric Guyard, Gröbner bases, invariant theory and equivariant dynamics, J. Symbolic Comput. 28 (1999), no. 1-2, 275–302.[MR]
  65. Karin Gatermann and Pablo A. Parrilo, Symmetry groups, semidefinite programs, and sums of squares, J. Pure Appl. Algebra 192 (2004), no. 1-3, 95–128.[MR]
  66. V. P. Gerdt and Yu. A. Blinkov, On selection of nonmultiplicative prolongations in computation of Janet bases, Programming and Computer Software 33 (2007), no. 3, 147–153.
  67. V. P. Gerdt and Yu. A. Blinkov, Strategies for selecting non-multiplicative prolongations in computing Janet bases, Programmirovanie (2007), no. 3, 34–43.[MR]
  68. Vladimir P. Gerdt, Involutive algorithms for computing Gröbner bases, Computational Commutative and Non-commutative Algebraic Geometry, NATO Sci. Ser. III Comput. Syst. Sci., vol. 196, IOS, Amsterdam, 2005, pp. 199–225.[MR/link]
  69. Vladimir P. Gerdt and Yuri A. Blinkov, On computing Janet bases for degree compatible orderings, Proceedings of the 10th Rhine Workshop on Computer Algebra (Basel), 2006, University of Basel, Basel, 2006, pp. 107–117.
  70. Massimo Giulietti, Inviluppi di k-archi in piani proiettivi sopra campi finiti e basi di Gröbner, Rendiconti del Circolo Matematico di Palermo 48 (1999), no. 1, 191–200.
  71. Marc Giusti, Grégoire Lecerf, and Bruno Salvy, A Gröbner free alternative for polynomial system solving, J. Complexity 17 (2001), no. 1, 154–211.[MR]
  72. Marc Giusti and Éric Schost, Solving some overdetermined polynomial systems, in ISSAC '99: Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation (Vancouver, BC), ACM, New York, 1999, pp. 1–8 (electronic).[MR]
  73. Gert-Martin Greuel, Santiago Laplagne, and Frank Seelisch, Normalization of rings, J. Symbolic Comput. 45 (2010), no. 9, 887–901.[doi/arXiv]
  74. Renault Guénaél and Yokoyama Kazuhiro, Multi-modular algorithm for computing the splitting field of a polynomial, in ISSAC '08: International Symposium on Symbolic and Algebraic Computation, ACM, New York, NY, USA, 2008, pp. 247–254.[doi]
  75. Julia Hartmann, Invariants and differential Galois groups in degree four, Differential Galois Theory, Banach Center Publ., vol. 58, Polish Acad. Sci., Warsaw, 2002, pp. 79–87.[MR]
  76. David Harvey, A cache-friendly truncated FFT, Theor. Comput. Sci. 410 (2009), no. 27-29, 2649–2658.[arXiv]
  77. David Harvey, Faster polynomial multiplication via multipoint Kronecker substitution, J. Symbolic Comp. 44 (2009), no. 10, 1502–1510.
  78. Sabrina A. Hessinger, Computing the Galois group of a linear differential equation of order four, Appl. Algebra Engrg. Comm. Comput. 11 (2001), no. 6, 489–536.[MR]
  79. Mark van Hoeij, Factoring polynomials and the knapsack problem, J. Number Theory 95 (2002), no. 2, 167–189.[MR]
  80. Ian Hughes and Gregor Kemper, Symmetric powers of modular representations, Hilbert series and degree bounds, Comm. Algebra 28 (2000), no. 4, 2059–2088.[MR]
  81. Ian Hughes and Gregor Kemper, Symmetric powers of modular representations for groups with a Sylow subgroup of prime order, J. Algebra 241 (2001), no. 2, 759–788.[MR]
  82. Mikael Johansson, Computation of Poincaré-Betti series for monomial rings, Rend. Istit. Mat. Univ. Trieste 37 (2005), no. 1-2, 85–94 (2006).[MR]
  83. D. B. Karagueuzian and P. Symonds, The module structure of a group action on a polynomial ring: Examples, generalizations, and applications, Invariant Theory in all Characteristics, CRM Proc. Lecture Notes, vol. 35, Amer. Math. Soc., Providence, RI, 2004, pp. 139–158.[MR/link]
  84. Gregor Kemper, Calculating invariants of modular reflection groups with Magma, Preprint (1997), 5 pages.
  85. Gregor Kemper, Computational invariant theory, The Curves Seminar at Queen's. Vol. XII (Kingston, ON, 1998), Queen's Papers in Pure and Appl. Math., vol. 114, Queen's Univ., Kingston, ON, 1998, pp. 5–26.[MR]
  86. Gregor Kemper, An algorithm to calculate optimal homogeneous systems of parameters, J. Symbolic Comput. 27 (1999), no. 2, 171–184.[MR]
  87. Gregor Kemper, The depth of invariant rings and cohomology, J. Algebra 245 (2001), no. 2, 463–531.[MR]
  88. Gregor Kemper, The calculation of radical ideals in positive characteristic, J. Symbolic Comput. 34 (2002), no. 3, 229–238.[MR]
  89. Gregor Kemper, Computing invariants of reductive groups in positive characteristic, Transform. Groups 8 (2003), no. 2, 159–176.[MR]
  90. Gregor Kemper, The computation of invariant fields and a constructive version of a theorem by Rosenlicht, Transform. Groups 12 (2007), no. 4, 657–670.[MR]
  91. Gregor Kemper, Elmar Körding, Gunter Malle, B. Heinrich Matzat, Denis Vogel, and Gabor Wiese, A database of invariant rings, Experiment. Math. 10 (2001), no. 4, 537–542.[MR]
  92. Gregor Kemper and Gunter Malle, Invariant fields of finite irreducible reflection groups, Math. Ann. 315 (1999), no. 4, 569–586.[MR]
  93. Gregor Kemper and Allan Steel, Some algorithms in invariant theory of finite groups, Computational Methods for Representations of Groups and Algebras (Essen, 1997), Progr. Math., vol. 173, Birkhäuser, Basel, 1999, pp. 267–285.[MR]
  94. Simon King, Fast computation of secondary invariants, preprint (2007), 13 pages.[arXiv]
  95. Simon King, Minimal generating sets of non-modular invariant rings of finite groups, preprint (2007), 14 pages.[arXiv]
  96. Jennifer de Kleine, Michael Monagan, and Allan Wittkopf, Algorithms for the non-monic case of the sparse modular GCD algorithm, Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation: ISSAC'05, ACM, New York, 2005, pp. 124–131 (electronic).[MR]
  97. Martin Kohls, Invarianten zusammenhaengender gruppen und die Cohen-Macaulay eigenschaft, Master's Thesis, Technische Universitaet Muechen, 2005.
  98. Martin Kohls, Üeber die tiefe von invariantenringen unendlicher gruppen, PhD Thesis, Technische Universitaet Muechen, 2007.
  99. Martin Kohls, On the depth of invariant rings of infinite groups, J. Algebra 322 (2009), no. 1, 210–218.[MR/arXiv]
  100. Alexey Koloydenko, Symmetric measures via moments, Bernoulli 14 (2008), no. 2, 362-390.[arXiv]
  101. V. A. Krasikov and T. M. Sadykov, Linear differential operators for generic algebraic curves, preprint (2010).[arXiv]
  102. Teresa Krick, Straight-line programs in polynomial equation solving, Foundations of Computational Mathematics: Minneapolis, 2002, London Math. Soc. Lecture Note Ser., vol. 312, Cambridge Univ. Press, Cambridge, 2004, pp. 96–136.[MR]
  103. P. H. Kropholler, S. Mohseni Rajaei, and J. Segal, Invariant rings of orthogonal groups over \bf F2, Glasg. Math. J. 47 (2005), no. 1, 7–54.[MR]
  104. G. Lecerf, Quadratic Newton iteration for systems with multiplicity, Found. Comput. Math. 2 (2002), no. 3, 247–293.[MR]
  105. Grégoire Lecerf, Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers, J. Complexity 19 (2003), no. 4, 564–596.[MR]
  106. Grégoire Lecerf, Fast separable factorization and applications, Appl. Algebra Engrg. Comm. Comput. 19 (2008), no. 2, 135–160.[MR]
  107. Grégoire Lecerf, New recombination algorithms for bivariate polynomial factorization based on Hensel lifting, Appl. Algebra Engrg. Comm. Comput. 21 (2010), no. 2, 151–176.[MR/doi]
  108. Douglas A. Leonard, A weighted module view of integral closures of affine domains of type I, Adv. Math. Commun. 3 (2009), no. 1, 1-11.
  109. Xin Li, Marc Moreno Maza, Raqeeb Rasheed, and Eric Schost, High-performance symbolic computation in a hybrid compiled-interpreted programming environment, International Conference on Computational Sciences and Its Applications. ICCSA. June 30- July 3, 2008, 2008, pp. 331–341.
  110. Xin Li, Marc Moreno Maza, and Éric Schost, Fast arithmetic for triangular sets: from theory to practice, ISSAC 2007, ACM, New York, 2007, pp. 269–276.[MR]
  111. Xin Li, Marc Moreno Maza, and Éric Schost, Fast arithmetic for triangular sets: from theory to practice, J. Symbolic Comput. 44 (2009), no. 7, 891–907.[MR]
  112. Martin Lorenz, Multiplicative Invariant Theory, Encyclopaedia of Mathematical Sciences, vol. 135, Springer-Verlag, Berlin, 2005, pp. xii+177.[MR]
  113. A. Marschner and J. Müller, On a certain algebra of higher modular forms, Algebra Colloq. 16 (2009), 371–380.
  114. Mbakop Guy Merlin, Eziente losung reeller polynomialer gleichungssysteme, PhD Thesis, Humboldt-Universität, Berlin, 1999.[link]
  115. V. A. Mityunin and E. V. Pankratiev, Parallel algorithms for Gröbner-basis construction, J. Math. Sci. (N. Y.) 142 (2007), no. 4, 2248–2266.
  116. Michael Monagan and Mark van Hoeij, A modular algorithm for computing polynomial GCDs over number fields presented with multiple extensions, preprint http://www.cecm.sfu.ca/CAG/papers/HoeijMonGCD.pdf, 36 pages.
  117. Teo Mora, The FGLM problem and Möller's algorithm on zero-dimensional ideals, Sala, Massimiliano (ed.) and Mora, Teo (ed.) and Perret, Ludovic (ed.) and Sakata, Shojiro (ed.) and Traverso, Carlo (ed.), Gröbner Bases, Coding, and Cryptography, Springer, Berlin, 2009.
  118. Marc Moreno Maza, Greg Reid, Robin Scott, and Wenyuan Wu, On approximate triangular decompositions in dimension zero, J. Symbolic Comput. 42 (2007), no. 7, 693–716.[MR]
  119. Bernard Mourrain, Generalized normal forms and polynomial system solving, ISSAC'05: Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2005, pp. 253–260 (electronic).[MR]
  120. Bernard Mourrain and Philippe Trébuchet, Stable normal forms for polynomial system solving, Theoret. Comput. Sci. 409 (2008), no. 2, 229–240.[MR/doi]
  121. Jürgen Müller and Christophe Ritzenthaler, On the ring of invariants of ordinary quartic curves in characteristic 2, J. Algebra 303 (2006), no. 2, 530–542.[MR/link]
  122. Jörn Müller-Quade and Rainer Steinwandt, Basic algorithms for rational function fields, J. Symbolic Comput. 27 (1999), no. 2, 143–170.[MR]
  123. Jörn Müller-Quade and Rainer Steinwandt, Gröbner bases applied to finitely generated field extensions, J. Symbolic Comput. 30 (2000), no. 4, 469–490.[MR]
  124. Gabriele Nebe, Eric M. Rains, and Neil J. A. Sloane, Self-dual Codes and Invariant Theory, Algorithms and Computation in Mathematics, vol. 17, Springer-Verlag, Berlin, 2006, pp. xxviii+430.[MR]
  125. Mara D. Neusel and Müfit Sezer, The invariants of modular indecomposable representations of Zp2, Math. Ann. 341 (2008), no. 3, 575–587.[MR]
  126. G. H. Norton and A. Salagean, Cyclic codes and minimal strong Gröbner bases over a principal ideal ring, Finite Fields Appl. 9 (2003), no. 2, 237–249.[MR/doi]
  127. Graham H. Norton and Ana Sălăgean, Strong Gröbner bases for polynomials over a principal ideal ring, Bull. Austral. Math. Soc. 64 (2001), no. 3, 505–528.[MR]
  128. Ariane Péladan-Germa, Testing equality in differential ring extensions defined by PDE's and limit conditions, Appl. Algebra Engrg. Comm. Comput. 13 (2002), no. 4, 257–288.[MR]
  129. W. Plesken and D. Robertz, Constructing invariants for finite groups, Experiment. Math. 14 (2005), no. 2, 175–188.[MR]
  130. Miles Reid, Graded rings and birational geometry, Preprint (2000), 72 pages.
  131. Marc Stetson Renault, Computing Generators for Rings of Multiplicative Invariants, PhD Thesis, Temple University, 2002.
  132. Daniel Robertz, Noether normalization guided by monomial cone decompositions, J. Symbolic Comput. 44 (2009), no. 10, 1359–1373.[MR/doi]
  133. Fabrice Rouillier, Mohab Safey El Din, and Éric Schost, Solving the Birkhoff interpolation problem via the critical point method: an experimental study, ADG '00: Revised Papers from the Third International Workshop on Automated Deduction in Geometry (Zurich, 2000), Lecture Notes in Computer Science, vol. 2061, Springer-Verlag, Berlin, 2001, pp. viii+325.[MR]
  134. Kira Samol and Duco van Straten, Frobenius polynomials for Calabi-Yau equations, Commun. Number Theory Phys. 2 (2008), no. 3, 537–561.[MR/arXiv]
  135. Luciano Sbaiz, Patrick Vandewalle, and Martin Vetterli, Groebner basis methods for multichannel sampling with unknown offsets, Appl. Comput. Harmon. Anal. 25 (2008), no. 3, 277–294.[doi]
  136. Roberto La Scala and Viktor Levandovskyy, Letterplace ideals and non-commutative Gröbner bases, J. Symbolic Comp. 44 (2009), no. 10, 1374-1393.
  137. Éric Schost, Degree bounds and lifting techniques for triangular sets, in Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2002, pp. 238–245 (electronic).[MR]
  138. Éric Schost, Complexity results for triangular sets, J. Symbolic Comput. 36 (2003), no. 3-4, 555–594.[MR]
  139. Éric Schost, Computing parametric geometric resolutions, Appl. Algebra Engrg. Comm. Comput. 13 (2003), no. 5, 349–393.[MR]
  140. Müfit Sezer and R. James Shank, On the coinvariants of modular representations of cyclic groups of prime order, J. Pure Appl. Algebra 205 (2006), no. 1, 210–225.[MR]
  141. R. J. Shank, Classical covariants and modular invariants, Invariant Theory in all Characteristics, CRM Proc. Lecture Notes, vol. 35, Amer. Math. Soc., Providence, RI, 2004, pp. 241–249.[MR]
  142. R. James Shank and David L. Wehlau, On the depth of the invariants of the symmetric power representations of SL2(Fp), J. Algebra 218 (1999), no. 2, 642–653.[MR]
  143. R. James Shank and David L. Wehlau, Computing modular invariants of p-groups, J. Symbolic Comput. 34 (2002), no. 5, 307–327.[MR]
  144. R. James Shank and David L. Wehlau, Noether numbers for subrepresentations of cyclic groups of prime order, Bull. London Math. Soc. 34 (2002), no. 4, 438–450.[MR]
  145. R. James Shank and David L. Wehlau, Decomposing symmetric powers of certain modular representations of cyclic groups, Progress in Mathematics 278 (2010), 169–196.[arXiv]
  146. Jessica Sidman and Seth Sullivant, Prolongations and computational algebra, Canad. J. Math. 61 (2009), no. 4, 930–949.[MR/link]
  147. Michael F. Singer, Testing reducibility of linear differential operators: A group-theoretic perspective, Appl. Algebra Engrg. Comm. Comput. 7 (1996), no. 2, 77–104.[MR]
  148. Michael F. Singer and Felix Ulmer, Galois groups of second and third order linear differential equations, J. Symbolic Comput. 16 (1993), no. 1, 9–36.[MR]
  149. Michael F. Singer and Felix Ulmer, Liouvillian and algebraic solutions of second and third order linear differential equations, J. Symbolic Comput. 16 (1993), no. 1, 37–73.[MR]
  150. Michael F. Singer and Felix Ulmer, On a third order differential equation whose differential Galois group is the simple group of 168 elements, Applied algebra, algebraic algorithms and error-correcting codes (San Juan, PR, 1993), Lecture Notes in Comput. Sci., vol. 673, Springer, Berlin, 1993, pp. 316–324.[MR]
  151. Michael F. Singer and Felix Ulmer, Necessary conditions for Liouvillian solutions of (third order) linear differential equations, Appl. Algebra Engrg. Comm. Comput. 6 (1995), no. 1, 1–22.[MR]
  152. 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]
  153. Till Stegers, Faugère's F5 algorithm revisited, Master's Thesis, Technische Universiteit Darmstadt, 2005.[link]
  154. Rainer Steinwandt, Decomposing systems of polynomial equations, Computer Algebra in Scientific Computing—CASC'99 (Munich), Springer, Berlin, 1999, pp. 387–407.[MR]
  155. Rainer Steinwandt, Implicitizing without tag variables, Proceedings of the 8th Rhine Workshop on Computer Algebra, 2002, pp. 217-224.
  156. Rainer Steinwandt and Jörn Müller-Quade, Freeness, linear disjointness, and implicitization—a classical approach, Beiträge Algebra Geom. 41 (2000), no. 1, 57–66.[MR]
  157. Peter Symonds, Cyclic group actions on polynomial rings, Bull. Lond. Math. Soc. 39 (2007), no. 2, 181–188.[MR/link]
  158. Nicolas M. Thiéry, Algebraic invariants of graphs; A study based on computer exploration, SIGSAM Bulletin 34 (2000), no. 3, 9–20.
  159. Felix Ulmer, On algebraic solutions of linear differential equations with primitive unimodular Galois group, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (New Orleans, LA, 1991), Lecture Notes in Comput. Sci., vol. 539, Springer, Berlin, 1991, pp. 446–455.[MR]
  160. Felix Ulmer, On Liouvillian solutions of linear differential equations, Appl. Algebra Engrg. Comm. Comput. 2 (1992), no. 3, 171–193.[MR]
  161. Felix Ulmer, Liouvillian solutions of third order differential equations, J. Symbolic Comput. 36 (2003), no. 6, 855–889.[MR]
  162. Pawel Wocjan, Brill-Noether algorithm construction of geometric Goppa codes and absolute factorization of polynomials, PhD Thesis, Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, 1999.