Sudokus and Gröbner bases: Not only a divertimento

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4194 LNCS, Issue , 2006, Pages 155-165

  Gago Vargas, Jesús ^a   Hartillo Hermoso, Isabel ^b   Martín Morales, Jorge ^c   Ucha Enríquez, José María ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF CÁDIZ   (Spain)

^c UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; PROBLEM SOLVING; SYSTEMS ANALYSIS;

PUZZLES; SUDOKU;

ALGEBRA;

EID: 33845192600     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11870814_13     Document Type: Conference Paper

References (14)

1. W. W. Adams and P. Loustaunau. An introduction to Gröbner bases, volume 3 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1994.
2. Bayer, Dave The division algorithm and the Hilbert scheme. Ph. D. Thesis. Harvard University, June 1982.
3. T. Becker and V. Weispfenning. Gröbner bases, volume 141 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1993. A computational approach to commutative algebra, In cooperation with Heinz Kredel.
4. Cox, D., J. Little, D. O'Shea. Ideals, Varieties and Algorithms. Springer, Berlin, 1997.
5. Cox, D., J. Little, D. O'Shea. Using Algebraic Geometry. Springer, Berlin, 1998.
6. B. Felgenhauer and F. Jarvis. Enumerating possible sudoku grids, 2005. http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf. [Online; accessed 30-December-2005].
7. G.-M. Greuel, G. Pfister, and H. Schönemann. SINGULAR 3.0. http://www.singular.uni-kl.de. A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern, 2005.
8. R. Kaye. Minesweeper is NP-complete. Math. Intelligencer, 22(2):9-15, 2000.
9. C. T. Kelley. Iterative methods for linear and nonlinear equations, volume 16 of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995. With separately available software.
10. Knuth, D.E. Dancing links. Preprint.
11. M. Kreuzer and L. Robbiano. Computational commutative algebra. 1. Springer-Verlag, Berlin, 2000.
12. E. Pegg. Sudoku variations, 2005. http://www.maa.org/editorial/mathgames/ mathgames_09_05_05.html. [Online; accessed 12-December-2005].
13. Sturmfels, B. Solving Systems of Polynomial Equations. Amer.Math.Soc., CBMS Regional Conferences Series, No 97, Providence, Rhode Island, 2002.
14. J. Verschelde. PHCcpack: A general-purpose solver for polynomial systems by homotopy continuation, 2005. ACM Transactions on Mathematical Software volume 25, number 2: 251-276, 1999.