Sudokus and Gröbner bases: not only a divertimento

Authors:
Jesús Gago-Vargas;Isabel Hartillo-Hermoso;Jorge Martín-Morales;José María Ucha-Enríquez
Affiliations:
Dpto. de Álgebra, Univ. de Sevilla, Sevilla, Spain;Dpto. de Matemáticas, Univ. de Cádiz, Puerto Real, Cádiz, Spain;Depto. de Matemáticas, Univ. de Zaragoza, Zaragoza, Spain;Dpto. de Álgebra, Univ. de Sevilla, Sevilla, Spain
Venue:
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Year:
2006

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Abstract

Sudoku is a logic-based placement puzzle. We recall how to translate this puzzle into a 9-colouring problem which is equivalent to a (big) algebraic system of polynomial equations. We study how far Gröbner bases techniques can be used to treat these systems produced by Sudokus. This general purpose tool can not be considered as a good solver, but we show that it can be useful to provide information on systems that are —in spite of their origin— hard to solve.