\select@language {english}
\contentsline {chapter}{\numberline {1}Introduction}{3}{chapter.1}
\contentsline {section}{\numberline {1.1}Configurations and divisors}{3}{section.1.1}
\contentsline {section}{\numberline {1.2}Stabilization}{3}{section.1.2}
\contentsline {section}{\numberline {1.3}Laplacian}{5}{section.1.3}
\contentsline {section}{\numberline {1.4}Recurrent elements}{6}{section.1.4}
\contentsline {section}{\numberline {1.5}Burning Configuration}{6}{section.1.5}
\contentsline {section}{\numberline {1.6}Sandpile group}{7}{section.1.6}
\contentsline {section}{\numberline {1.7}Self-organized criticality}{8}{section.1.7}
\contentsline {section}{\numberline {1.8}Divisors and Discrete Riemann surfaces}{8}{section.1.8}
\contentsline {subsection}{\numberline {1.8.1}Riemann-Roch}{9}{subsection.1.8.1}
\contentsline {subsection}{\numberline {1.8.2}Picturing linear systems}{10}{subsection.1.8.2}
\contentsline {section}{\numberline {1.9}Algebraic geometry of sandpiles}{10}{section.1.9}
\contentsline {subsection}{\numberline {1.9.1}Affine}{10}{subsection.1.9.1}
\contentsline {subsection}{\numberline {1.9.2}Projective}{12}{subsection.1.9.2}
\contentsline {subsection}{\numberline {1.9.3}Zeros}{13}{subsection.1.9.3}
\contentsline {subsection}{\numberline {1.9.4}Resolutions}{14}{subsection.1.9.4}
\contentsline {subsection}{\numberline {1.9.5}Complete Intersections and Arithmetically Gorenstein toppling ideals}{15}{subsection.1.9.5}
\contentsline {subsection}{\numberline {1.9.6}Betti numbers for undirected graphs}{15}{subsection.1.9.6}
\contentsline {chapter}{\numberline {2}4ti2 installation}{17}{chapter.2}
\contentsline {chapter}{\numberline {3}Usage}{19}{chapter.3}
\contentsline {section}{\numberline {3.1}Initialization}{19}{section.3.1}
\contentsline {section}{\numberline {3.2}Methods}{21}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Sandpile}{21}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}SandpileConfig}{40}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}SandpileDivisor}{51}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}Other}{61}{subsection.3.2.4}
\contentsline {section}{\numberline {3.3}Help}{68}{section.3.3}
\contentsline {chapter}{\numberline {4}Contact}{69}{chapter.4}
\contentsline {chapter}{Bibliography}{71}{chapter*.120}