\contentsline {section}{\numberline {1}Computing Stark-Heegner points}{3}
\contentsline {subsection}{\numberline {1.1}Modular symbols}{4}
\contentsline {subsection}{\numberline {1.2}$p$-adic measures}{5}
\contentsline {subsection}{\numberline {1.3}Double integrals}{7}
\contentsline {subsection}{\numberline {1.4}Indefinite integrals}{10}
\contentsline {subsection}{\numberline {1.5}Definition of $P_\tau $}{11}
\contentsline {subsection}{\numberline {1.6}Recognizing $p$-adic numbers as rational numbers}{13}
\contentsline {section}{\numberline {2}Computing the moments of Mazur's measure}{15}
\contentsline {subsection}{\numberline {2.1}Overconvergent modular symbols}{15}
\contentsline {subsection}{\numberline {2.2}Iterating $U_p$}{18}
\contentsline {subsection}{\numberline {2.3}Lifting modular symbols}{18}
\contentsline {subsection}{\numberline {2.4}Finite approximation modules}{21}
\contentsline {subsection}{\numberline {2.5}Computing the moments}{22}
\contentsline {subsection}{\numberline {2.6}Complexity analysis}{22}
\contentsline {section}{\numberline {3}The {\tt shp} package}{24}
\contentsline {section}{\numberline {4}Numerical examples}{25}