\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}