cload(heegner); cload(cremona); cload(modsymb); cload(tate); kill(libname); libname = concat(componentfolder,"cmtools.so"); read(concat(componentfolder,"src/hpxh.pari")); kill(hpxh); addhelp(hpxh,"The hpxh package includes the functions hpxhint and ellStarkHeegner. For more information on a function *, type ?*"); kill(hpxhint); /* hpxhint(tau1,tau2,z1,z2,table,prec) = hpxhint0(tau1,tau2,z1,z2,table,prec); */ install(hpxhint,GGGGGG,hpxhint,libname); addhelp(hpxhint,"hpxhint(tau1,tau2,z1,z2,table,prec) evaluates the Darmon double integral on H_p x H in the region [tau1,tau2] x [z1,z2] to precision prec using the Manin symbols in table"); kill(hpxhint9); install(hpxhint9,GGGGGG,hpxhint9,libname); /* kill(hpxhballs); install(hpxhballs,GGG,hpxhballs,libname); addhelp(hpxhballs,"hpxhballs(table,p,prec) makes list of balls in H_p of radius prec with corresponding measures"); */ kill(hpxhmutable); install(hpxhmutable,GGG,hpxhmutable,libname); addhelp(hpxhmutable,"hpxhmutable(manintable,p,prec) generates table of measures for balls in H_p of radius prec; output is a pair of addresses for the generated arrays"); kill(hpxhshowarray); install(hpxhshowarray,GGGv,hpxhshowarray,libname); addhelp(hpxhshowarray,"hpxhshowarray(address,start,end) displays integer array"); kill(hpxheval); install(hpxheval,GG,hpxheval,libname); addhelp(hpxheval,"hpxheval(mus,taus) evaluates for mus a vector of vectors of form [up/down, array address, start, end] and taus a vector of vectors of form [tau1, tau2, pow]"); kill(ellStarkHeegner); ellStarkHeegner(rawmaninid,functional,F,Oprec) = hpxhmodsymb18(rawmaninid,functional,F,Oprec); addhelp(ellStarkHeegner,"ellStarkHeegner(rawmininid,functional,F,Oprec) returns the Stark-Heegner period corresponding to the raw Manin table database entry rawminid (see the help for the modsymb package), the vector functional which is an element of the Z-dual of the complex period lattice written with respect to the real-imaginary period basis, the binary quadratic form F, and the precision Oprec written in the form O(p^k); for example, the call ellStarkHeegner(\"37A\",[1,0],Qfb(1,6,-6),O(37^4)) yields the real period coefficient of the Stark-Heegner period for the isogeny class 37A (Cremona) and the point tau=-3+sqrt(15) generating the order of discriminat 60, calculated to a precision of 37^(-4).");