Bill Allombert on Fri, 05 Feb 2021 16:53:29 +0100 |
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New GP function ellrank (2-descent) |
Dear PARI developers, I have added a new GP function 'ellrank' to the master branch. This is a port of Denis Simon GP script ellQ.gp. However the interface is different, it returns [r,R,V] where r is a lower bound for the rank, R is an upper bound and V is a list of point. If the full gorup is determined, r==R==#V. ? E = ellinit([-157^2,0]); ? ellrank(E) %2 = [1,1,[]] The rank is 1 but no points was found. It is possible to ask ellrank to try harder ? ellrank(E,10) %5 = [1,1,[[-43565582610691407250551997/609760250665615167250729,562653616877773225244609387368307126580/476144382506163554005382044222449067]]] It should compare favorably to John Cremona mwrank (which use a different algorithm), except it does not do saturation yet, but this will be added soon. Finally, I like to thanks Denis Simon for improving ellQ.gp over all this years. Cheers, Bill