Victor, First of all I invite you to join sage-nt, the sage number theory group!
Secondly... On Dec 21, 5:37 pm, victor <[email protected]> wrote: > Let m be a modular symbol for the congruence subgroup G=Gamma0(N) for > some N. > > If one assumes m is cuspidal, there exist elements g in G such that m > is equivalent to the symbol {0,g(0)}. > > How can I compute one such g with sage? If possible, I'd like to find > g with as small coefficients as possible. I'd particularly interested > in finding g=[[a,b],[c,d]] with c small. > > If m={c1,c2} then we can just type > G.are_equivalent_cusps(c1,c2,trans=True) and the answer is True, > because cuspidality means that c1 and c2 are equivalent cusps under G. > > How can we compute g when, say, m={c1,c2}+{c3,c4} is cuspidal but c1 > is not equivalent to c2, and c3 is not equivalent to c4? Is there an > optimal way of computing it? In this case since m is cupsidal you must have (in the free abelian groups on the cusp classes) 0 = [c2]-[c1]+[c4]-[c3] so either [c1]=[c2] and [c3]=[c4] (the easy case) or [c1]=[c4] and [c2]=[c3], which is just as easy since in fact m is also = {c1,c4}+ {c2,c3} and we are back in the easy case. (William calls this property of modular symbols being "transportable".) I am assuming that your modular symbols are of weight 2. John Cremona -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
