Curiously, Gauss sums are defined in the reference manual http://www.sagemath.org/doc/reference/sage/modular/dirichlet.html
but Jacobi sums are not. Maybe that accounts for the following problem: "jacobi_sum()" incorrectly computes Jacobi sums J(Y, Z) when exactly one of the characters Y, Z is trivial. Example: sage: G=DirichletGroup(5); X=G.list(); Y=X[0]; Z=X[1]; # Y is trivial and Z is quartic sage: sum([Y(x)*Z(1-x) for x in IntegerModRing(5)]) -1 # The value -1 above is the correct value of the Jacobi sum J(Y, Z). sage: Y.jacobi_sum(Z); Z.jacobi_sum(Y) 0 0 #The 0 values above are incorrect values of J(Y, Z). Remark: Since unlike Gauss sums mod p, Jacobi sums mod p never involve p-th roots of unity, the following is also a bit curious: sage: parent(Z.jacobi_sum(Z)) Cyclotomic Field of order 20 and degree 8 rje --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
