Hello, suppose that K is a number field and U the group of units in the maximal order of K. Then the rank r of U, i.e. the rank r of the free group U_f= U/Tor(U) (where Tor(U) denotes the group of torsion elements in U) is given by Dirichlet's unit theorem. Clearly r is the dimension of the Q-vector space U_Q = U (x)_Z Q.
Sage gives a basis of U_Q (sage: K.units()). Now given r units u_1,...,u_r how can it be tested that the u's generate U_Q - or are linearly independent over Q? If the structure of U_Q was additive, this might not be a problem for SAGE as it is a standard problem in linear algebra boiling down to calculate a determinant. But how to tackle this problem when the structure of the Q-vector space is multiplicative, at least in notation. Thanks for any help. Please do not hesitate to ask for more information if something is unclear or needs more information. Best wishes, J. ps: This is my first posting here. Hope that this email will get through to the forum. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com 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 -~----------~----~----~----~------~----~------~--~---
