One SUFFICIENT condition for equivalence between "f represented in Q" and "f represented in Z" is given by Davenport-Cassels Lemma in J.P.Serre ' A course of Arithmetic' book.
(note : wikipedia page about it needs rewriting): given f(X) = sum(aij Xi Xj) a definite positive quadratic form, with matrix (aij) symetric and with integer coefficients given the hypothesis (H) "for every x=(x1,x2,..xp) in Q^p it exists at leat one y in Z^p such as f(x-y) < 1" then, if n is represented by f in Q field, then n is represented by f in Z field Follows one example (Gauss's theorem) with the form x^2 + y^2 + z^2 representing n in Q field when n not equals to 4^a (8b-1)..such n is represented in Z field too, because (H) hypothesis holds. for the form. Challenge : try to check if (H) hypothesis is true or false for your form.. Dominique. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
