Please check my answer below...I am newbie in these subjects... The point of Edna's Jones question is about "locally", no ?
As Pete L.Clark points out in http://www.math.uga.edu/~pete/*CasselsLemma* .pdf a number n can be "locally" (in Qp) represented but not integrally represented....read some examples in Clark's paper The ZZ field is forced in DiagonalQuadraticForm() first argument to specify integer quadratic forms (with integer coefficients). It doesn't matter if you use ZZ or python int for locally_represented_number() argument (+1 : previous answer). You have Gauss's theorem for representing number n different of 4^k(8l+7) by the form x^2 + y^2 + z^2 with x,y,z in Q and 42 is represented by it, so it is represented by the equivalent form x^2 + (2y)^2 + (2z)^2. That's why function locally_represented returns true ... while obviously no integers x,y,z can be set to have x^2 + 4y^2 + 4z^2 = 42 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.
