Hello, First of all, I was not able to run your code. It fails on the line
sage: L = [list(u^i) for i in [0..3]] Hopefully, with list(K(u^i)) instead of list(u^i) it works fine. I did not check the reference but the units of a quadratic number fields are the solution of Pell equation with either 1 or -1 (which are the invertible elements in Z). And actually, the subgroup of solutions which corresponds to 1 always form a subgroup (which is either the whole group or a subgroup of index 2). As you can see with the same example, taking the square of a solution with -1 you get 1 because the norm is multiplicative sage: x,y = K(u) sage: x^2-1621*y^2 -1 sage: K(u).norm() -1 sage: x,y = K(u)**2 sage: x^2-1621*y^2 1 sage: K(u**2).norm() 1 I am not sure it solves the issue from the reference. Vincent 2014-10-31 10:14 UTC−06:00, Michael Beeson <profbee...@gmail.com>: > Here I attempt to solve Pell's equation with d = 1621 following the method > on page 93 of Stein's book. > But the solution produced is instead a solution of the negative Pell > equation x^2-y^2 = -1 (instead of 1). > Actually, the example on page 93 (after correcting the typo "v" to "u") has > > the same problem: it claims > that [-2,1] solves Pell's equation with d=5, whereas, it really solves > the negative Pell equation. > > sage: K.<a> = QuadraticField(1621) > sage: G = K.unit_group() > sage: u = G.1 > sage: L = [list(u^i) for i in [0..3]] > sage: L > [[1, 0], [4823622127875/2, 119806883557/2], [23267330432525342852015627/2, > 577903134597288688851375/2], [56116404965454319198851772383057215250, > 1393793173905903098261469193463230841]] > sage: x = L[2][0]; > sage: y = L[2][1]; > sage: x > 23267330432525342852015627/2 > sage: x = L[3][0]; > sage: y = L[3][1]; > sage: x > 56116404965454319198851772383057215250 > sage: y > 1393793173905903098261469193463230841 > sage: x^2-1621*y^2 > -1 > > > -- > 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. > -- 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.
