[sage-support] Re: rational solutions to a bivariate polynomial

2007-09-21 Thread William Stein
On 9/21/07, John Cremona <[EMAIL PROTECTED]> wrote: > > It *is* a ternary quadratic form once you homogenize with a 3rd variable z. > > Finding rational points on plane conics (which is what this is) has > advanced substantially in the last few years. My paper with Rusin > (Mathematics of Computa

[sage-support] Re: rational solutions to a bivariate polynomial

2007-09-21 Thread John Cremona
It *is* a ternary quadratic form once you homogenize with a 3rd variable z. Finding rational points on plane conics (which is what this is) has advanced substantially in the last few years. My paper with Rusin (Mathematics of Computation, 72 (2003), no. 243, pages 1417-1441.) works well for diag

[sage-support] Re: rational solutions to a bivariate polynomial

2007-09-20 Thread David Stahl
Hi Utpal, Does the Hasse-Minkowski theorem apply for a non-quadratic form like mine? David On Sep 20, 2:34 pm, Utpal Sarkar <[EMAIL PROTECTED]> wrote: > There is not always a solution. Whether or not there is a solution is > the contents of the Hasse-Minkowski theorem. I couldn't find a > funct

[sage-support] Re: rational solutions to a bivariate polynomial

2007-09-20 Thread Utpal Sarkar
There is not always a solution. Whether or not there is a solution is the contents of the Hasse-Minkowski theorem. I couldn't find a function in sage that immediately tells you whether there is a rational solution. There is a function that tells you whether there is a local solution at a prime p,