|Bill Allombert on Fri, 20 May 2016 15:20:17 +0200|
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|Re: What am I doing wrong?|
On Fri, May 20, 2016 at 02:28:51PM +0200, Dirk Laurie wrote: > 2016-05-20 14:21 GMT+02:00 Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>: > > On Fri, May 20, 2016 at 01:59:14PM +0200, Dirk Laurie wrote: > >> % qfbsolve(Qfb(1,0,-5),4) > >> %2 = 0 > >> > >> Why are the solutions x=3,y=1; x=7,y=3; x=18,y=8; etc not found? > > > > Because 4 is not prime: > > > > ? ?qfbsolve > > qfbsolve(Q,p): Return [x,y] so that Q(x,y)=p where Q is a binary > > quadratic form and p a prime > > number, or 0 if there is no solution. > > Follow-up question: can Pari handle equations like x^2 - 5*y^2 = 4 > directly, or must I write the code exploiting Diophantine approximation > of sqrt(5) by hand? This is complicated. We provide the function bnfisinitnorm that does what you want, with a caveats: it returns solution in the maximal order Z[(1+sqrt(5))/2] instead of Z[sqrt(5)]. ? bnfisintnorm(bnfinit(x^2-5),4) %1 =  Cheers, Bill.