This is because c in your loop below is a rational number, and the
GCD of any set of rational numbers (not all 0) is 1 (because
everything is a unit). Write
> c = ZZ((d - r*s*t
> +a*r*r + b*s*s)/(4*a*b - t*t))
On Jun 7, 2009, at 10:58 AM, salte...@gmail.com wrote:
> I am running into problems using the gcd function in sage. (version
> 3.4.2)
>
> Specifically, I am iterating over a set of integers [a,b,c,r,s,t]
> which I want to be coprime. I check this using gcd([a,b,c,r,s,t]). The
> problem is that it returns 1 for tuples that should not have gcd = 1.
> For example, for [a,b,c,r,s,t]=[2,2,2,0,0,0], it passes gcd
> ([a,b,c,r,s,t]) == 1. When I check this directly (by evaluating gcd
> ([2,2,2,0,0,0]) it evaluates correctly. This is driving me insane -
> any help would be greatly appreciated. Here is the pertinent code: (If
> you want to run into the [2,2,2,0,0,0] case, try d = 32 and N = 8)
>
> def MakeTernaryQF(d,N):
>
> ## Make the list##
> #r,s,t <= 0
> QFlist = []
> for a in range(1, 1+ceil((d/2)^(1/3))):
> for b in range(a, floor(sqrt(d / (2*a)))+1):
> for r in range(-b, 1):
> for s in range(-a,1):
> for t in range(-a,1):
> if (d - r*s*t +a*r*r +
> b*s*s)%(4*a*b - t*t) == 0:
> c = (d - r*s*t +a*r*r +
> b*s*s)/(4*a*b - t*t)
> if gcd([a,b,c,r,s,t])
> == 1 and a+b+c+r+s+t >= 0:
> #print 'This
> dumb thing thinks gcd('+str(a)+','+str(b)+','+str
> (c)+','+str(r)+','+str(s)+','+str(t)+') = '+str(gcd([a,b,c,r,s,t]))
>
> QFlist.append([a,b,c,r,s,t])
>
> #r,s,t > 0
> for a in range(1, 1+ceil((d/2)^(1/3))):
> for b in range(a, floor(sqrt(d / (2*a)))+1):
> for r in range(1, b+1):
> for s in range(1,a+1):
> for t in range(1,a+1):
> if (d - r*s*t +a*r*r +
> b*s*s)%(4*a*b - t*t) == 0:
> c = (d - r*s*t +a*r*r +
> b*s*s)/(4*a*b - t*t)
> if gcd([a,b,c,r,s,t])
> == 1 and a+b+c+r+s+t >= 0:
> #print
> 'This dumb thing thinks gcd('+str(a)+','+str(b)
> +','+str
> (c)+','+str(r)+','+str(s)+','+str(t)+') = '+str(gcd([a,b,c,r,s,t]))
>
> QFlist.append([a,b,c,r,s,t])
>
> return QFlist
>
> >
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