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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