Thanks for the report. This is indeed a bug in sage. The problem is that for
some reason the algorithm in sage is asuming the moduli are coprime. If you
need the functionality now, here is an updated version of the function is
sage.
def CRT_list(v, moduli):
if not isinstance(v,list) or not isinstance(moduli,list):
raise ValueError, "Arguments to CRT_list should be lists"
if len(v) != len(moduli):
raise ValueError, "Arguments to CRT_list should be lists of the same
length"
if len(v) == 0:
return ZZ(0)
if len(v) == 1:
return moduli[0].parent()(v[0])
x = v[0]
m = moduli[0]
for i in range(1,len(v)):
x = CRT(x,v[i],m,moduli[i])
m=m.lcm(moduli[i])
return x%m
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