def isIntBasis(self):
"""
Determine whether self.basis is integral basis of self field.
"""
D = self.disc()
if squarefree.trial_division(abs(D)):
return True
else:
if D % 4 == 0:
if squarefree.trial_division(abs(D)//4) and (D//4) % 4 != 1:
return True
# compare with real integer ring
return abs(self.integer_ring().determinant()) == 1
def isIntBasis(self):
"""
Determine whether self.basis is integral basis of self field.
"""
D = self.disc()
if squarefree.trial_division(abs(D)):
return True
else:
if D & 3 == 0:
if squarefree.trial_division(abs(D) >> 2) and (D >> 2) & 3 != 1:
return True
# compare with real integer ring
return abs(self.integer_ring().determinant()) == 1
def next_disc(d, absbound):
"""
Return fundamental discriminant D, such that D < d.
If there is no D with |d| < |D| < absbound, return False
"""
# -disc % 16
negdisc_mod16 = (3, 4, 7, 8, 11, 15)
for negdisc in bigrange.range(-d + 1, absbound):
if negdisc & 15 not in negdisc_mod16:
continue
if negdisc & 1 and not squarefree.trial_division(negdisc):
continue
if arith1.issquare(negdisc):
continue
return -negdisc
return False
def next_disc(d, absbound):
"""
Return fundamental discriminant D, such that D < d.
If there is no D with |d| < |D| < absbound, return False
"""
# -disc % 16
negdisc_mod16 = (3, 4, 7, 8, 11, 15)
for negdisc in bigrange.range(-d + 1, absbound):
if negdisc % 16 not in negdisc_mod16:
continue
if negdisc % 2 == 1 and not squarefree.trial_division(negdisc):
continue
if arith1.issquare(negdisc):
continue
return -negdisc
return False
