def ideals_of_norm(v):
"""
INPUT:
- `v` -- integer >= 2, or list of integers >= 2
OUTPUT:
- list of ideals of all ideals that have norm in v that is >= 2.
EXAMPLES::
sage: sage.modular.hilbert.sqrt5_tables.ideals_of_norm(4)
[Fractional ideal (2)]
sage: sage.modular.hilbert.sqrt5_tables.ideals_of_norm([9,11])
[Fractional ideal (3), Fractional ideal (-3*a + 1), Fractional ideal (-3*a + 2)]
sage: sage.modular.hilbert.sqrt5_tables.ideals_of_norm([4*5])
[Fractional ideal (-4*a + 2)]
sage: sage.modular.hilbert.sqrt5_tables.ideals_of_norm(4*5)
[Fractional ideal (-4*a + 2)]
"""
try:
v = list(v)
except TypeError:
v = [Integer(v)]
z = F.ideals_of_bdd_norm(max(v))
return sum([z[n] for n in v if n > 1], [])
def ideals_of_bounded_norm(B):
r"""
Return all ideals in the ring of integers of Q(sqrt(5)) with norm
bigger than 1 and <= B.
INPUT:
- `B` -- positive integer
OUTPUT:
- list of ideals
EXAMPLES::
sage: v = sage.modular.hilbert.sqrt5_tables.ideals_of_bounded_norm(11); v
[Fractional ideal (2), Fractional ideal (-2*a + 1), Fractional ideal (3), Fractional ideal (-3*a + 1), Fractional ideal (-3*a + 2)]
sage: [I.norm() for I in v]
[4, 5, 9, 11, 11]
"""
return sum([v for n, v in F.ideals_of_bdd_norm(B).iteritems() if n != 1], [])
