def primes_of_bounded_norm_iter(self, B):
r"""
Iterator yielding all primes less than or equal to `B`.
INPUT:
- ``B`` -- a positive integer; upper bound on the primes generated.
OUTPUT:
An iterator over all integer primes less than or equal to `B`.
.. note::
This function exists for compatibility with the related number
field method, though it returns prime integers, not ideals.
EXAMPLES::
sage: it = QQ.primes_of_bounded_norm_iter(10)
sage: list(it)
[2, 3, 5, 7]
sage: list(QQ.primes_of_bounded_norm_iter(1))
[]
"""
try:
B = ZZ(B.ceil())
except (TypeError, AttributeError):
raise TypeError("%s is not valid bound on prime ideals" % B)
if B < 2:
raise StopIteration
from sage.rings.arith import primes
for p in primes(B + 1):
yield p
def primes_of_bounded_norm_iter(self, B):
r"""
Iterator yielding all primes less than or equal to `B`.
INPUT:
- ``B`` -- a positive integer; upper bound on the primes generated.
OUTPUT:
An iterator over all integer primes less than or equal to `B`.
.. note::
This function exists for compatibility with the related number
field method, though it returns prime integers, not ideals.
EXAMPLES::
sage: it = QQ.primes_of_bounded_norm_iter(10)
sage: list(it)
[2, 3, 5, 7]
sage: list(QQ.primes_of_bounded_norm_iter(1))
[]
"""
try:
B = ZZ(B.ceil())
except (TypeError, AttributeError):
raise TypeError("%s is not valid bound on prime ideals" % B)
if B < 2:
raise StopIteration
from sage.rings.arith import primes
for p in primes(B + 1):
yield p
