def lift(self):
"""
If this element lies in a prime finite field, return a lift of this
element to an integer.
EXAMPLES::
sage: k.<t> = GF(next_prime(10^10)^2, impl='pari_mod')
sage: a = k(17)/k(19)
sage: b = a.lift(); b
7894736858
sage: b.parent()
Integer Ring
"""
return integer_ring.IntegerRing()(self.__value.lift().lift())
def create_object(self, version, order):
"""
EXAMPLES::
sage: R = Integers(10)
sage: TestSuite(R).run() # indirect doctest
"""
category = None
if isinstance(order, tuple):
order, category = order
if order < 0:
order = -order
if order == 0:
return integer_ring.IntegerRing()
else:
return IntegerModRing_generic(order, category=category)
def lift(self):
"""
If this element lies in a prime finite field, return a lift of this
element to an integer.
EXAMPLES::
sage: from sage.rings.finite_rings.finite_field_ext_pari import FiniteField_ext_pari
sage: k = GF(next_prime(10**10))
sage: a = k(17)/k(19)
sage: b = a.lift(); b
7894736858
sage: b.parent()
Integer Ring
"""
return integer_ring.IntegerRing()(self.__value.lift().lift())
def create_object(self, version, order, **kwds):
"""
EXAMPLES::
sage: R = Integers(10)
sage: TestSuite(R).run() # indirect doctest
"""
if isinstance(order, tuple):
# this is for unpickling old data
order, category = order
kwds.setdefault('category', category)
if order < 0:
order = -order
if order == 0:
return integer_ring.IntegerRing(**kwds)
else:
return IntegerModRing_generic(order, **kwds)
True
sage: is_IntegerModRing(GF(4, 'a'))
False
sage: is_IntegerModRing(10)
False
sage: is_IntegerModRing(ZZ)
False
"""
return isinstance(x, IntegerModRing_generic)
from sage.categories.commutative_rings import CommutativeRings
from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
from sage.categories.category import JoinCategory
default_category = JoinCategory((CommutativeRings(), FiniteEnumeratedSets()))
ZZ = integer_ring.IntegerRing()
def _unit_gens_primepowercase(p, r):
r"""
Return a list of generators for `(\ZZ/p^r\ZZ)^*` and their orders.
EXAMPLES::
sage: from sage.rings.finite_rings.integer_mod_ring import _unit_gens_primepowercase
sage: _unit_gens_primepowercase(2, 3)
[(7, 2), (5, 2)]
sage: _unit_gens_primepowercase(17, 1)
[(3, 16)]
sage: _unit_gens_primepowercase(3, 3)
[(2, 18)]
