def __new__(cls):
"""
This method actually is not needed for using :class:`RationalField`.
But it is used to unpickle some very old pickles.
TESTS::
sage: RationalField() in Fields() # indirect doctest
True
"""
try:
return QQ
except BaseException:
from sage.rings.number_field.number_field_base import NumberField
return NumberField.__new__(cls)
def __new__(cls):
"""
This method actually is not needed for using :class:`RationalField`.
But it is used to unpickle some very old pickles.
TESTS::
sage: RationalField() in Fields() # indirect doctest
True
"""
try:
from sage.rings.rational_field import QQ
return QQ
except BaseException:
from sage.rings.number_field.number_field_base import NumberField
return NumberField.__new__(cls)
def extension(self, poly, names, **kwds):
r"""
Create a field extension of `\QQ`.
EXAMPLES:
We make a single absolute extension::
sage: K.<a> = QQ.extension(x^3 + 5); K
Number Field in a with defining polynomial x^3 + 5
We make an extension generated by roots of two polynomials::
sage: K.<a,b> = QQ.extension([x^3 + 5, x^2 + 3]); K
Number Field in a with defining polynomial x^3 + 5 over its base field
sage: b^2
-3
sage: a^3
-5
"""
from sage.rings.number_field.all import NumberField
return NumberField(poly, names=names, **kwds)