def is_PrimeField(R):
r"""
Determine if ``R`` is a field that is equal to its own prime subfield.
INPUT:
- ``R`` -- a ring or field
OUTPUT:
- ``True`` if R is `\QQ` or a finite field `\GF{p}` for `p` prime,
``False`` otherwise.
EXAMPLES::
sage: import sage.rings.field
doctest:...: DeprecationWarning: the module sage.rings.field is deprecated and will be removed
See http://trac.sagemath.org/18108 for details.
sage: sage.rings.field.is_PrimeField(QQ)
True
sage: sage.rings.field.is_PrimeField(GF(7))
True
sage: sage.rings.field.is_PrimeField(GF(7^2,'t'))
False
"""
from finite_rings.constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False
def is_PrimeField(R):
r"""
Determine if ``R`` is a field that is equal to its own prime subfield.
INPUT:
- ``R`` -- a ring or field
OUTPUT:
- ``True`` if R is `\QQ` or a finite field `\GF{p}` for `p` prime,
``False`` otherwise.
EXAMPLES::
sage: sage.rings.field.is_PrimeField(QQ)
True
sage: sage.rings.field.is_PrimeField(GF(7))
True
sage: sage.rings.field.is_PrimeField(GF(7^2,'t'))
False
"""
from finite_rings.constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False
def is_PrimeField(R):
r"""
Determine if ``R`` is a field that is equal to its own prime subfield.
INPUT:
- ``R`` -- a ring or field
OUTPUT:
- ``True`` if R is `\QQ` or a finite field `\GF{p}` for `p` prime,
``False`` otherwise.
EXAMPLES::
sage: import sage.rings.field
doctest:...: DeprecationWarning: the module sage.rings.field is deprecated and will be removed
See http://trac.sagemath.org/18108 for details.
sage: sage.rings.field.is_PrimeField(QQ)
True
sage: sage.rings.field.is_PrimeField(GF(7))
True
sage: sage.rings.field.is_PrimeField(GF(7^2,'t'))
False
"""
from finite_rings.finite_field_constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False
def is_PrimeField(R):
r"""
Determine if ``R`` is a field that is equal to its own prime subfield.
INPUT:
- ``R`` -- a ring or field
OUTPUT:
- ``True`` if R is `\QQ` or a finite field `\GF{p}` for `p` prime,
``False`` otherwise.
EXAMPLES::
sage: sage.rings.field.is_PrimeField(QQ)
True
sage: sage.rings.field.is_PrimeField(GF(7))
True
sage: sage.rings.field.is_PrimeField(GF(7^2,'t'))
False
"""
from finite_rings.constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False
def is_PrimeField(R):
from finite_field.constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False
def is_PrimeField(R):
"""
Determine if R is a field that is equal to its own prime subfield.
INPUT:
- R - a ring or field
OUTPUT:
- True - if R is `\QQ` or a finite field `GF(p)` for p prime.
- False - otherwise
EXAMPLES::
sage: sage.rings.field.is_PrimeField(QQ)
True
::
sage: sage.rings.field.is_PrimeField(GF(7))
True
::
sage: sage.rings.field.is_PrimeField(GF(7^2,'t'))
False
"""
from finite_rings.constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False
def is_PrimeField(R):
"""
Determine if R is a field that is equal to its own prime subfield.
INPUT:
- R - a ring or field
OUTPUT:
- True - if R is `\QQ` or a finite field `GF(p)` for p prime.
- False - otherwise
EXAMPLES::
sage: sage.rings.field.is_PrimeField(QQ)
True
::
sage: sage.rings.field.is_PrimeField(GF(7))
True
::
sage: sage.rings.field.is_PrimeField(GF(7^2,'t'))
False
"""
from finite_rings.constructor import is_FiniteField
from rational_field import is_RationalField
if is_RationalField(R):
return True
if is_FiniteField(R):
return R.degree() == 1
return False