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Fix finite field GF(p).extension(1, names=tuple) #40947

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Fix finite field GF(p).extension(1, names=tuple) #40947

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15 changes: 15 additions & 0 deletions src/sage/rings/finite_rings/finite_field_base.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -1421,6 +1421,21 @@ cdef class FiniteField(Field):
sage: L.<v> = K.extension(b)
sage: L(u).minpoly() == u.minpoly()
True

Check the test above when `a=b=1`, see :issue:`40926`.
While in general it doesn't make much sense to talk about the generator
of a prime finite field (:meth:`gen` returns 1), generic code may find
it convenient to always specify the variable name when it is not known
in advance whether the exponent is 1.

The reason why one may want to specify ``name`` is :issue:`38376`.

::

sage: K.<u> = GF((random_prime(10^100), 1))
sage: L.<v> = K.extension(1)
sage: L(u).minpoly() == u.minpoly()
True
"""
from sage.rings.finite_rings.finite_field_constructor import GF
from sage.rings.polynomial.polynomial_element import Polynomial
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33 changes: 31 additions & 2 deletions src/sage/rings/finite_rings/finite_field_constructor.py
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Expand Up @@ -597,7 +597,7 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
sage: GF((5, 1), 3)
Traceback (most recent call last):
...
TypeError: variable name 3 must be a string, not <class 'sage.rings.integer.Integer'>
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: GF((5, 2), 3)
Traceback (most recent call last):
...
Expand All @@ -610,6 +610,35 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
Traceback (most recent call last):
...
ValueError: the order of a finite field must be a prime power

We expect ``name`` to be a string (if it is a single name) and ``names`` to be
a tuple of strings, but for backwards compatibility this is not enforced.
This behavior might change in the future. ::

sage: GF(7, name='aa')
Finite Field of size 7
sage: GF(7^2, name='aa')
Finite Field in aa of size 7^2
sage: GF(7, name=('aa',))
Finite Field of size 7
sage: GF(7^2, name=('aa',))
Finite Field in aa of size 7^2
sage: GF(7, name=['aa'])
Finite Field of size 7
sage: GF(7^2, name=['aa'])
Finite Field in aa of size 7^2
sage: GF(7, names='aa')
Finite Field of size 7
sage: GF(7^2, names='aa')
Finite Field in aa of size 7^2
sage: GF(7, names=('aa',))
Finite Field of size 7
sage: GF(7^2, names=('aa',))
Finite Field in aa of size 7^2
sage: GF(7, names=['aa'])
Finite Field of size 7
sage: GF(7^2, names=['aa'])
Finite Field in aa of size 7^2
"""
for key, val in kwds.items():
if key not in ['structure', 'implementation', 'prec', 'embedding', 'latex_names']:
Expand Down Expand Up @@ -646,7 +675,7 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
if impl is None:
impl = 'modn'
if name is not None:
certify_names((name,))
certify_names((name,) if isinstance(name, str) else name)
name = ('x',) # Ignore name
# Every polynomial of degree 1 is irreducible
check_irreducible = False
Expand Down
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