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Deprecate name=('a',) for FiniteField #40949

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Deprecate name=('a',) for FiniteField #40949

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f67d72d
Fix finite field GF(p).extension(1, names=tuple)
user202729 Oct 1, 2025
7b59ba9
Deprecate name=('a',) for FiniteField
user202729 Oct 1, 2025
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5 changes: 5 additions & 0 deletions src/sage/modules/ore_module.py
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Original file line number Diff line number Diff line change
Expand Up @@ -269,6 +269,11 @@ def normalize_names(names, rank):
r"""
Return a normalized form of ``names``.

.. WARNING::

This has different signature and slightly different functionality
from :func:`sage.structure.category_object.normalize_names`!

INPUT:

- ``names`` -- a string, a list of strings or ``None``
Expand Down
2 changes: 1 addition & 1 deletion src/sage/rings/finite_rings/conway_polynomials.py
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Expand Up @@ -234,7 +234,7 @@ def polynomial(self, n):
return f

# Work in an arbitrary field K of order p**n.
K = FiniteField(p**n, names='a')
K = FiniteField(p**n, name='a')

# TODO: something like the following
# gcds = [n.gcd(d) for d in self.nodes.keys()]
Expand Down
36 changes: 28 additions & 8 deletions src/sage/rings/finite_rings/finite_field_base.pyx
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Expand Up @@ -1421,26 +1421,46 @@ 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
from sage.rings.integer import Integer
if name is None and names is not None:
name = names
if name is not None and names is None:
if isinstance(name, str):
names = (name,)
else:
from sage.misc.superseded import deprecation
deprecation(40948, "name should be a str, if you want to pass a tuple use names instead")
names = name
if latex_name is None and latex_names is not None:
latex_name = latex_names
if self.degree() == 1:
if isinstance(modulus, (int, Integer)):
E = GF((self.characteristic(), modulus), name=name, **kwds)
E = GF((self.characteristic(), modulus), names=names, **kwds)
elif isinstance(modulus, (list, tuple)):
E = GF((self.characteristic(), len(modulus) - 1), name=name, modulus=modulus, **kwds)
E = GF((self.characteristic(), len(modulus) - 1), names=names, modulus=modulus, **kwds)
elif isinstance(modulus, Polynomial):
if modulus.change_ring(self).is_irreducible():
E = GF((self.characteristic(), modulus.degree()), name=name, modulus=modulus, **kwds)
E = GF((self.characteristic(), modulus.degree()), names=names, modulus=modulus, **kwds)
else:
E = Field.extension(self, modulus, name=name, embedding=embedding, **kwds)
E = Field.extension(self, modulus, names=names, embedding=embedding, **kwds)
elif isinstance(modulus, (int, Integer)):
E = GF((self.characteristic(), self.degree() * modulus), name=name, **kwds)
E = GF((self.characteristic(), self.degree() * modulus), names=names, **kwds)
if E is self:
pass # coercion map (identity map) is automatically found
elif hasattr(E, '_prefix') and hasattr(self, '_prefix'):
Expand All @@ -1455,7 +1475,7 @@ cdef class FiniteField(Field):
except AssertionError: # coercion already exists
pass
else:
E = Field.extension(self, modulus, name=name, embedding=embedding, latex_name=latex_name, **kwds)
E = Field.extension(self, modulus, names=names, embedding=embedding, latex_name=latex_name, **kwds)
if map:
return (E, E.coerce_map_from(self))
else:
Expand Down
37 changes: 35 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
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this ought to fail (warn), but it doesn't. Why?

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 @@ -642,11 +671,15 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
# at this point, order = p**n
# note that we haven't tested p for primality

if name is not None and not isinstance(name, str):
from sage.misc.superseded import deprecation
deprecation(40948, "name should be a str, if you want to pass a tuple use names instead")

if n == 1:
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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