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sage.rings.finite_rings: Modularization fixes, # needs #36056

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merged 23 commits into from
Aug 13, 2023
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sage.rings.finite_rings: Modularization fixes, # needs #36056

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bfc5cdf
src/sage/rings/finite_rings/integer_mod.pyx: Move import from sage.gr…
mkoeppe Feb 20, 2023
4c437cb
sage.rings: More # optional
mkoeppe Jun 4, 2023
97b5398
More # optional
mkoeppe Jun 9, 2023
d1f5704
sage.rings.finite_rings: More # optional
mkoeppe Jun 28, 2023
a1e4409
sage.rings.finite_rings: ./sage -fixdoctests --only-tags
mkoeppe Jun 28, 2023
a44af4d
sage.schemes: Update # needs
mkoeppe Jun 30, 2023
1f7e48a
Update # optional/needs
mkoeppe Jul 1, 2023
173d3c3
sage.rings: Update # optional / # needs
mkoeppe Jul 2, 2023
c0118ba
src/sage/rings/polynomial/polynomial_ring.py: Use '# needs sage.libs.…
mkoeppe Jul 8, 2023
19222fb
./sage -fixdoctests --distribution sagemath-categories --probe sage.r…
mkoeppe Jul 13, 2023
a04dbbc
src/sage/rings/finite_rings/conway_polynomials.py: Use lazy_import fo…
mkoeppe Jul 15, 2023
e78d4ea
sage.rings: Update # needs
mkoeppe Jul 16, 2023
6042ff7
sage.rings.{finite_rings,polynomial}: Modularization fixes for imports
mkoeppe Jul 17, 2023
1bc26c2
sage.rings.finite_rings: Update # needs
mkoeppe Jul 17, 2023
1b54228
src/sage/rings/finite_rings/conway_polynomials.py: Add # needs
mkoeppe Jul 22, 2023
baca60e
sage.rings: Update # needs
mkoeppe Jul 22, 2023
1810daf
sage.rings.finite_rings: Update # needs
mkoeppe Aug 6, 2023
a3ef387
sage.rings.finite_rings: Update # needs
mkoeppe Aug 7, 2023
a18e1ab
src/sage/rings: sage -fixdoctests --only-tags
mkoeppe Aug 8, 2023
e9630a6
pkgs/sagemath-categories/MANIFEST.in.m4: Add sage.rings.finite_rings.…
mkoeppe Jan 27, 2023
8a823ff
src/sage/rings/finite_rings: Use more block tags
mkoeppe Aug 10, 2023
98283ea
src/sage/rings/finite_rings/conway_polynomials.py: Fix # needs
mkoeppe Aug 11, 2023
744ddf8
src/sage/rings/finite_rings/residue_field.pyx: Make a doctest work wh…
mkoeppe Aug 12, 2023
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37 changes: 27 additions & 10 deletions src/sage/rings/finite_rings/conway_polynomials.py
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Original file line number Diff line number Diff line change
Expand Up @@ -11,10 +11,13 @@
"""

from sage.misc.fast_methods import WithEqualityById
from sage.misc.lazy_import import lazy_import
from sage.structure.sage_object import SageObject
from sage.rings.finite_rings.finite_field_constructor import FiniteField
from sage.rings.integer import Integer
import sage.databases.conway

lazy_import('sage.databases.conway', 'ConwayPolynomials')


def conway_polynomial(p, n):
"""
Expand Down Expand Up @@ -45,19 +48,19 @@ def conway_polynomial(p, n):

EXAMPLES::

sage: conway_polynomial(2,5)
sage: conway_polynomial(2,5) # needs conway_polynomials
x^5 + x^2 + 1
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Shouldn't the tag be file-scoped?

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This module also contains code for computing pseudo-Conway polynomials, which has to be used when the database is not available

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OK.

sage: conway_polynomial(101,5)
sage: conway_polynomial(101,5) # needs conway_polynomials
x^5 + 2*x + 99
sage: conway_polynomial(97,101)
sage: conway_polynomial(97,101) # needs conway_polynomials
Traceback (most recent call last):
...
RuntimeError: requested Conway polynomial not in database.
"""
(p, n) = (int(p), int(n))
R = FiniteField(p)['x']
try:
return R(sage.databases.conway.ConwayPolynomials()[p][n])
return R(ConwayPolynomials()[p][n])
except KeyError:
raise RuntimeError("requested Conway polynomial not in database.")

Expand All @@ -82,7 +85,7 @@ def exists_conway_polynomial(p, n):

EXAMPLES::

sage: exists_conway_polynomial(2,3)
sage: exists_conway_polynomial(2,3) # needs conway_polynomials
True
sage: exists_conway_polynomial(2,-1)
False
Expand All @@ -91,7 +94,10 @@ def exists_conway_polynomial(p, n):
sage: exists_conway_polynomial(6,6)
False
"""
return sage.databases.conway.ConwayPolynomials().has_polynomial(p,n)
try:
return ConwayPolynomials().has_polynomial(p,n)
except ImportError:
return False
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Isn't it incorrect to return False when the database is not available? Why catch ImportError?

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The method is named exists_conway_polynomial, but it actually only tests whether it is known to Sage. When the database is not installed, nothing is known to Sage.
Return False here triggers the use of pseudo-Conway polynomials in the relevant code paths.

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I see. That is reasonable. Thanks.


class PseudoConwayLattice(WithEqualityById, SageObject):
r"""
Expand Down Expand Up @@ -127,6 +133,7 @@ class PseudoConwayLattice(WithEqualityById, SageObject):

EXAMPLES::

sage: # needs sage.rings.finite_rings
sage: from sage.rings.finite_rings.conway_polynomials import PseudoConwayLattice
sage: PCL = PseudoConwayLattice(2, use_database=False)
sage: PCL.polynomial(3)
Expand Down Expand Up @@ -154,11 +161,13 @@ def __init__(self, p, use_database=True):
"""
TESTS::

sage: # needs sage.rings.finite_rings
sage: from sage.rings.finite_rings.conway_polynomials import PseudoConwayLattice
sage: PCL = PseudoConwayLattice(3)
sage: PCL.polynomial(3)
x^3 + 2*x + 1

sage: # needs sage.rings.finite_rings
sage: PCL = PseudoConwayLattice(5, use_database=False)
sage: PCL.polynomial(12)
x^12 + 4*x^11 + 2*x^10 + 4*x^9 + 2*x^8 + 2*x^7 + 4*x^6 + x^5 + 2*x^4 + 2*x^2 + x + 2
Expand All @@ -171,9 +180,13 @@ def __init__(self, p, use_database=True):
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
self.ring = PolynomialRing(FiniteField(p), 'x')
if use_database:
C = sage.databases.conway.ConwayPolynomials()
self.nodes = {n: self.ring(C.polynomial(p, n))
for n in C.degrees(p)}
try:
C = ConwayPolynomials()
except ImportError:
self.nodes = {}
else:
self.nodes = {n: self.ring(C.polynomial(p, n))
for n in C.degrees(p)}
else:
self.nodes = {}

Expand All @@ -199,6 +212,7 @@ def polynomial(self, n):

EXAMPLES::

sage: # needs sage.rings.finite_rings
sage: from sage.rings.finite_rings.conway_polynomials import PseudoConwayLattice
sage: PCL = PseudoConwayLattice(2, use_database=False)
sage: PCL.polynomial(3)
Expand Down Expand Up @@ -267,6 +281,7 @@ def check_consistency(self, n):

EXAMPLES::

sage: # needs sage.rings.finite_rings
sage: from sage.rings.finite_rings.conway_polynomials import PseudoConwayLattice
sage: PCL = PseudoConwayLattice(2, use_database=False)
sage: PCL.check_consistency(6)
Expand Down Expand Up @@ -301,6 +316,7 @@ def _find_pow_of_frobenius(p, n, x, y):

EXAMPLES::

sage: # needs sage.rings.finite_rings
sage: from sage.rings.finite_rings.conway_polynomials import _find_pow_of_frobenius
sage: K.<a> = GF(3^14)
sage: x = K.multiplicative_generator()
Expand Down Expand Up @@ -380,6 +396,7 @@ def _frobenius_shift(K, generators, check_only=False):

EXAMPLES::

sage: # needs sage.libs.ntl sage.rings.finite_rings
sage: R.<x> = GF(2)[]
sage: f30 = x^30 + x^28 + x^27 + x^25 + x^24 + x^20 + x^19 + x^18 + x^16 + x^15 + x^12 + x^10 + x^7 + x^2 + 1
sage: f20 = x^20 + x^19 + x^15 + x^13 + x^12 + x^11 + x^9 + x^8 + x^7 + x^4 + x^2 + x + 1
Expand Down
23 changes: 12 additions & 11 deletions src/sage/rings/finite_rings/element_base.pyx
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@@ -1,4 +1,4 @@
# sage.doctest: optional - sage.rings.finite_rings
# sage.doctest: needs sage.rings.finite_rings
"""
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Aren't all files in src/sage/rings/finite_rings installed by the distribution that provides the feature?

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No, sagemath-categories ships the basic modules of sage.rings.finite_rings - https://github.com/mkoeppe/sage/blob/t/32432/modularization_of_sagelib__break_out_a_separate_package_sagemath_polyhedra/pkgs/sagemath-categories/MANIFEST.in.m4#L109-L123

This makes the prime fields and the integer mod rings available.

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Right. I missed it.

Base class for finite field elements

Expand Down Expand Up @@ -711,23 +711,23 @@ cdef class FinitePolyExtElement(FiniteRingElement):

EXAMPLES::

sage: k.<a> = FiniteField(9, impl='givaro', modulus='primitive')
sage: a.is_square()
sage: k.<a> = FiniteField(9, impl='givaro', modulus='primitive') # needs sage.libs.linbox
sage: a.is_square() # needs sage.libs.linbox
False
sage: (a**2).is_square()
sage: (a**2).is_square() # needs sage.libs.linbox
True
sage: k.<a> = FiniteField(4, impl='ntl', modulus='primitive')
sage: (a**2).is_square()
sage: k.<a> = FiniteField(4, impl='ntl', modulus='primitive') # needs sage.libs.ntl
sage: (a**2).is_square() # needs sage.libs.ntl
True
sage: k.<a> = FiniteField(17^5, impl='pari_ffelt', modulus='primitive')
sage: a.is_square()
sage: k.<a> = FiniteField(17^5, impl='pari_ffelt', modulus='primitive') # needs sage.libs.pari
sage: a.is_square() # needs sage.libs.pari
False
sage: (a**2).is_square()
sage: (a**2).is_square() # needs sage.libs.pari
True

::

sage: k(0).is_square()
sage: k(0).is_square() # needs sage.libs.linbox
True
"""
K = self.parent()
Expand Down Expand Up @@ -1049,6 +1049,7 @@ cdef class FinitePolyExtElement(FiniteRingElement):

TESTS::

sage: # needs sage.modules
sage: p = random_prime(2^99)
sage: k = randrange(2,10)
sage: F.<t> = GF((p, k))
Expand Down Expand Up @@ -1086,7 +1087,7 @@ cdef class Cache_base(SageObject):
EXAMPLES::

sage: k.<a> = GF(2^48)
sage: k._cache.fetch_int(2^33 + 2 + 1)
sage: k._cache.fetch_int(2^33 + 2 + 1) # needs sage.libs.ntl
a^33 + a + 1
"""
raise NotImplementedError("this must be implemented by subclasses")
10 changes: 8 additions & 2 deletions src/sage/rings/finite_rings/element_pari_ffelt.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -28,13 +28,16 @@ from .element_base cimport FinitePolyExtElement
from .integer_mod import IntegerMod_abstract

import sage.rings.integer
from sage.modules.free_module_element import FreeModuleElement
from sage.rings.integer cimport Integer
from sage.rings.polynomial.polynomial_element import Polynomial
from sage.rings.polynomial.multi_polynomial_element import MPolynomial
from sage.rings.rational import Rational
from sage.structure.richcmp cimport rich_to_bool

try:
from sage.modules.free_module_element import FreeModuleElement
except ImportError:
FreeModuleElement = ()

from sage.interfaces.abc import GapElement

Expand Down Expand Up @@ -1330,9 +1333,10 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):

EXAMPLES::

sage: # needs sage.libs.gap
sage: F = FiniteField(2^3, 'aa', impl='pari_ffelt')
sage: aa = F.multiplicative_generator()
sage: gap(aa) # indirect doctest
sage: gap(aa) # indirect doctest
Z(2^3)
sage: b = F.multiplicative_generator()
sage: a = b^3
Expand All @@ -1347,6 +1351,7 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):

You can specify the instance of the Gap interpreter that is used::

sage: # needs sage.libs.gap
sage: F = FiniteField(next_prime(200)^2, 'a', impl='pari_ffelt')
sage: a = F.multiplicative_generator()
sage: a._gap_ (gap)
Expand All @@ -1356,6 +1361,7 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):

Gap only supports relatively small finite fields::

sage: # needs sage.libs.gap
sage: F = FiniteField(next_prime(1000)^2, 'a', impl='pari_ffelt')
sage: a = F.multiplicative_generator()
sage: a._gap_init_()
Expand Down
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