gh-35106: sage.{arith,crypto,databases,dynamics,lfunctions,quadratic_forms}: Replace imports from sage.*.all for namespace packages
    
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### 📚 Description
Fixes #34955

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### ⌛ Dependencies
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Depends on #35119
    
URL: #35106
Reported by: Matthias Köppe
Reviewer(s): Dima Pasechnik, Matthias Köppe, Tobias Diez

Author: Release Manager

src/.relint.yml

@@ -49,6 +49,6 @@
     Hint: namespace package. Type import_statements("SOME_IDENTIFIER") to find a more specific import,
     Hint: or use 'sage --fiximports' to fix automatically in the source file.
   # Keep in sync with SAGE_ROOT/src/sage/misc/replace_dot_all.py
-  pattern: 'from\s+sage(|[.](arith|categories|combinat|ext|graphs(|[.]decompositions)|interfaces|libs|matrix|misc|numerical(|[.]backends)|rings|sets))[.]all\s+import'
+  pattern: 'from\s+sage(|[.](arith|categories|combinat|ext|graphs(|[.]decompositions)|interfaces|libs|matrix|misc|numerical(|[.]backends)|rings(|[.]finite_rings)|sets))[.]all\s+import'
   filePattern: '.*[.](py|pyx|pxi)$'
   error: false # Make this a warning instead of an error for now

src/sage/arith/multi_modular.pyx

@@ -16,7 +16,7 @@ from cysignals.memory cimport check_allocarray, check_reallocarray, sig_free
 
 from sage.libs.gmp.mpz cimport *
 from sage.rings.integer cimport Integer, smallInteger
-from sage.arith.all import random_prime
+from sage.arith.misc import random_prime
 from types import GeneratorType
 from sage.ext.stdsage cimport PY_NEW
 from cpython.object cimport PyObject_RichCompare

src/sage/arith/numerical_approx.pyx

@@ -15,7 +15,9 @@ Generic numerical approximation function
 from sage.structure.parent cimport Parent
 from sage.structure.element cimport parent
 cdef Parent CDF
-from sage.rings.all import RealField, ComplexField, CDF
+from sage.rings.real_mpfr import RealField
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.complex_double import CDF
 
 
 def numerical_approx_generic(x, prec):

src/sage/crypto/boolean_function.pyx

@@ -38,8 +38,7 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.integer cimport Integer
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.polynomial.pbori.pbori import BooleanPolynomial
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
-from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_element import Polynomial
 
 from sage.misc.superseded import deprecated_function_alias
@@ -329,11 +328,15 @@ cdef class BooleanFunction(SageObject):
 
         elif isinstance(x, Polynomial):
             K = x.base_ring()
-            if is_FiniteField(K) and K.characteristic() == 2:
+            if isinstance(K, FiniteField) and K.characteristic() == 2:
                 self._nvariables = K.degree()
                 bitset_init(self._truth_table, <mp_bitcnt_t> (1<<self._nvariables))
                 bitset_zero(self._truth_table)
-                if isinstance(K,FiniteField_givaro): #the ordering is not the same in this case
+                try:
+                    from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
+                except ImportError:
+                    FiniteField_givaro = ()
+                if isinstance(K, FiniteField_givaro):  # the ordering is not the same in this case
                     for u in K:
                         bitset_set_to(self._truth_table, ZZ(u._vector_().list(),2) , (x(u)).trace())
                 else:
@@ -1008,7 +1011,7 @@ cdef class BooleanFunction(SageObject):
         from sage.misc.misc_c import prod
 
         from sage.matrix.constructor import Matrix
-        from sage.arith.all import binomial
+        from sage.arith.misc import binomial
         M = Matrix(GF(2), sum(binomial(self._nvariables,i) for i in range(d+1)), len(s))
 
         cdef long i

src/sage/crypto/classical.py

@@ -55,7 +55,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
-from sage.arith.all import xgcd, inverse_mod
+from sage.arith.misc import inverse_mod, xgcd
 from random import randint
 from sage.matrix.matrix_space import MatrixSpace
 

src/sage/crypto/lattice.py

@@ -256,7 +256,7 @@ def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
             A = A.stack(R.random_element().matrix())
 
     elif type == 'cyclotomic':
-        from sage.arith.all import euler_phi
+        from sage.arith.misc import euler_phi
         from sage.misc.functional import cyclotomic_polynomial
 
         # we assume that n+1 <= min( euler_phi^{-1}(n) ) <= 2*n

src/sage/crypto/lfsr.py

@@ -128,8 +128,9 @@
 import copy
 
 from sage.structure.all import Sequence
-from sage.rings.all import Integer, PolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
+from sage.rings.integer import Integer
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 
 def lfsr_sequence(key, fill, n):
@@ -179,7 +180,7 @@ def lfsr_sequence(key, fill, n):
         raise TypeError("key must be a list")
     key = Sequence(key)
     F = key.universe()
-    if not is_FiniteField(F):
+    if not isinstance(F, FiniteField):
         raise TypeError("universe of sequence must be a finite field")
 
     s = fill

src/sage/crypto/lwe.py

@@ -91,23 +91,25 @@
 - [CGW2013]_
 """
 
+from sage.arith.misc import euler_phi, next_prime
 from sage.functions.log import log
 from sage.functions.other import floor, ceil
-from sage.misc.functional import sqrt
 from sage.misc.functional import cyclotomic_polynomial, round
-from sage.misc.randstate import set_random_seed
+from sage.misc.functional import sqrt
 from sage.misc.prandom import randint
+from sage.misc.randstate import set_random_seed
 from sage.modules.free_module import FreeModule
 from sage.modules.free_module_element import random_vector, vector
 from sage.numerical.optimize import find_root
-from sage.rings.all import ZZ, IntegerModRing, RR
-from sage.arith.all import next_prime, euler_phi
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_mpfr import RR
+from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
+from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 from sage.structure.element import parent
 from sage.structure.sage_object import SageObject
 from sage.symbolic.constants import pi
 from sage.symbolic.ring import SR
-from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
-from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 
 
 class UniformSampler(SageObject):

src/sage/crypto/mq/rijndael_gf.py

@@ -424,7 +424,8 @@
 
 from sage.matrix.constructor import matrix
 from sage.matrix.constructor import column_matrix
-from sage.structure.element import Matrix
+from sage.structure.element import Element, Matrix
+from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_base
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.structure.sage_object import SageObject
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -757,10 +758,9 @@ def _GF_to_hex(self, GF):
             sage: rgf._GF_to_hex(output)
             'e142cd5fcd9d6d94a3340793034391b5'
         """
-        from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         if not isinstance(GF, Matrix) and \
            not isinstance(GF, list) and \
-           not is_FiniteFieldElement(GF):
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField_base)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self._F))
@@ -883,10 +883,9 @@ def _GF_to_bin(self, GF):
             sage: rgf._GF_to_bin(output)
             '11011000000111111111100000011011110110000001111111111000000110111101100000011111111110000001101111011000000111111111100000011011'
         """
-        from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         if not isinstance(GF, Matrix) and \
            not isinstance(GF, list) and \
-           not is_FiniteFieldElement(GF):
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField_base)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self))

src/sage/crypto/public_key/blum_goldwasser.py

@@ -30,17 +30,16 @@
 
 from operator import xor
 
+from sage.arith.misc import gcd, power_mod, xgcd
 from sage.crypto.cryptosystem import PublicKeyCryptosystem
-from sage.crypto.util import is_blum_prime
-from sage.crypto.util import least_significant_bits
-from sage.crypto.util import random_blum_prime
+from sage.crypto.util import is_blum_prime, least_significant_bits, random_blum_prime
 from sage.functions.log import log
 from sage.functions.other import Function_floor
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.all import gcd, power_mod, xgcd
 from sage.rings.finite_rings.integer_mod import Mod as mod
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
 
+
 floor = Function_floor()
 IntegerModRing = IntegerModFactory("IntegerModRing")
 

src/sage/crypto/sbox.pyx

@@ -17,7 +17,7 @@ from sage.misc.functional import is_even
 from sage.misc.misc_c import prod as mul
 from sage.misc.superseded import deprecated_function_alias
 from sage.modules.free_module_element import vector
-from sage.rings.finite_rings.element_base import is_FiniteFieldElement
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.ideal import FieldIdeal, Ideal
 from sage.rings.integer_ring import ZZ
@@ -195,7 +195,7 @@ cdef class SBox(SageObject):
 
         _S_list = []
         for e in S:
-            if is_FiniteFieldElement(e):
+            if isinstance(e, Element) and isinstance(e.parent(), FiniteField):
                 e = e.polynomial().change_ring(ZZ).subs(e.parent().characteristic())
             _S_list.append(e)
         S = _S_list

src/sage/crypto/stream.py

@@ -12,12 +12,11 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .cryptosystem import SymmetricKeyCryptosystem
-from .stream_cipher import LFSRCipher, ShrinkingGeneratorCipher
-
+from sage.arith.misc import gcd, power_mod
+from sage.crypto.cryptosystem import SymmetricKeyCryptosystem
+from sage.crypto.stream_cipher import LFSRCipher, ShrinkingGeneratorCipher
 from sage.crypto.util import random_blum_prime
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.all import gcd, power_mod
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
 from sage.rings.polynomial.polynomial_element import Polynomial

src/sage/crypto/util.py

@@ -20,14 +20,16 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+from sage.arith.functions import lcm
+from sage.arith.misc import is_prime, primes, random_prime
+from sage.misc.lazy_import import lazy_import
 from sage.monoids.string_monoid import BinaryStrings
-from sage.arith.all import is_prime, lcm, primes, random_prime
-from sage.rings.integer import Integer
 from sage.rings.finite_rings.integer_mod import Mod as mod
+from sage.rings.integer import Integer
 
-from sage.misc.lazy_import import lazy_import
 lazy_import('sage.arith.misc', ('carmichael_lambda'), deprecation=34719)
 
+
 def ascii_integer(B):
     r"""
     Return the ASCII integer corresponding to the binary string ``B``.

src/sage/databases/findstat.py

@@ -1499,7 +1499,8 @@ def __call__(self, elt):
             from sage.repl.preparse import preparse
             try:
                 l = {}
-                code = "from sage.all import *\n" + preparse(self.sage_code())
+                environment = 'sage.all'
+                code = f"from {environment} import *\n" + preparse(self.sage_code())
                 exec(code, l)
             except SyntaxError:
                 raise ValueError("could not execute verified code for %s" % self)

src/sage/databases/jones.py

@@ -68,7 +68,9 @@
 
 import os
 
-from sage.rings.all import NumberField, RationalField, PolynomialRing
+from sage.rings.number_field.number_field import NumberField
+from sage.rings.rational_field import RationalField
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.misc.misc import powerset
 from sage.env import SAGE_SHARE
 

src/sage/dynamics/arithmetic_dynamics/affine_ds.py

@@ -43,8 +43,7 @@ class initialization directly.
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import typecall
 from sage.rings.integer import Integer
-from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import FractionField
 from sage.rings.fraction_field import is_FractionField
 from sage.rings.quotient_ring import is_QuotientRing
@@ -251,7 +250,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
                 raise ValueError('domain and codomain do not agree')
             if R not in Fields():
                 return typecall(cls, polys, domain)
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 return DynamicalSystem_affine_finite_field(polys, domain)
             return DynamicalSystem_affine_field(polys, domain)
         elif isinstance(morphism_or_polys,(list, tuple)):
@@ -299,7 +298,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
 
         if R not in Fields():
             return typecall(cls, polys, domain)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             return DynamicalSystem_affine_finite_field(polys, domain)
         return DynamicalSystem_affine_field(polys, domain)
 
@@ -319,7 +318,8 @@ def __init__(self, polys_or_rat_fncts, domain):
         """
         L = polys_or_rat_fncts
         # Next attribute needed for _fast_eval and _fastpolys
-        self._is_prime_finite_field = is_PrimeFiniteField(L[0].base_ring())
+        R = L[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
         DynamicalSystem.__init__(self, L, domain)
 
     def __copy__(self):

src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py

@@ -22,22 +22,23 @@
 from copy import copy, deepcopy
 from itertools import permutations, combinations, product
 
+from sage.arith.functions import lcm
+from sage.arith.misc import CRT, divisors, gcd, is_square
+from sage.combinat.permutation import Arrangements
 from sage.combinat.subset import Subsets
-from sage.misc.functional import sqrt
 from sage.matrix.constructor import matrix
-from sage.structure.element import is_Matrix
+from sage.misc.functional import sqrt
 from sage.misc.misc_c import prod
+from sage.parallel.use_fork import p_iter_fork
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Integers
 from sage.rings.integer_ring import ZZ
 from sage.rings.number_field.number_field import NumberField
-from sage.arith.all import gcd, lcm, CRT, is_square, divisors
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
 from sage.sets.primes import Primes
 from sage.sets.set import Set
-from sage.combinat.permutation import Arrangements
-from sage.parallel.use_fork import p_iter_fork
+from sage.structure.element import is_Matrix
 
 
 def automorphism_group_QQ_fixedpoints(rational_function, return_functions=False, iso_type=False):

src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py

@@ -34,7 +34,7 @@
 from sage.rings.rational_field import QQ
 from sage.schemes.affine.affine_space import AffineSpace
 from sage.symbolic.constants import e
-from sage.arith.all import gcd
+from sage.arith.misc import gcd
 from copy import copy
 
 def bCheck(c, v, p, b):

src/sage/dynamics/arithmetic_dynamics/generic_ds.py

@@ -33,7 +33,7 @@ class initialization directly.
 from sage.schemes.affine.affine_space import is_AffineSpace
 from sage.schemes.affine.affine_subscheme import AlgebraicScheme_subscheme_affine
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.qqbar import AlgebraicField_common
 from sage.schemes.berkovich.berkovich_space import is_Berkovich_Cp
 from sage.rings.rational_field import QQ
@@ -416,7 +416,7 @@ def field_of_definition_critical(self, return_embedding=False, simplify_all=Fals
             CR = CR.ring()
         x = CR.gen(0)
         poly = (g*CR(f).derivative(x) - f*CR(g).derivative(x)).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
@@ -536,7 +536,7 @@ def field_of_definition_periodic(self, n, formal=False, return_embedding=False,
             fn = ds.nth_iterate_map(n)
             f,g = fn[0].numerator(), fn[0].denominator()
             poly = (f - g*x).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
@@ -630,7 +630,7 @@ def field_of_definition_preimage(self, point, n, return_embedding=False, simplif
             #want the polynomial ring not the fraction field
             CR = CR.ring()
         poly = (f*point[1] - g*CR(point[0])).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)