gh-36589: Replace relative imports by absolute ones in a few packages
    
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As preparation for compiling with meson, we replace relative imports by
absolute ones.
Moreover, relative imports are not used consistently in the codebase and
result in issues for doctesting with pytest (which admittedly is a
limitation of pytest). We normalize the relative imports in a few
smaller packages to be absolute imports. Small code-style improvements
along the way (mainly to nicely order the imports)

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URL: #36589
Reported by: Tobias Diez
Reviewer(s): Dima Pasechnik

Author: Release Manager

src/sage/arith/all.py

@@ -1,35 +1,96 @@
 from sage.misc.lazy_import import lazy_import
 
-from .misc import (algdep, bernoulli, is_prime, is_prime_power,
-    is_pseudoprime, is_pseudoprime_power,
-    prime_powers, primes_first_n, eratosthenes, primes,
-    next_prime_power, next_probable_prime, next_prime,
-    previous_prime, previous_prime_power, random_prime,
-    divisors, sigma, gcd, GCD, xlcm, xgcd, xkcd,
-    inverse_mod, get_gcd, get_inverse_mod, power_mod,
-    rational_reconstruction, mqrr_rational_reconstruction,
-    trial_division, factor, prime_divisors, odd_part, prime_to_m_part,
-    is_square, is_squarefree, euler_phi, carmichael_lambda, crt, CRT,
-    CRT_list, CRT_basis, CRT_vectors, multinomial, multinomial_coefficients,
-    binomial, factorial, kronecker_symbol, kronecker, legendre_symbol,
-    primitive_root, nth_prime, quadratic_residues, moebius,
-    continuant, number_of_divisors, hilbert_symbol, hilbert_conductor,
-    hilbert_conductor_inverse, falling_factorial, rising_factorial,
-    integer_ceil, integer_floor,
-    two_squares, three_squares, four_squares, sum_of_k_squares,
-    subfactorial, is_power_of_two, differences,
+from sage.arith.misc import (
+    algdep,
+    bernoulli,
+    is_prime,
+    is_prime_power,
+    is_pseudoprime,
+    is_pseudoprime_power,
+    prime_powers,
+    primes_first_n,
+    eratosthenes,
+    primes,
+    next_prime_power,
+    next_probable_prime,
+    next_prime,
+    previous_prime,
+    previous_prime_power,
+    random_prime,
+    divisors,
+    sigma,
+    gcd,
+    GCD,
+    xlcm,
+    xgcd,
+    xkcd,
+    inverse_mod,
+    get_gcd,
+    get_inverse_mod,
+    power_mod,
+    rational_reconstruction,
+    mqrr_rational_reconstruction,
+    trial_division,
+    factor,
+    prime_divisors,
+    odd_part,
+    prime_to_m_part,
+    is_square,
+    is_squarefree,
+    euler_phi,
+    carmichael_lambda,
+    crt,
+    CRT,
+    CRT_list,
+    CRT_basis,
+    CRT_vectors,
+    multinomial,
+    multinomial_coefficients,
+    binomial,
+    factorial,
+    kronecker_symbol,
+    kronecker,
+    legendre_symbol,
+    primitive_root,
+    nth_prime,
+    quadratic_residues,
+    moebius,
+    continuant,
+    number_of_divisors,
+    hilbert_symbol,
+    hilbert_conductor,
+    hilbert_conductor_inverse,
+    falling_factorial,
+    rising_factorial,
+    integer_ceil,
+    integer_floor,
+    two_squares,
+    three_squares,
+    four_squares,
+    sum_of_k_squares,
+    subfactorial,
+    is_power_of_two,
+    differences,
     sort_complex_numbers_for_display,
-    fundamental_discriminant, squarefree_divisors,
-    radical, binomial_coefficients, jacobi_symbol,
+    fundamental_discriminant,
+    squarefree_divisors,
+    radical,
+    binomial_coefficients,
+    jacobi_symbol,
     dedekind_sum,
-    prime_factors, prime_range, valuation)
+    prime_factors,
+    prime_range,
+    valuation,
+)
 
-lazy_import('sage.arith.misc', ('Sigma', 'Moebius', 'Euler_Phi'), deprecation=30322)
+lazy_import("sage.arith.misc", ("Sigma", "Moebius", "Euler_Phi"), deprecation=30322)
+
+from sage.arith.functions import lcm
 
-from .functions import lcm
 LCM = lcm
 
-from .srange import xsrange, srange, ellipsis_iter, ellipsis_range
+from sage.arith.srange import xsrange, srange, ellipsis_iter, ellipsis_range
+
 sxrange = xsrange
 
 σ = sigma

src/sage/arith/power.pyx

@@ -17,7 +17,7 @@ square-and-multiply algorithm.
 
 from cysignals.signals cimport sig_check
 
-from .long cimport integer_check_long
+from sage.arith.long cimport integer_check_long
 
 
 cpdef generic_power(a, n) noexcept:

src/sage/cpython/all.py

@@ -1,2 +1,2 @@
-from .debug import getattr_debug, type_debug
-from .getattr import raw_getattr
+from sage.cpython.debug import getattr_debug, type_debug
+from sage.cpython.getattr import raw_getattr

src/sage/cpython/debug.pyx

@@ -21,7 +21,7 @@ cdef extern from "Python.h":
 cdef extern from "sage/cpython/debugimpl.c":
     void _type_debug(PyTypeObject*)
 
-from .getattr cimport AttributeErrorMessage
+from sage.cpython.getattr cimport AttributeErrorMessage
 
 
 # Determine subtype_traverse, subtype_clear, subtype_dealloc functions

src/sage/data_structures/all.py

@@ -1,2 +1,2 @@
 
-from .bitset import Bitset, FrozenBitset
+from sage.data_structures.bitset import Bitset, FrozenBitset

src/sage/data_structures/bitset.pxd

@@ -7,7 +7,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .bitset_base cimport bitset_t
+from sage.data_structures.bitset_base cimport bitset_t
 
 # Python layer over bitset_t
 cdef class FrozenBitset:

src/sage/data_structures/bitset.pyx

@@ -31,7 +31,7 @@ linear in ``capacity``.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .bitset_base cimport *
+from sage.data_structures.bitset_base cimport *
 from cpython.object cimport Py_LT, Py_LE, Py_EQ, Py_NE, Py_GT, Py_GE
 
 

src/sage/misc/all.py

@@ -1,11 +1,11 @@
-from .lazy_attribute import lazy_attribute, lazy_class_attribute
-from .lazy_import import lazy_import
+from sage.misc.lazy_attribute import lazy_attribute, lazy_class_attribute
+from sage.misc.lazy_import import lazy_import
 
-from .all__sagemath_objects import *
-from .all__sagemath_environment import *
-from .all__sagemath_repl import *
+from sage.misc.all__sagemath_objects import *
+from sage.misc.all__sagemath_environment import *
+from sage.misc.all__sagemath_repl import *
 
-from .misc import (BackslashOperator,
+from sage.misc.misc import (BackslashOperator,
                   exists, forall, is_iterator,
                   random_sublist,
                   pad_zeros,
@@ -15,27 +15,27 @@
 lazy_import('sage.misc.misc', 'union',
             deprecation=32096)
 
-from .banner import version
+from sage.misc.banner import version
 
-from .dev_tools import import_statements
+from sage.misc.dev_tools import import_statements
 
-from .html import html, pretty_print_default
+from sage.misc.html import html, pretty_print_default
 
-from .table import table
+from sage.misc.table import table
 
-from .sage_timeit_class import timeit
+from sage.misc.sage_timeit_class import timeit
 
-from .edit_module import edit
+from sage.misc.edit_module import edit
 
-from .map_threaded import map_threaded
+from sage.misc.map_threaded import map_threaded
 
-from .session import load_session, save_session, show_identifiers
+from sage.misc.session import load_session, save_session, show_identifiers
 
-from .remote_file import get_remote_file
+from sage.misc.remote_file import get_remote_file
 
-from .mrange import xmrange, mrange, xmrange_iter, mrange_iter, cartesian_product_iterator
+from sage.misc.mrange import xmrange, mrange, xmrange_iter, mrange_iter, cartesian_product_iterator
 
-from .fpickle import pickle_function, unpickle_function
+from sage.misc.fpickle import pickle_function, unpickle_function
 
 lazy_import('sage.misc.pager', 'pager')
 
@@ -45,21 +45,21 @@
         'constructions', 'help'])
 lazy_import('pydoc', 'help', 'python_help')
 
-from .classgraph import class_graph
+from sage.misc.classgraph import class_graph
 
-from .reset import reset, restore
+from sage.misc.reset import reset, restore
 
-from .mathml import mathml
+from sage.misc.mathml import mathml
 
-from .defaults import (set_default_variable_name,
+from sage.misc.defaults import (set_default_variable_name,
                        series_precision, set_series_precision)
 
 lazy_import("sage.misc.cython", "cython_lambda")
 lazy_import("sage.misc.cython", "cython_compile", "cython")
 
-from .func_persist import func_persist
+from sage.misc.func_persist import func_persist
 
-from .functional import (additive_order,
+from sage.misc.functional import (additive_order,
                         base_ring,
                         base_field,
                         basis,
@@ -118,15 +118,15 @@
                         transpose)
 
 
-from .latex import LatexExpr, latex, view
+from sage.misc.latex import LatexExpr, latex, view
 
-from .randstate import seed, set_random_seed, initial_seed, current_randstate
+from sage.misc.randstate import seed, set_random_seed, initial_seed, current_randstate
 
-from .prandom import *
+from sage.misc.prandom import *
 
-from .timing import walltime, cputime
+from sage.misc.timing import walltime, cputime
 
-from .explain_pickle import explain_pickle, unpickle_newobj, unpickle_global, unpickle_build, unpickle_instantiate, unpickle_persistent, unpickle_extension, unpickle_appends
+from sage.misc.explain_pickle import explain_pickle, unpickle_newobj, unpickle_global, unpickle_build, unpickle_instantiate, unpickle_persistent, unpickle_extension, unpickle_appends
 
 lazy_import('sage.misc.inline_fortran', 'fortran')
 

src/sage/misc/all__sagemath_environment.py

@@ -1 +1 @@
-from .temporary_file import tmp_dir, tmp_filename
+from sage.misc.temporary_file import tmp_dir, tmp_filename

src/sage/misc/all__sagemath_objects.py

@@ -2,35 +2,35 @@
 
 import sage.structure.all   # to break a cyclic import
 
-from .lazy_attribute import lazy_attribute, lazy_class_attribute
-from .lazy_import import lazy_import
+from sage.misc.lazy_attribute import lazy_attribute, lazy_class_attribute
+from sage.misc.lazy_import import lazy_import
 
-from .verbose import (set_verbose, set_verbose_files,
+from sage.misc.verbose import (set_verbose, set_verbose_files,
                       get_verbose_files, unset_verbose_files, get_verbose)
 lazy_import('sage.misc.verbose', 'verbose',
             deprecation=17815)
-from .call import attrcall
+from sage.misc.call import attrcall
 
-from .misc_c import prod, running_total, balanced_sum
+from sage.misc.misc_c import prod, running_total, balanced_sum
 mul = prod
 add = sum
 
-from .repr import repr_lincomb
+from sage.misc.repr import repr_lincomb
 
-from .flatten import flatten
+from sage.misc.flatten import flatten
 
-from .persist import save, load, dumps, loads, db, db_save
+from sage.misc.persist import save, load, dumps, loads, db, db_save
 
-from .constant_function import ConstantFunction
+from sage.misc.constant_function import ConstantFunction
 
-from .sage_unittest import TestSuite
+from sage.misc.sage_unittest import TestSuite
 
-from .decorators import specialize, sage_wraps, infix_operator
+from sage.misc.decorators import specialize, sage_wraps, infix_operator
 
-from .unknown import Unknown, UnknownError
+from sage.misc.unknown import Unknown, UnknownError
 
-from .cachefunc import CachedFunction, cached_function, cached_method, cached_in_parent_method, disk_cached_function
+from sage.misc.cachefunc import CachedFunction, cached_function, cached_method, cached_in_parent_method, disk_cached_function
 
-from .abstract_method import abstract_method
+from sage.misc.abstract_method import abstract_method
 
-from .timing import walltime, cputime
+from sage.misc.timing import walltime, cputime