gh-36588: Replace relative imports by absolute ones in rings

    
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As preparation for compiling with meson, we replace relative imports by
absolute ones.
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 `sage.rings` to be
absolute imports. Small code-style improvements along the way (mainly to
nicely order the imports)

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URL: #36588
Reported by: Tobias Diez
Reviewer(s): Dima Pasechnik

src/sage/rings/abc.pxd

@@ -1,4 +1,4 @@
-from .ring cimport CommutativeRing, Field
+from sage.rings.ring cimport CommutativeRing, Field
 
 cdef class RealField(Field):
 

src/sage/rings/all.py

@@ -12,10 +12,10 @@
 # ****************************************************************************
 from sage.misc.lazy_import import lazy_import
 
-from .all__sagemath_categories import *
+from sage.rings.all__sagemath_categories import *
 
 # Ring base classes
-from .ring import (Ring, Field, CommutativeRing, IntegralDomain,
+from sage.rings.ring import (Ring, Field, CommutativeRing, IntegralDomain,
     DedekindDomain, PrincipalIdealDomain, EuclideanDomain)
 
 # Ring element base classes
@@ -25,22 +25,22 @@
         EuclideanDomainElement, FieldElement)
 
 # Ideals
-from .ideal import Ideal
+from sage.rings.ideal import Ideal
 ideal = Ideal
 
 # Quotient
-from .quotient_ring import QuotientRing
+from sage.rings.quotient_ring import QuotientRing
 
 # Infinities
-from .infinity import infinity, Infinity, InfinityRing, unsigned_infinity, UnsignedInfinityRing
+from sage.rings.infinity import infinity, Infinity, InfinityRing, unsigned_infinity, UnsignedInfinityRing
 
 # Rational integers.
-from .integer_ring import IntegerRing, ZZ, crt_basis
-from .integer import Integer
+from sage.rings.integer_ring import IntegerRing, ZZ, crt_basis
+from sage.rings.integer import Integer
 
 # Rational numbers
-from .rational_field import RationalField, QQ
-from .rational import Rational
+from sage.rings.rational_field import RationalField, QQ
+from sage.rings.rational import Rational
 Rationals = RationalField
 
 # Integers modulo n.
@@ -49,120 +49,120 @@
 Integers = IntegerModRing
 
 # Finite fields
-from .finite_rings.all import *
+from sage.rings.finite_rings.all import *
 
 # Number field
-from .number_field.all import *
+from sage.rings.number_field.all import *
 
 # Function field
-from .function_field.all import *
+from sage.rings.function_field.all import *
 
 # Finite residue fields
-from .finite_rings.residue_field import ResidueField
+from sage.rings.finite_rings.residue_field import ResidueField
 
 # p-adic field
-from .padics.all import *
-from .padics.padic_printing import _printer_defaults as padic_printing
+from sage.rings.padics.all import *
+from sage.rings.padics.padic_printing import _printer_defaults as padic_printing
 
 # valuations
-from .valuation.all import *
+from sage.rings.valuation.all import *
 
 # Semirings
-from .semirings.all import *
+from sage.rings.semirings.all import *
 
 # Real numbers
-from .real_mpfr import (RealField, RR,
+from sage.rings.real_mpfr import (RealField, RR,
                        create_RealNumber as RealNumber)   # this is used by the preparser to wrap real literals -- very important.
 Reals = RealField
 
-from .real_double import RealDoubleField, RDF, RealDoubleElement
+from sage.rings.real_double import RealDoubleField, RDF, RealDoubleElement
 
-from .real_lazy import RealLazyField, RLF, ComplexLazyField, CLF
+from sage.rings.real_lazy import RealLazyField, RLF, ComplexLazyField, CLF
 
 from sage.rings.real_arb import RealBallField, RBF
 
 # Polynomial Rings and Polynomial Quotient Rings
-from .polynomial.all import *
+from sage.rings.polynomial.all import *
 
 
 # Algebraic numbers
-from .qqbar import (AlgebraicRealField, AA,
+from sage.rings.qqbar import (AlgebraicRealField, AA,
                    AlgebraicReal,
                    AlgebraicField, QQbar,
                    AlgebraicNumber,
                    number_field_elements_from_algebraics)
-from .universal_cyclotomic_field import UniversalCyclotomicField, E
+from sage.rings.universal_cyclotomic_field import UniversalCyclotomicField, E
 
 # Intervals
-from .real_mpfi import (RealIntervalField,
+from sage.rings.real_mpfi import (RealIntervalField,
                        RIF,
                        RealInterval)
 
 # Complex numbers
-from .complex_mpfr import ComplexField
-from .complex_mpfr import create_ComplexNumber as ComplexNumber
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.complex_mpfr import create_ComplexNumber as ComplexNumber
 Complexes = ComplexField
-from .complex_interval_field import ComplexIntervalField
-from .complex_interval import (create_ComplexIntervalFieldElement as ComplexIntervalFieldElement)
+from sage.rings.complex_interval_field import ComplexIntervalField
+from sage.rings.complex_interval import (create_ComplexIntervalFieldElement as ComplexIntervalFieldElement)
 
-from .complex_double import ComplexDoubleField, ComplexDoubleElement, CDF
+from sage.rings.complex_double import ComplexDoubleField, ComplexDoubleElement, CDF
 
-from .complex_mpc import MPComplexField
+from sage.rings.complex_mpc import MPComplexField
 
 from sage.rings.complex_arb import ComplexBallField, CBF
 
 lazy_import("sage.rings.imaginary_unit", "I")
 
 # Power series rings
-from .power_series_ring import PowerSeriesRing
+from sage.rings.power_series_ring import PowerSeriesRing
 
 # Laurent series ring in one variable
-from .laurent_series_ring import LaurentSeriesRing
+from sage.rings.laurent_series_ring import LaurentSeriesRing
 
 # Lazy Laurent series ring
 lazy_import('sage.rings.lazy_series_ring', ['LazyLaurentSeriesRing', 'LazyPowerSeriesRing',
                                             'LazySymmetricFunctions', 'LazyDirichletSeriesRing'])
 
 # Tate algebras
-from .tate_algebra import TateAlgebra
+from sage.rings.tate_algebra import TateAlgebra
 
 # Puiseux series ring
-from .puiseux_series_ring import PuiseuxSeriesRing
+from sage.rings.puiseux_series_ring import PuiseuxSeriesRing
 
 # Pseudo-ring of PARI objects.
-from .pari_ring import PariRing, Pari
+from sage.rings.pari_ring import PariRing, Pari
 
 # Big-oh notation
-from .big_oh import O
+from sage.rings.big_oh import O
 
 # Fraction field
-from .fraction_field import FractionField
+from sage.rings.fraction_field import FractionField
 Frac = FractionField
 
 # Localization
-from .localization import Localization
+from sage.rings.localization import Localization
 
 # c-finite sequences
-from .cfinite_sequence import CFiniteSequence, CFiniteSequences
+from sage.rings.cfinite_sequence import CFiniteSequence, CFiniteSequences
 
-from .bernoulli_mod_p import bernoulli_mod_p, bernoulli_mod_p_single
+from sage.rings.bernoulli_mod_p import bernoulli_mod_p, bernoulli_mod_p_single
 
-from .monomials import monomials
+from sage.rings.monomials import monomials
 
-from .cc import CC
-from .cif import CIF
+from sage.rings.cc import CC
+from sage.rings.cif import CIF
 
 # invariant theory
-from .invariants.all import *
+from sage.rings.invariants.all import *
 
-from .fast_arith import prime_range
+from sage.rings.fast_arith import prime_range
 
 # continued fractions
 from sage.rings.continued_fraction import (continued_fraction,
                                            continued_fraction_list)
 
 # asymptotic ring
-from .asymptotic.all import *
+from sage.rings.asymptotic.all import *
 
 # Register classes in numbers abc
-from . import numbers_abc
+from sage.rings import numbers_abc

src/sage/rings/all__sagemath_categories.py

@@ -1,6 +1,6 @@
 # Ring base classes
-from .ring import Ring
-
+from sage.rings.ring import Ring
 # Ideals
-from .ideal import Ideal
+from sage.rings.ideal import Ideal
+
 ideal = Ideal

src/sage/rings/big_oh.py

@@ -11,6 +11,7 @@
 
 from sage.arith.misc import factor
 from sage.misc.lazy_import import lazy_import
+
 lazy_import('sage.rings.padics.factory', ['Qp', 'Zp'])
 lazy_import('sage.rings.padics.padic_generic_element', 'pAdicGenericElement')
 from sage.rings.polynomial.polynomial_element import Polynomial
@@ -25,10 +26,12 @@
 except ImportError:
     PuiseuxSeries = ()
 
-from . import power_series_ring_element
-from . import integer
-from . import rational
-from . import multi_power_series_ring_element
+from sage.rings import (
+    integer,
+    multi_power_series_ring_element,
+    power_series_ring_element,
+    rational,
+)
 
 
 def O(*x, **kwds):

src/sage/rings/cc.py

@@ -1,3 +1,3 @@
-from .complex_mpfr import ComplexField
+from sage.rings.complex_mpfr import ComplexField
 
 CC = ComplexField()

src/sage/rings/cif.py

@@ -1,3 +1,3 @@
-from .complex_interval_field import ComplexIntervalField
+from sage.rings.complex_interval_field import ComplexIntervalField
 
 CIF = ComplexIntervalField()

src/sage/rings/complex_conversion.pyx

@@ -1,5 +1,5 @@
-from .complex_double cimport ComplexDoubleElement
-from .complex_mpfr cimport ComplexNumber
+from sage.rings.complex_double cimport ComplexDoubleElement
+from sage.rings.complex_mpfr cimport ComplexNumber
 from sage.libs.mpfr cimport mpfr_get_d, MPFR_RNDN
 from sage.libs.gsl.complex cimport GSL_SET_COMPLEX
 

src/sage/rings/complex_double.pyx

@@ -105,10 +105,10 @@ complex_double_element_gamma = None
 complex_double_element_gamma_inc = None
 complex_double_element_zeta = None
 
-from .complex_conversion cimport CCtoCDF
+from sage.rings.complex_conversion cimport CCtoCDF
 
-from .real_double cimport RealDoubleElement, double_repr
-from .real_double import RDF
+from sage.rings.real_double cimport RealDoubleElement, double_repr
+from sage.rings.real_double import RDF
 from sage.rings.integer_ring import ZZ
 from sage.structure.richcmp cimport rich_to_bool
 

src/sage/rings/complex_interval.pxd

@@ -2,7 +2,7 @@ from sage.libs.mpfr.types cimport mpfr_prec_t
 from sage.libs.mpfi.types cimport mpfi_t
 
 cimport sage.structure.element
-from .real_mpfi cimport RealIntervalFieldElement, RealIntervalField_class
+from sage.rings.real_mpfi cimport RealIntervalFieldElement, RealIntervalField_class
 
 
 cdef class ComplexIntervalFieldElement(sage.structure.element.FieldElement):

src/sage/rings/complex_interval.pyx

@@ -66,12 +66,12 @@ from sage.arith.constants cimport LOG_TEN_TWO_PLUS_EPSILON
 
 from sage.structure.element cimport FieldElement
 from sage.structure.parent cimport Parent
-from .complex_mpfr cimport ComplexNumber
+from sage.rings.complex_mpfr cimport ComplexNumber
 from sage.rings.integer cimport Integer
 cimport sage.rings.real_mpfi as real_mpfi
-from .real_mpfr cimport RealNumber
-from .convert.mpfi cimport mpfi_set_sage
-from .infinity import infinity
+from sage.rings.real_mpfr cimport RealNumber
+from sage.rings.convert.mpfi cimport mpfi_set_sage
+from sage.rings.infinity import infinity
 
 
 def is_ComplexIntervalFieldElement(x):

src/sage/rings/complex_interval_field.py

@@ -36,18 +36,17 @@
 # ****************************************************************************
 
 
-from sage.structure.parent import Parent
-from .integer_ring import ZZ
-from .rational_field import QQ
-from .ring import Field
-import sage.rings.abc
-from . import integer
-from . import complex_interval
 import weakref
-from .real_mpfi import RealIntervalField, RealIntervalField_class
-from .complex_mpfr import ComplexField
-from sage.misc.cachefunc import cached_method
 
+import sage.rings.abc
+from sage.misc.cachefunc import cached_method
+from sage.rings import complex_interval, integer
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.real_mpfi import RealIntervalField, RealIntervalField_class
+from sage.rings.ring import Field
+from sage.structure.parent import Parent
 
 cache = {}
 def ComplexIntervalField(prec=53, names=None):

src/sage/rings/complex_mpc.pyx

@@ -59,7 +59,7 @@ EXAMPLES::
 # ****************************************************************************
 
 import re
-from . import real_mpfr
+from sage.rings import real_mpfr
 import weakref
 from cpython.object cimport Py_NE
 
@@ -74,13 +74,13 @@ from sage.structure.richcmp cimport rich_to_bool
 from sage.categories.map cimport Map
 from sage.libs.pari.all import pari
 
-from .integer cimport Integer
-from .complex_mpfr cimport ComplexNumber
-from .complex_mpfr import ComplexField_class
+from sage.rings.integer cimport Integer
+from sage.rings.complex_mpfr cimport ComplexNumber
+from sage.rings.complex_mpfr import ComplexField_class
 
 from sage.misc.randstate cimport randstate, current_randstate
-from .real_mpfr cimport RealField_class, RealNumber
-from .real_mpfr import mpfr_prec_min, mpfr_prec_max
+from sage.rings.real_mpfr cimport RealField_class, RealNumber
+from sage.rings.real_mpfr import mpfr_prec_min, mpfr_prec_max
 from sage.structure.richcmp cimport rich_to_bool, richcmp
 from sage.categories.fields import Fields
 

src/sage/rings/complex_mpfr.pxd

@@ -1,7 +1,7 @@
 from sage.libs.mpfr.types cimport mpfr_t, mpfr_prec_t
 
 cimport sage.structure.element
-from .real_mpfr cimport RealNumber
+from sage.rings.real_mpfr cimport RealNumber
 
 cdef class ComplexNumber(sage.structure.element.FieldElement):
     cdef mpfr_t __re

src/sage/rings/complex_mpfr.pyx

@@ -46,11 +46,11 @@ from sage.misc.sage_eval import sage_eval
 
 import sage.rings.abc
 from sage.arith.constants cimport LOG_TEN_TWO_PLUS_EPSILON
-from . import infinity
-from .integer cimport Integer
+from sage.rings import infinity
+from sage.rings.integer cimport Integer
 
-from .complex_double cimport ComplexDoubleElement
-from .real_mpfr cimport RealNumber
+from sage.rings.complex_double cimport ComplexDoubleElement
+from sage.rings.real_mpfr cimport RealNumber
 from sage.libs.gsl.complex cimport *
 
 from sage.libs.mpmath.utils cimport mpfr_to_mpfval