sagemathgh-36666: Replace relative imports by absolute ones in `sage.…

…{algebras,arith,categories,cpython,data_structures,misc,modular,rings,sat,symbolic}`

    
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Final chunk of the cherry-pick from sagemath#35095 for sagemath#36228, see also
sagemath#36572 (comment)

This PR overlaps with sagemath#36572, sagemath#36588, sagemath#36589, but it does not touch
`.all*` files (no changes there are needed for sagemath#36228), thus avoiding
conflicts with sagemath#35095 (see also
sagemath#36524 (comment))
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### ⌛ Dependencies

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URL: sagemath#36666
Reported by: Matthias Köppe
Reviewer(s): David Coudert, John H. Palmieri

src/sage/algebras/quatalg/quaternion_algebra_cython.pyx

@@ -35,7 +35,7 @@ from sage.matrix.matrix_space import MatrixSpace
 from sage.matrix.matrix_integer_dense cimport Matrix_integer_dense
 from sage.matrix.matrix_rational_dense cimport Matrix_rational_dense
 
-from .quaternion_algebra_element cimport QuaternionAlgebraElement_rational_field
+from sage.algebras.quatalg.quaternion_algebra_element cimport QuaternionAlgebraElement_rational_field
 
 from sage.libs.gmp.mpz cimport mpz_t, mpz_lcm, mpz_init, mpz_set, mpz_clear, mpz_init_set, mpz_mul, mpz_fdiv_q, mpz_cmp_si
 

src/sage/categories/action.pyx

@@ -91,7 +91,7 @@ cdef class Action(Functor):
       :class:`Action` itself, but other classes may use it
     """
     def __init__(self, G, S, is_left=True, op=None):
-        from .groupoid import Groupoid
+        from sage.categories.groupoid import Groupoid
         Functor.__init__(self, Groupoid(G), category(S))
         self.G = G
         self.US = ref(S)

src/sage/categories/morphism.pyx

@@ -467,7 +467,7 @@ cdef class CallMorphism(Morphism):
 cdef class IdentityMorphism(Morphism):
 
     def __init__(self, parent):
-        from .homset import Homset, Hom
+        from sage.categories.homset import Homset, Hom
         if not isinstance(parent, Homset):
             parent = Hom(parent, parent)
         Morphism.__init__(self, parent)

src/sage/cpython/getattr.pyx

@@ -4,7 +4,7 @@ Variants of getattr()
 
 from cpython.object cimport PyObject, PyTypeObject, Py_TYPE, descrgetfunc
 
-from .string cimport bytes_to_str
+from sage.cpython.string cimport bytes_to_str
 
 cdef extern from "Python.h":
     r"""

src/sage/cpython/wrapperdescr.pyx

@@ -30,7 +30,7 @@ Pure Python classes have normal methods, not slot wrappers::
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from .string import bytes_to_str
+from sage.cpython.string import bytes_to_str
 
 
 def wrapperdescr_call(slotwrapper, self, *args, **kwds):

src/sage/misc/cachefunc.pxd

@@ -1,4 +1,4 @@
-from .function_mangling cimport ArgumentFixer
+from sage.misc.function_mangling cimport ArgumentFixer
 
 cpdef dict_key(o) noexcept
 cpdef cache_key(o) noexcept

src/sage/misc/lazy_import.pyx

@@ -66,7 +66,7 @@ import os
 import pickle
 from warnings import warn
 import inspect
-from . import sageinspect
+from sage.misc import sageinspect
 
 
 # LazyImport.__repr__ uses try... except FeatureNotPresentError.
@@ -1137,7 +1137,7 @@ def save_cache_file():
         sage: sage.misc.lazy_import.save_cache_file()
     """
     from sage.misc.temporary_file import atomic_write
-    from .lazy_import_cache import get_cache_file
+    from sage.misc.lazy_import_cache import get_cache_file
 
     global star_imports
     if star_imports is None:
@@ -1180,7 +1180,7 @@ def get_star_imports(module_name):
     """
     global star_imports
     if star_imports is None:
-        from .lazy_import_cache import get_cache_file
+        from sage.misc.lazy_import_cache import get_cache_file
         star_imports = {}
         try:
             with open(get_cache_file(), "rb") as cache_file:

src/sage/misc/persist.pyx

@@ -42,7 +42,7 @@ import bz2
 comp = zlib
 comp_other = bz2
 
-from .sage_unittest import TestSuite
+from sage.misc.sage_unittest import TestSuite
 
 
 # We define two global dictionaries `already_pickled` and
@@ -1237,7 +1237,7 @@ def db(name):
 
     The database directory is ``$HOME/.sage/db``.
     """
-    from .misc import SAGE_DB
+    from sage.misc.misc import SAGE_DB
     return load('%s/%s'%(SAGE_DB,name))
 
 
@@ -1250,5 +1250,5 @@ def db_save(x, name=None):
     try:
         x.db(name)
     except AttributeError:
-        from .misc import SAGE_DB
+        from sage.misc.misc import SAGE_DB
         save(x, '%s/%s'%(SAGE_DB,name))

src/sage/misc/sage_timeit_class.pyx

@@ -6,7 +6,7 @@ The ``timeit`` command
 This uses the function :func:`~sage.misc.sage_timeit.sage_timeit`.
 """
 
-from . import sage_timeit
+from sage.misc import sage_timeit
 
 
 class SageTimeit:

src/sage/modular/modsym/heilbronn.pyx

@@ -34,11 +34,11 @@ cdef extern from "<math.h>":
     float roundf(float x)
 
 cimport sage.modular.modsym.p1list as p1list
-from . import p1list
+from sage.modular.modsym import p1list
 cdef p1list.export export
 export = p1list.export()
 
-from .apply cimport Apply
+from sage.modular.modsym.apply cimport Apply
 cdef Apply PolyApply= Apply()
 
 from sage.matrix.matrix_rational_dense cimport Matrix_rational_dense

src/sage/modular/pollack_stevens/dist.pyx

@@ -44,7 +44,7 @@ from sage.rings.infinity import Infinity
 
 #from sage.libs.flint.ulong_extras cimport *
 
-from .sigma0 import Sigma0
+from sage.modular.pollack_stevens.sigma0 import Sigma0
 
 cdef long overflow = 1 << (4 * sizeof(long) - 1)
 cdef long underflow = -overflow

src/sage/rings/complex_double.pyx

@@ -213,7 +213,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
             sage: CDF.characteristic()
             0
         """
-        from .integer import Integer
+        from sage.rings.integer import Integer
         return Integer(0)
 
     def random_element(self, double xmin=-1, double xmax=1, double ymin=-1, double ymax=1):
@@ -351,7 +351,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
             sage: CDF((1,2)) # indirect doctest
             1.0 + 2.0*I
         """
-        from . import complex_mpfr
+        from sage.rings import complex_mpfr
         if isinstance(x, ComplexDoubleElement):
             return x
         elif isinstance(x, tuple):
@@ -417,10 +417,10 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
         """
         if S is int or S is float:
             return FloatToCDF(S)
-        from .rational_field import QQ
-        from .real_lazy import RLF
-        from .real_mpfr import RR
-        from .cc import CC
+        from sage.rings.rational_field import QQ
+        from sage.rings.real_lazy import RLF
+        from sage.rings.real_mpfr import RR
+        from sage.rings.cc import CC
 
         if S is ZZ or S is QQ or S is RDF or S is RLF:
             return FloatToCDF(S)
@@ -502,7 +502,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
         if prec == 53:
             return self
         else:
-            from .complex_mpfr import ComplexField
+            from sage.rings.complex_mpfr import ComplexField
             return ComplexField(prec)
 
 
@@ -621,7 +621,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
             ...
             ValueError: n must be a positive integer
         """
-        from .integer import Integer
+        from sage.rings.integer import Integer
         try:
             n = Integer(n)
         except TypeError:
@@ -968,7 +968,7 @@ cdef class ComplexDoubleElement(FieldElement):
             True
         """
         # Sending to another computer algebra system is slow anyway, right?
-        from .complex_mpfr import ComplexField
+        from sage.rings.complex_mpfr import ComplexField
         return ComplexField()(self)._interface_init_(I)
 
     def _mathematica_init_(self):
@@ -980,7 +980,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: mathematica(CDF(1e-25, 1e25))  # optional - mathematica
             1.*^-25 + 1.*^25*I
         """
-        from .complex_mpfr import ComplexField
+        from sage.rings.complex_mpfr import ComplexField
         return ComplexField()(self)._mathematica_init_()
 
     def _maxima_init_(self, I=None):
@@ -995,7 +995,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: CDF(.5 + I)._maxima_init_()                                           # needs sage.symbolic
             '0.50000000000000000 + 1.0000000000000000*%i'
         """
-        from .complex_mpfr import ComplexField
+        from sage.rings.complex_mpfr import ComplexField
         return ComplexField()(self)._maxima_init_(I)
 
     def _sympy_(self):
@@ -1097,7 +1097,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: format(CDF(0, 0), '+#.4')
             '+0.000'
         """
-        from .complex_mpfr import _format_complex_number
+        from sage.rings.complex_mpfr import _format_complex_number
         return _format_complex_number(GSL_REAL(self._complex),
                                                      GSL_IMAG(self._complex),
                                                      format_spec)
@@ -2382,12 +2382,12 @@ cdef class ComplexDoubleElement(FieldElement):
         """
         if not GSL_IMAG(self._complex):
             if GSL_REAL(self._complex) == 0:
-                from .infinity import unsigned_infinity
+                from sage.rings.infinity import unsigned_infinity
                 return unsigned_infinity
             try:
-                from .integer import Integer
+                from sage.rings.integer import Integer
                 if Integer(GSL_REAL(self._complex)) < 0:
-                    from .cc import CC
+                    from sage.rings.cc import CC
                     return CC(self).gamma()
             except TypeError:
                 pass
@@ -2429,7 +2429,7 @@ cdef class ComplexDoubleElement(FieldElement):
             Infinity
         """
         if GSL_REAL(self._complex) == 1 and GSL_IMAG(self._complex) == 0:
-            from .infinity import unsigned_infinity
+            from sage.rings.infinity import unsigned_infinity
             return unsigned_infinity
 
         global complex_double_element_zeta

src/sage/rings/complex_interval.pyx

@@ -1914,7 +1914,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
             0.500000000000000? + 3.39927010637040?*I
         """
         if not self:
-            from .real_mpfi import RIF
+            from sage.rings.real_mpfi import RIF
             return RIF(0).log()
         re = abs(self).log()
         im = self.argument()
@@ -2291,6 +2291,6 @@ def create_ComplexIntervalFieldElement(s_real, s_imag=None, int pad=0, min_prec=
     #else:
     #    bits = max(int(math.log(base,2)*len(s_imag)),int(math.log(base,2)*len(s_imag)))
 
-    from .complex_interval_field import ComplexIntervalField
+    from sage.rings.complex_interval_field import ComplexIntervalField
     C = ComplexIntervalField(prec=max(bits+pad, min_prec))
     return ComplexIntervalFieldElement(C, s_real, s_imag)

src/sage/rings/complex_mpc.pyx

@@ -105,8 +105,8 @@ def late_import():
         import sage.rings.qqbar
         AA = sage.rings.qqbar.AA
         QQbar = sage.rings.qqbar.QQbar
-        from .real_lazy import CLF, RLF
-        from .complex_double import CDF
+        from sage.rings.real_lazy import CLF, RLF
+        from sage.rings.complex_double import CDF
 
 _mpfr_rounding_modes = ['RNDN', 'RNDZ', 'RNDU', 'RNDD']
 

src/sage/rings/complex_mpfr.pyx

@@ -102,8 +102,8 @@ def late_import():
         QQbar = sage.rings.qqbar.QQbar
         import sage.symbolic.ring
         SR = sage.symbolic.ring.SR
-        from .real_lazy import CLF, RLF
-        from .complex_double import CDF
+        from sage.rings.real_lazy import CLF, RLF
+        from sage.rings.complex_double import CDF
 
 cdef object numpy_complex_interface = {'typestr': '=c16'}
 cdef object numpy_object_interface = {'typestr': '|O'}
@@ -372,7 +372,7 @@ class ComplexField_class(sage.rings.abc.ComplexField):
         try:
             return self.__real_field
         except AttributeError:
-            from .real_mpfr import RealField
+            from sage.rings.real_mpfr import RealField
             self.__real_field = RealField(self._prec)
             return self.__real_field
 
@@ -2931,7 +2931,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
         if base is None:
             return ComplexNumber(self._parent, rho.log(), theta)
         else:
-            from .real_mpfr import RealField
+            from sage.rings.real_mpfr import RealField
             return ComplexNumber(self._parent, rho.log()/RealNumber(RealField(self.prec()),base).log(), theta/RealNumber(RealField(self.prec()),base).log())
 
     def additive_order(self):

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -1045,7 +1045,7 @@ cdef class FiniteField(Field):
             pass
 
         from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-        from .finite_field_constructor import GF
+        from sage.rings.finite_rings.finite_field_constructor import GF
         R = PolynomialRing(GF(self.characteristic()), 'x')
         self._modulus = R((-1,1))  # Polynomial x - 1
         return self._modulus
@@ -1288,7 +1288,7 @@ cdef class FiniteField(Field):
             inclusion_map = self.coerce_map_from(base)
 
         from sage.matrix.constructor import matrix
-        from .maps_finite_field import (
+        from sage.rings.finite_rings.maps_finite_field import (
             MorphismVectorSpaceToFiniteField, MorphismFiniteFieldToVectorSpace)
 
         E = self
@@ -1379,7 +1379,7 @@ cdef class FiniteField(Field):
         if isinstance(R, FiniteField):
             if R is self:
                 return True
-            from .residue_field import ResidueField_generic
+            from sage.rings.finite_rings.residue_field import ResidueField_generic
             if isinstance(R, ResidueField_generic):
                 return False
             if R.characteristic() == self.characteristic():
@@ -1543,7 +1543,7 @@ cdef class FiniteField(Field):
             sage: L(u).minpoly() == u.minpoly()
             True
         """
-        from .finite_field_constructor import GF
+        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:
@@ -1719,7 +1719,7 @@ cdef class FiniteField(Field):
             sage: GF(3^8, 'a').subfield(4)
             Finite Field in a4 of size 3^4
         """
-        from .finite_field_constructor import GF
+        from sage.rings.finite_rings.finite_field_constructor import GF
         p = self.characteristic()
         n = self.degree()
         if not n % degree == 0:
@@ -1926,7 +1926,7 @@ cdef class FiniteField(Field):
             sage: GF(next_prime(2^16, 2), 'a').is_conway()
             False
         """
-        from .conway_polynomials import conway_polynomial, exists_conway_polynomial
+        from sage.rings.finite_rings.conway_polynomials import conway_polynomial, exists_conway_polynomial
         p = self.characteristic()
         n = self.degree()
         return (exists_conway_polynomial(p, n)

src/sage/rings/finite_rings/hom_finite_field.pyx

@@ -763,7 +763,7 @@ cdef class FrobeniusEndomorphism_finite_field(FrobeniusEndomorphism_generic):
         """
         if self._degree_fixed == 1:
             k = FiniteField(self.domain().characteristic())
-            from .hom_prime_finite_field import FiniteFieldHomomorphism_prime
+            from sage.rings.finite_rings.hom_prime_finite_field import FiniteFieldHomomorphism_prime
             f = FiniteFieldHomomorphism_prime(Hom(k, self.domain()))
         else:
             k = FiniteField(self.domain().characteristic()**self._degree_fixed,