Trac #22273: py3 compatible imports in sage/rings

URL: https://trac.sagemath.org/22273
Reported by: aapitzsch
Ticket author(s): André Apitzsch
Reviewer(s): Frédéric Chapoton

src/sage/rings/complex_double.pyx

@@ -61,6 +61,7 @@ AUTHORS:
 #  the License, or (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 import operator
@@ -88,16 +89,16 @@ from sage.structure.coerce cimport is_numpy_type
 from sage.libs.cypari2.gen cimport Gen as pari_gen
 from sage.libs.cypari2.convert cimport new_gen_from_double, new_t_COMPLEX_from_double
 
-import complex_number
+from . import complex_number
 
-import complex_field
-cdef CC = complex_field.ComplexField()
+from .complex_field import ComplexField
+cdef CC = ComplexField()
 
-import real_mpfr
-cdef RR = real_mpfr.RealField()
+from .real_mpfr import RealField
+cdef RR = RealField()
 
 from .real_double cimport RealDoubleElement, double_repr, double_str
-from real_double import RDF
+from .real_double import RDF
 from sage.rings.integer_ring import ZZ
 
 
@@ -205,8 +206,8 @@ cdef class ComplexDoubleField_class(sage.rings.ring.Field):
             sage: CDF.characteristic()
             0
         """
-        import integer
-        return integer.Integer(0)
+        from .integer import Integer
+        return Integer(0)
 
     def random_element(self, double xmin=-1, double xmax=1, double ymin=-1, double ymax=1):
         """
@@ -400,12 +401,10 @@ cdef class ComplexDoubleField_class(sage.rings.ring.Field):
         """
         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, RealField_class
-        from complex_field import ComplexField, ComplexField_class
-        CC = ComplexField()
-        from complex_number import CCtoCDF
+        from .rational_field import QQ
+        from .real_lazy import RLF
+        from .real_mpfr import RR, RealField_class
+        from .complex_field import ComplexField_class
         if S is ZZ or S is QQ or S is RDF or S is RLF:
             return FloatToCDF(S)
         if isinstance(S, RealField_class):
@@ -424,9 +423,9 @@ cdef class ComplexDoubleField_class(sage.rings.ring.Field):
         elif RR.has_coerce_map_from(S):
             return FloatToCDF(RR) * RR._internal_coerce_map_from(S)
         elif isinstance(S, ComplexField_class) and S.prec() >= 53:
-            return CCtoCDF(S, self)
+            return complex_number.CCtoCDF(S, self)
         elif CC.has_coerce_map_from(S):
-            return CCtoCDF(CC, self) * CC._internal_coerce_map_from(S)
+            return complex_number.CCtoCDF(CC, self) * CC._internal_coerce_map_from(S)
 
     def _magma_init_(self, magma):
         r"""
@@ -475,7 +474,6 @@ cdef class ComplexDoubleField_class(sage.rings.ring.Field):
         if prec == 53:
             return self
         else:
-            from complex_field import ComplexField
             return ComplexField(prec)
 
 
@@ -529,8 +527,7 @@ cdef class ComplexDoubleField_class(sage.rings.ring.Field):
             sage: CDF.real_double_field()
             Real Double Field
         """
-        import real_double
-        return real_double.RDF
+        return RDF
 
     def pi(self):
         r"""
@@ -595,7 +592,7 @@ cdef class ComplexDoubleField_class(sage.rings.ring.Field):
             ...
             ValueError: n must be a positive integer
         """
-        from integer import Integer
+        from .integer import Integer
         try:
            n = Integer(n)
         except TypeError:
@@ -2314,8 +2311,8 @@ cdef class ComplexDoubleElement(FieldElement):
         """
         if self._complex.dat[1] == 0:
             if self._complex.dat[0] == 0:
-                import infinity
-                return infinity.unsigned_infinity
+                from .infinity import unsigned_infinity
+                return unsigned_infinity
             try:
                 from sage.rings.all import Integer, CC
                 if Integer(self._complex.dat[0]) < 0:
@@ -2354,8 +2351,8 @@ cdef class ComplexDoubleElement(FieldElement):
             Infinity
         """
         if self._complex.dat[0] == 1 and self._complex.dat[1] == 0:
-            import infinity
-            return infinity.unsigned_infinity
+            from .infinity import unsigned_infinity
+            return unsigned_infinity
         return pari_to_cdf(self._pari_().zeta())
 
     def algdep(self, long n):
@@ -2386,8 +2383,8 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: CDF(1,5).algdep(2)
             x^2 - 2*x + 26
         """
-        from polynomial.polynomial_ring_constructor import PolynomialRing
-        from integer_ring import ZZ
+        from .polynomial.polynomial_ring_constructor import PolynomialRing
+        from .integer_ring import ZZ
         R = PolynomialRing(ZZ ,'x')
         return R(self._pari_().algdep(n))
 

src/sage/rings/complex_number.pyx

@@ -22,6 +22,7 @@ AUTHORS:
 #  the License, or (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 import math
@@ -34,8 +35,8 @@ from .complex_double cimport ComplexDoubleElement
 from .real_mpfr cimport RealNumber
 
 import sage.misc.misc
-import integer
-import infinity
+import sage.rings.integer as integer
+import sage.rings.infinity as infinity
 
 from sage.libs.mpmath.utils cimport mpfr_to_mpfval
 from sage.rings.integer_ring import ZZ
@@ -2092,7 +2093,7 @@ 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 .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):
@@ -2356,7 +2357,6 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
             Infinity
         """
         if mpfr_zero_p(self.__im) and mpfr_cmp_ui(self.__re, 1) == 0:
-            import infinity
             return infinity.unsigned_infinity
         return self._parent(self._pari_().zeta())
 

src/sage/rings/finite_rings/element_givaro.pyx

@@ -49,6 +49,7 @@ AUTHORS:
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 include "cysignals/signals.pxi"
@@ -58,13 +59,13 @@ from sage.libs.cypari2.paridecl cimport *
 from sage.misc.randstate cimport randstate, current_randstate
 from sage.rings.finite_rings.finite_field_base cimport FiniteField
 from sage.rings.ring cimport Ring
-from element_ext_pari import FiniteField_ext_pariElement
+from .element_ext_pari import FiniteField_ext_pariElement
 from .element_pari_ffelt cimport FiniteFieldElement_pari_ffelt
 from sage.structure.sage_object cimport SageObject, richcmp
 from sage.structure.element cimport Element, ModuleElement, RingElement
 import operator
 import sage.arith.all
-import finite_field_constructor as finite_field
+import sage.rings.finite_rings.finite_field_constructor as finite_field
 
 import sage.interfaces.gap
 from sage.libs.pari.all import pari

src/sage/rings/finite_rings/hom_finite_field.pyx

@@ -100,7 +100,7 @@ AUTHOR:
 #
 #                  http://www.gnu.org/licenses/
 #****************************************************************************
-
+from __future__ import absolute_import
 
 from sage.rings.integer cimport Integer
 
@@ -610,7 +610,7 @@ 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 .hom_prime_finite_field import FiniteFieldHomomorphism_prime
             f = FiniteFieldHomomorphism_prime(Hom(k, self.domain()))
         else:
             k = FiniteField(self.domain().characteristic()**self._degree_fixed,

src/sage/rings/finite_rings/hom_prime_finite_field.pyx

@@ -23,7 +23,7 @@ AUTHOR:
 #
 #                  http://www.gnu.org/licenses/
 #****************************************************************************
-
+from __future__ import absolute_import
 
 from sage.rings.integer cimport Integer
 

src/sage/rings/integer_ring.pyx

@@ -42,6 +42,7 @@ other types will also coerce to the integers, when it makes sense.
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 include "sage/ext/cdefs.pxi"
@@ -68,10 +69,10 @@ from sage.misc.misc_c import prod
 from sage.misc.randstate cimport randstate, current_randstate, SAGE_RAND_MAX
 from sage.libs.ntl.convert cimport ZZ_to_mpz
 
-cimport integer
-cimport rational
+cimport sage.rings.integer as integer
+cimport sage.rings.rational as rational
 
-import ring
+from . import ring
 
 arith = None
 cdef void late_import():

src/sage/rings/number_field/number_field_element.pyx

@@ -27,6 +27,7 @@ AUTHORS:
 #  the License, or (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 import operator
@@ -54,8 +55,7 @@ import sage.rings.integer
 
 from sage.rings.real_mpfi cimport RealIntervalFieldElement
 
-cimport number_field_base
-import number_field
+cimport sage.rings.number_field.number_field_base as number_field_base
 
 from sage.rings.integer_ring cimport IntegerRing_class
 from sage.rings.rational cimport Rational
@@ -366,8 +366,9 @@ cdef class NumberFieldElement(FieldElement):
           quadratic field elements)
         """
         if check:
-            if not isinstance(self.number_field(), number_field.NumberField_cyclotomic) \
-                   or not isinstance(new_parent, number_field.NumberField_cyclotomic):
+            from .number_field import NumberField_cyclotomic
+            if not isinstance(self.number_field(), NumberField_cyclotomic) \
+                   or not isinstance(new_parent, NumberField_cyclotomic):
                 raise TypeError("The field and the new parent field must both be cyclotomic fields.")
 
         if rel == 0:
@@ -1900,7 +1901,7 @@ cdef class NumberFieldElement(FieldElement):
         if R.is_field():
             return R.one()
 
-        from order import is_NumberFieldOrder
+        from .order import is_NumberFieldOrder
         if not is_NumberFieldOrder(R) or not R.is_maximal():
             raise NotImplementedError("gcd() for %r is not implemented" % R)
 
@@ -2544,7 +2545,8 @@ cdef class NumberFieldElement(FieldElement):
             raise ValueError("need a real or complex embedding to convert "
                              "a non rational element of a number field "
                              "into an algebraic number")
-        emb = number_field.refine_embedding(emb, infinity)
+        from .number_field import refine_embedding
+        emb = refine_embedding(emb, infinity)
         return parent(emb(self))
 
     def _symbolic_(self, SR):
@@ -2642,7 +2644,8 @@ cdef class NumberFieldElement(FieldElement):
         if embedding is None:
             raise TypeError("an embedding into RR or CC must be specified")
 
-        if isinstance(K, number_field.NumberField_cyclotomic):
+        from .number_field import NumberField_cyclotomic
+        if isinstance(K, NumberField_cyclotomic):
             # solution by radicals may be difficult, but we have a closed form
             from sage.all import exp, I, pi, ComplexField, RR
             CC = ComplexField(53)
@@ -2651,8 +2654,9 @@ cdef class NumberFieldElement(FieldElement):
             gen_image = exp(k*two_pi_i/K._n())
             return self.polynomial()(gen_image)
         else:
+            from .number_field import refine_embedding
             # Convert the embedding to an embedding into AA or QQbar
-            embedding = number_field.refine_embedding(embedding, infinity)
+            embedding = refine_embedding(embedding, infinity)
             a = embedding(self).radical_expression()
             if a.parent() == SR:
                 return a
@@ -2929,6 +2933,7 @@ cdef class NumberFieldElement(FieldElement):
 
         """
         if self.__multiplicative_order is None:
+            from .number_field import NumberField_cyclotomic
             if self.is_rational():
                 if self.is_one():
                     self.__multiplicative_order = ZZ(1)
@@ -2938,7 +2943,7 @@ cdef class NumberFieldElement(FieldElement):
                     self.__multiplicative_order = sage.rings.infinity.infinity
             elif not (self.is_integral() and self.norm().is_one()):
                 self.__multiplicative_order = sage.rings.infinity.infinity
-            elif isinstance(self.number_field(), number_field.NumberField_cyclotomic):
+            elif isinstance(self.number_field(), NumberField_cyclotomic):
                 t = self.number_field()._multiplicative_order_table()
                 f = self.polynomial()
                 if f in t:
@@ -3392,11 +3397,12 @@ cdef class NumberFieldElement(FieldElement):
             sage: foo.matrix(R) == matrix(1,1,[foo])
             True
         """
-        import sage.matrix.matrix_space
+        from sage.matrix.matrix_space import MatrixSpace
         if base is self.parent():
-            return sage.matrix.matrix_space.MatrixSpace(base,1)([self])
+            return MatrixSpace(base,1)([self])
         if base is not None and base is not self.base_ring():
-            if number_field.is_NumberField(base):
+            from sage.rings.number_field.number_field_base import is_NumberField
+            if is_NumberField(base):
                 return self._matrix_over_base(base)
             else:
                 return self._matrix_over_base_morphism(base)
@@ -3413,7 +3419,7 @@ cdef class NumberFieldElement(FieldElement):
             for n in range(d-1):
                 cur = cur * X
                 v += cur.list()
-            M = sage.matrix.matrix_space.MatrixSpace(K.base_ring(), d)
+            M = MatrixSpace(K.base_ring(), d)
             self.__matrix = M(v)
             self.__matrix.set_immutable()
         return self.__matrix
@@ -3453,7 +3459,7 @@ cdef class NumberFieldElement(FieldElement):
             sage: [L(6).valuation(P) for P in L.primes_above(3)]
             [2, 2]
         """
-        from number_field_ideal import is_NumberFieldIdeal
+        from .number_field_ideal import is_NumberFieldIdeal
         if not is_NumberFieldIdeal(P):
             if is_NumberFieldElement(P):
                 P = self.number_field().fractional_ideal(P)