Trac #32870: sage.rings: Modularization changes

split out from #32432.

URL: https://trac.sagemath.org/32870
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe, Jonathan Kliem
Reviewer(s): Jonathan Kliem, Matthias Koeppe

src/sage/algebras/free_algebra_quotient.py

@@ -59,7 +59,7 @@
 # ****************************************************************************
 
 from sage.modules.free_module import FreeModule
-from sage.algebras.algebra import Algebra
+from sage.rings.ring import Algebra
 from sage.algebras.free_algebra import is_FreeAlgebra
 from sage.algebras.free_algebra_quotient_element import FreeAlgebraQuotientElement
 from sage.structure.unique_representation import UniqueRepresentation

src/sage/combinat/species/series.py

@@ -40,7 +40,7 @@
 from sage.misc.repr import repr_lincomb
 from sage.misc.cachefunc import cached_method
 
-from sage.algebras.algebra import Algebra
+from sage.rings.ring import Algebra
 from sage.structure.parent import Parent
 from sage.categories.all import Rings
 from sage.structure.element import Element, parent, AlgebraElement

src/sage/modular/hecke/algebra.py

@@ -27,11 +27,11 @@
 # ****************************************************************************
 
 import sage.rings.infinity
-import sage.rings.commutative_algebra
 from sage.matrix.constructor import matrix
 from sage.arith.all import lcm, gcd
 from sage.misc.latex import latex
 from sage.matrix.matrix_space import MatrixSpace
+from sage.rings.ring import CommutativeAlgebra
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.structure.element import Element
@@ -103,7 +103,7 @@ def _heckebasis(M):
 
 
 @richcmp_method
-class HeckeAlgebra_base(CachedRepresentation, sage.rings.commutative_algebra.CommutativeAlgebra):
+class HeckeAlgebra_base(CachedRepresentation, CommutativeAlgebra):
     """
     Base class for algebras of Hecke operators on a fixed Hecke module.
 
@@ -179,7 +179,7 @@ def __init__(self, M):
         if not module.is_HeckeModule(M):
             raise TypeError("M (=%s) must be a HeckeModule" % M)
         self.__M = M
-        sage.rings.commutative_algebra.CommutativeAlgebra.__init__(self, M.base_ring())
+        CommutativeAlgebra.__init__(self, M.base_ring())
 
     def _an_element_impl(self):
         r"""

src/sage/rings/commutative_algebra.py

@@ -25,7 +25,9 @@ def is_CommutativeAlgebra(x):
 
     EXAMPLES::
 
-        sage: sage.rings.commutative_algebra.is_CommutativeAlgebra(sage.rings.ring.CommutativeAlgebra(ZZ))
+        sage: from sage.rings.commutative_algebra import is_CommutativeAlgebra
+        sage: from sage.rings.ring import CommutativeAlgebra
+        sage: is_CommutativeAlgebra(CommutativeAlgebra(ZZ))
         True
     """
     return isinstance(x, CommutativeAlgebra)

src/sage/rings/finite_rings/finite_field_constructor.py

@@ -176,16 +176,17 @@
 
 from sage.rings.integer import Integer
 
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-
 # the import below is just a redirection
 from sage.rings.finite_rings.finite_field_base import is_FiniteField
 assert is_FiniteField  # just to silent pyflakes
 
-# We don't late import this because this means trouble with the Givaro library
-# On a Macbook Pro OSX 10.5.8, this manifests as a Bus Error on exiting Sage.
-# TODO: figure out why
-from .finite_field_givaro import FiniteField_givaro
+try:
+    # We don't late import this because this means trouble with the Givaro library
+    # On a Macbook Pro OSX 10.5.8, this manifests as a Bus Error on exiting Sage.
+    # TODO: figure out why
+    from .finite_field_givaro import FiniteField_givaro
+except ImportError:
+    FiniteField_givaro = None
 
 from sage.structure.factory import UniqueFactory
 
@@ -633,6 +634,7 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
             # optimization which we also need to avoid an infinite loop:
             # a modulus of None is a shorthand for x-1.
             if modulus is not None or impl != 'modn':
+                from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
                 R = PolynomialRing(FiniteField(p), 'x')
                 if modulus is None:
                     modulus = R.irreducible_element(n)

src/sage/rings/polynomial/polynomial_ring.py

@@ -147,8 +147,6 @@
 import sage.categories as categories
 from sage.categories.morphism import IdentityMorphism
 
-import sage.algebras.algebra
-import sage.rings.commutative_algebra as commutative_algebra
 import sage.rings.ring as ring
 from sage.structure.element import is_RingElement
 import sage.rings.polynomial.polynomial_element_generic as polynomial_element_generic
@@ -226,7 +224,7 @@ def is_PolynomialRing(x):
 
 #########################################################################################
 
-class PolynomialRing_general(sage.algebras.algebra.Algebra):
+class PolynomialRing_general(ring.Algebra):
     """
     Univariate polynomial ring over a ring.
     """
@@ -300,7 +298,7 @@ def __init__(self, base_ring, name=None, sparse=False, element_class=None, categ
         self.Element = self._polynomial_class
         self.__cyclopoly_cache = {}
         self._has_singular = False
-        sage.algebras.algebra.Algebra.__init__(self, base_ring, names=name, normalize=True, category=category)
+        ring.Algebra.__init__(self, base_ring, names=name, normalize=True, category=category)
         self._populate_coercion_lists_(convert_method_name='_polynomial_')
 
     def __reduce__(self):
@@ -1662,7 +1660,7 @@ def monics( self, of_degree = None, max_degree = None ):
         raise ValueError("you should pass exactly one of of_degree and max_degree")
 
 
-class PolynomialRing_commutative(PolynomialRing_general, commutative_algebra.CommutativeAlgebra):
+class PolynomialRing_commutative(PolynomialRing_general, ring.CommutativeAlgebra):
     """
     Univariate polynomial ring over a commutative ring.
     """

src/sage/rings/quotient_ring.py

@@ -110,15 +110,22 @@
 
 import sage.misc.latex as latex
 from . import ring, ideal, quotient_ring_element
-import sage.rings.polynomial.multi_polynomial_ideal
 from sage.structure.category_object import normalize_names
 from sage.structure.richcmp import richcmp_method, richcmp
 import sage.structure.parent_gens
-from sage.interfaces.singular import singular as singular_default, is_SingularElement
 from sage.misc.cachefunc import cached_method
 from sage.categories.rings import Rings
 from sage.categories.commutative_rings import CommutativeRings
 
+
+MPolynomialIdeal = None
+try:
+    from sage.interfaces.singular import singular as singular_default, is_SingularElement
+except ImportError:
+    is_singularElement = lambda x : False
+    singular_default = None
+
+
 def QuotientRing(R, I, names=None, **kwds):
     r"""
     Creates a quotient ring of the ring `R` by the twosided ideal `I`.
@@ -959,7 +966,11 @@ def ideal(self, *gens, **kwds):
             gens = [gens]
         if 'coerce' in kwds and kwds['coerce']:
             gens = [self(x) for x in gens]  # this will even coerce from singular ideals correctly!
-        return sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal(self, gens, **kwds)
+
+        global MPolynomialIdeal
+        if MPolynomialIdeal is None:
+            from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
+        return MPolynomialIdeal(self, gens, **kwds)
 
     def _element_constructor_(self, x, coerce=True):
         """
@@ -1006,7 +1017,7 @@ def _element_constructor_(self, x, coerce=True):
                 return x
             x = x.lift()
         if is_SingularElement(x):
-            #self._singular_().set_ring()
+            # self._singular_().set_ring()
             x = self.element_class(self, x.sage_poly(self.cover_ring()))
             return x
         if coerce:
@@ -1171,7 +1182,6 @@ def gen(self, i=0):
         """
         return self(self.__R.gen(i))
 
-
     def _singular_(self, singular=singular_default):
         """
         Returns the Singular quotient ring of ``self`` if the base ring is
@@ -1203,6 +1213,9 @@ def _singular_(self, singular=singular_default):
             // quotient ring from ideal
             _[1]=x2+y2
         """
+        if singular is None:
+            raise ImportError("could not import singular")
+
         try:
             Q = self.__singular
             if not (Q.parent() is singular):
@@ -1212,7 +1225,7 @@ def _singular_(self, singular=singular_default):
         except (AttributeError, ValueError):
             return self._singular_init_(singular)
 
-    def _singular_init_(self,singular=singular_default):
+    def _singular_init_(self, singular=None):
         """
         Returns a newly created Singular quotient ring matching ``self`` if
         the base ring is coercible to Singular.
@@ -1229,6 +1242,8 @@ def _singular_init_(self,singular=singular_default):
             sage: parent(T)
             Singular
         """
+        if singular is None:
+            from sage.interfaces.singular import singular
         self.__R._singular_().set_ring()
         self.__singular = singular("%s"%self.__I._singular_().name(),"qring")
         return self.__singular

src/sage/rings/quotient_ring_element.py

@@ -18,7 +18,12 @@
 
 from sage.structure.element import RingElement
 from sage.structure.richcmp import richcmp, rich_to_bool
-from sage.interfaces.singular import singular as singular_default
+
+
+try:
+    from sage.interfaces.singular import singular as singular_default
+except ImportError:
+    singular_default = None
 
 
 class QuotientRingElement(RingElement):
@@ -797,6 +802,8 @@ def _singular_(self, singular=singular_default):
             sage: S((a-2/3*b)._singular_())
             a - 2/3*b
         """
+        if singular is None:
+            raise ImportError("could not import singular")
         return self.__rep._singular_(singular)
 
     def _magma_init_(self, magma):

src/sage/rings/rational.pyx

@@ -65,7 +65,6 @@ from cysignals.signals cimport sig_on, sig_off
 import operator
 import fractions
 
-from sage.misc.mathml import mathml
 from sage.arith.long cimport pyobject_to_long, integer_check_long_py
 from sage.cpython.string cimport char_to_str, str_to_bytes
 
@@ -1093,6 +1092,7 @@ cdef class Rational(sage.structure.element.FieldElement):
         if self.denom() == 1:
             return '<mn>%s</mn>'%(self.numer())
         else:
+            from sage.misc.mathml import mathml
             t = ''
             if self < 0:
                 t = t + '<mo>-</mo>'