sage.rings: Modularization fixes for singular

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -260,7 +260,6 @@
     from sage.libs.singular.standard_options import \
         libsingular_gb_standard_options
 except ImportError:
-    singular_default = None
     singular_gb_standard_options = libsingular_gb_standard_options = MethodDecorator
 
 try:
@@ -616,7 +615,7 @@ class MPolynomialIdeal_singular_repr(
     An ideal in a multivariate polynomial ring, which has an
     underlying Singular ring associated to it.
     """
-    def _singular_(self, singular=singular_default):
+    def _singular_(self, singular=None):
         """
         Return Singular ideal corresponding to this ideal.
 
@@ -629,6 +628,8 @@ def _singular_(self, singular=singular_default):
             x^3+y,
             y
         """
+        if singular is None:
+            singular = singular_default
         try:
             self.ring()._singular_(singular).set_ring()
             I = self.__singular
@@ -674,7 +675,7 @@ def _groebner_strategy(self):
 
         return GroebnerStrategy(MPolynomialIdeal(self.ring(), self.groebner_basis()))
 
-    def plot(self, singular=singular_default):
+    def plot(self, singular=None):
         r"""
         If you somehow manage to install surf, perhaps you can use
         this function to implicitly plot the real zero locus of this
@@ -723,6 +724,8 @@ def plot(self, singular=singular_default):
             raise TypeError("base ring must have characteristic 0")
         if not self.is_principal():
             raise TypeError("self must be principal")
+        if singular is None:
+            singular = singular_default
         singular.lib('surf')
         I = singular(self)
         I.plot()
@@ -1027,7 +1030,7 @@ def is_prime(self, **kwds):
     @handle_AA_and_QQbar
     @singular_gb_standard_options
     @libsingular_gb_standard_options
-    def triangular_decomposition(self, algorithm=None, singular=singular_default):
+    def triangular_decomposition(self, algorithm=None, singular=None):
         """
         Decompose zero-dimensional ideal ``self`` into triangular
         sets.
@@ -1163,7 +1166,7 @@ def triangular_decomposition(self, algorithm=None, singular=singular_default):
 
     @require_field
     @handle_AA_and_QQbar
-    def dimension(self, singular=singular_default):
+    def dimension(self, singular=None):
         """
         The dimension of the ring modulo this ideal.
 
@@ -1478,7 +1481,7 @@ def _groebner_basis_singular(self, algorithm="groebner", *args, **kwds):
         return S
 
     @cached_method
-    def _groebner_basis_singular_raw(self, algorithm="groebner", singular=singular_default, *args, **kwds):
+    def _groebner_basis_singular_raw(self, algorithm="groebner", singular=None, *args, **kwds):
         r"""
         Return a Groebner basis in Singular format.
 
@@ -1501,6 +1504,8 @@ def _groebner_basis_singular_raw(self, algorithm="groebner", singular=singular_d
              b*d^4 - b + d^5 - d, b*c - b*d + c^2*d^4 + c*d - 2*d^2,
              b^2 + 2*b*d + d^2, a + b + c + d]
         """
+        if singular is None:
+            singular = singular_default
         #try:
         #    return self.__gb_singular
         #except AttributeError:
@@ -1790,7 +1795,7 @@ def radical(self):
 
     @require_field
     @libsingular_gb_standard_options
-    def integral_closure(self, p=0, r=True, singular=singular_default):
+    def integral_closure(self, p=0, r=True, singular=None):
         """
         Let `I` = ``self``.
 
@@ -2025,7 +2030,7 @@ def interreduced_basis(self):
     @cached_method
     @handle_AA_and_QQbar
     @singular_gb_standard_options
-    def basis_is_groebner(self, singular=singular_default):
+    def basis_is_groebner(self, singular=None):
         r"""
         Return ``True`` if the generators of this ideal
         (``self.gens()``) form a Groebner basis.
@@ -2152,6 +2157,8 @@ def basis_is_groebner(self, singular=singular_default):
                 return False
             return True
         except TypeError:
+            if singular is None:
+                singular = singular_default
             R._singular_().set_ring()
             F = singular( tuple(self.gens()), "module" )
             LTF = singular( [f.lt() for f in self.gens()] , "module" )
@@ -2168,7 +2175,7 @@ def basis_is_groebner(self, singular=singular_default):
     @handle_AA_and_QQbar
     @singular_gb_standard_options
     @libsingular_gb_standard_options
-    def transformed_basis(self, algorithm="gwalk", other_ring=None, singular=singular_default):
+    def transformed_basis(self, algorithm="gwalk", other_ring=None, singular=None):
         """
         Return a lex or ``other_ring`` Groebner Basis for this ideal.
 
@@ -2260,6 +2267,8 @@ def transformed_basis(self, algorithm="gwalk", other_ring=None, singular=singula
                 nR = R.change_ring(order='lex')
             else:
                 nR = other_ring
+            if singular is None:
+                singular = singular_default
             Rs = singular(R)
             Is = singular(I)
             Is.attrib('isSB',1)
@@ -3139,9 +3148,9 @@ def hilbert_numerator(self, grading=None, algorithm='sage'):
 
         TESTS::
 
-            sage: I.hilbert_numerator() == I.hilbert_numerator(algorithm='singular')                                    # needs sage.libs.flint
+            sage: I.hilbert_numerator() == I.hilbert_numerator(algorithm='singular')    # needs sage.libs.flint
             True
-            sage: J.hilbert_numerator() == J.hilbert_numerator(algorithm='singular')                                    # needs sage.libs.flint
+            sage: J.hilbert_numerator() == J.hilbert_numerator(algorithm='singular')    # needs sage.libs.flint
             True
             sage: J.hilbert_numerator(grading=(10,3)) == J.hilbert_numerator(grading=(10,3), algorithm='singular')      # needs sage.libs.flint
             True
@@ -3279,7 +3288,7 @@ def _normal_basis_libsingular(self, degree, weights=None):
     @require_field
     @handle_AA_and_QQbar
     def normal_basis(self, degree=None, algorithm='libsingular',
-                     singular=singular_default):
+                     singular=None):
         """
         Return a vector space basis of the quotient ring of this ideal.
 
@@ -3360,6 +3369,8 @@ def normal_basis(self, degree=None, algorithm='libsingular',
         if algorithm == 'libsingular':
             return self._normal_basis_libsingular(degree, weights=weights)
         else:
+            if singular is None:
+                singular = singular_default
             gb = self.groebner_basis()
             R = self.ring()
             if degree is None:

src/sage/rings/polynomial/polynomial_modn_dense_ntl.pyx

@@ -47,8 +47,6 @@ from sage.rings.fraction_field_element import FractionFieldElement
 
 from sage.rings.infinity import infinity
 
-from sage.interfaces.singular import singular as singular_default
-
 from sage.structure.element import canonical_coercion, coerce_binop, have_same_parent
 
 from sage.libs.ntl.types cimport NTL_SP_BOUND
@@ -360,7 +358,7 @@ cdef class Polynomial_dense_mod_n(Polynomial):
         self._poly = ZZ_pX(v, self.parent().modulus())
 
     # Polynomial_singular_repr stuff, copied due to lack of multiple inheritance
-    def _singular_(self, singular=singular_default, force=False):
+    def _singular_(self, singular=None, force=False):
         self.parent()._singular_(singular, force=force).set_ring()  # this is expensive
         if self.__singular is not None:
             try:
@@ -371,7 +369,7 @@ cdef class Polynomial_dense_mod_n(Polynomial):
                 pass
         return self._singular_init_(singular)
 
-    def _singular_init_(self, singular=singular_default, force=False):
+    def _singular_init_(self, singular=None, force=False):
         self.parent()._singular_(singular, force=force).set_ring()  # this is expensive
         self.__singular = singular(str(self))
         return self.__singular

src/sage/rings/polynomial/polynomial_rational_flint.pyx

@@ -39,8 +39,6 @@ from sage.libs.flint.fmpq_poly_sage cimport *
 from sage.libs.gmp.mpz cimport *
 from sage.libs.gmp.mpq cimport *
 
-from sage.interfaces.singular import singular as singular_default
-
 from cypari2.gen import Gen as pari_gen
 
 from sage.rings.complex_arb cimport ComplexBall
@@ -330,7 +328,7 @@ cdef class Polynomial_rational_flint(Polynomial):
         fmpq_poly_set(res._poly, self._poly)
         return res
 
-    def _singular_(self, singular=singular_default):
+    def _singular_(self, singular=None):
         """
         Return a Singular representation of ``self``.
 
@@ -345,6 +343,8 @@ cdef class Polynomial_rational_flint(Polynomial):
             sage: singular(f)                                                           # needs sage.libs.singular
             3*x^2+2*x+5
         """
+        if singular is None:
+            from sage.interfaces.singular import singular
         self._parent._singular_(singular).set_ring()  # Expensive!
         return singular(self._singular_init_())
 

src/sage/rings/polynomial/polynomial_singular_interface.py

@@ -41,11 +41,6 @@
 import sage.rings.abc
 import sage.rings.number_field as number_field
 
-try:
-    from sage.interfaces.singular import singular
-except ImportError:
-    singular = None
-
 from sage.rings.rational_field import is_RationalField
 from sage.rings.function_field.function_field_rational import RationalFunctionField
 from sage.rings.finite_rings.finite_field_base import FiniteField
@@ -54,6 +49,7 @@
 
 import sage.rings.finite_rings.finite_field_constructor
 
+
 def _do_singular_init_(singular, base_ring, char, _vars, order):
     r"""
     Implementation of :meth:`PolynomialRing_singular_repr._singular_init_`.
@@ -183,7 +179,7 @@ class PolynomialRing_singular_repr:
     polynomial rings which support conversion from and to Singular
     rings.
     """
-    def _singular_(self, singular=singular):
+    def _singular_(self, singular=None):
         r"""
         Return a Singular ring for this polynomial ring.
 
@@ -331,9 +327,11 @@ def _singular_(self, singular=singular):
             - Singular represents precision of floating point numbers base 10
               while Sage represents floating point precision base 2.
         """
+        if singular is None:
+            from sage.interfaces.singular import singular
         try:
             R = self.__singular
-            if not (R.parent() is singular):
+            if R.parent() is not singular:
                 raise ValueError
             R._check_valid()
             if self.base_ring() is ZZ or self.base_ring().is_prime_field():
@@ -348,7 +346,7 @@ def _singular_(self, singular=singular):
         except (AttributeError, ValueError):
             return self._singular_init_(singular)
 
-    def _singular_init_(self, singular=singular):
+    def _singular_init_(self, singular=None):
         """
         Return a newly created Singular ring matching this ring.
 
@@ -374,6 +372,9 @@ def _singular_init_(self, singular=singular):
             _vars = str(self.gens())
             order = self.term_order().singular_str()
 
+        if singular is None:
+            from sage.interfaces.singular import singular
+
         self.__singular, self.__minpoly = _do_singular_init_(singular, self.base_ring(), self.characteristic(), _vars, order)
 
         return self.__singular
@@ -460,14 +461,18 @@ class Polynomial_singular_repr:
     Due to the incompatibility of Python extension classes and multiple inheritance,
     this just defers to module-level functions.
     """
-    def _singular_(self, singular=singular):
+    def _singular_(self, singular=None):
+        if singular is None:
+            from sage.interfaces.singular import singular
         return _singular_func(self, singular)
 
-    def _singular_init_func(self, singular=singular):
+    def _singular_init_func(self, singular=None):
+        if singular is None:
+            from sage.interfaces.singular import singular
         return _singular_init_func(self, singular)
 
 
-def _singular_func(self, singular=singular):
+def _singular_func(self, singular=None):
     """
     Return Singular polynomial matching this polynomial.
 
@@ -500,8 +505,9 @@ def _singular_func(self, singular=singular):
         sage: R(h^20) == f^20
         True
     """
+    if singular is None:
+        from sage.interfaces.singular import singular
     self.parent()._singular_(singular).set_ring()  # this is expensive
-
     try:
         self.__singular._check_valid()
         if self.__singular.parent() is singular:
@@ -511,13 +517,15 @@ def _singular_func(self, singular=singular):
     return _singular_init_func(self, singular)
 
 
-def _singular_init_func(self, singular=singular):
+def _singular_init_func(self, singular=None):
     """
     Return corresponding Singular polynomial but enforce that a new
     instance is created in the Singular interpreter.
 
     Use ``self._singular_()`` instead.
     """
+    if singular is None:
+        from sage.interfaces.singular import singular
     self.parent()._singular_(singular).set_ring()  # this is expensive
     self.__singular = singular(str(self))
     return self.__singular

src/sage/rings/polynomial/polynomial_template.pxi

@@ -24,8 +24,6 @@ from sage.libs.pari.all import pari_gen
 
 import operator
 
-from sage.interfaces.singular import singular as singular_default
-
 def make_element(parent, args):
     return parent(*args)
 
@@ -816,7 +814,7 @@ cdef class Polynomial_template(Polynomial):
         celement_truncate(&r.x, &self.x, n, (<Polynomial_template>self)._cparent)
         return r
 
-    def _singular_(self, singular=singular_default):
+    def _singular_(self, singular=None):
         r"""
         Return Singular representation of this polynomial
 
@@ -831,5 +829,8 @@ cdef class Polynomial_template(Polynomial):
             sage: singular(f)                                                           # needs sage.libs.singular
             3*x^2+2*x-2
         """
+        if singular is None:
+            from sage.interfaces.singular import singular
+
         self.parent()._singular_(singular).set_ring()  # this is expensive
         return singular(self._singular_init_())

src/sage/rings/quotient_ring_element.py

@@ -801,7 +801,7 @@ def monomials(self):
         """
         return [self.__class__(self.parent(), m) for m in self.__rep.monomials()]
 
-    def _singular_(self, singular=singular_default):
+    def _singular_(self, singular=None):
         """
         Return Singular representation of self.
 
@@ -844,7 +844,9 @@ def _singular_(self, singular=singular_default):
             a - 2/3*b
         """
         if singular is None:
-            raise ImportError("could not import singular")
+            singular = singular_default
+            if singular is None:
+                raise ImportError("could not import singular")
         return self.__rep._singular_(singular)
 
     def _magma_init_(self, magma):