sage.geometry: Remove module-level imports of AA, RR, PolynomialRing

Author: Matthias Koeppe

src/sage/geometry/convex_set.py

@@ -855,10 +855,14 @@ def _test_contains(self, tester=None, **options):
                 tester.assertEqual(contains_space_point, self.contains(ambient_point))
             tester.assertEqual(contains_space_point, self.contains(space_coords))
             if space.base_ring().is_exact():
-                from sage.rings.qqbar import AA
-                ext_space = self.ambient_vector_space(AA)
-                ext_space_point = ext_space(space_point)
-                tester.assertEqual(contains_space_point, self.contains(ext_space_point))
+                try:
+                    from sage.rings.qqbar import AA
+                except ImportError:
+                    pass
+                else:
+                    ext_space = self.ambient_vector_space(AA)
+                    ext_space_point = ext_space(space_point)
+                    tester.assertEqual(contains_space_point, self.contains(ext_space_point))
             try:
                 from sage.symbolic.ring import SR
                 symbolic_space = self.ambient_vector_space(SR)

src/sage/geometry/polyhedron/backend_normaliz.py

@@ -30,8 +30,8 @@
 lazy_import('PyNormaliz', ['NmzResult', 'NmzCompute', 'NmzCone', 'NmzConeCopy'],
             feature=sage.features.normaliz.PyNormaliz())
 
-from sage.rings.all import ZZ, QQ, QQbar
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
 from sage.arith.functions import LCM_list
 from sage.misc.functional import denominator
 from sage.matrix.constructor import vector
@@ -1082,10 +1082,11 @@ def _number_field_triple(normaliz_field):
             sage: Pn._number_field_triple(QuadraticField(5))  # optional - sage.rings.number_field
             ['a^2 - 5', 'a', '[2.236067977499789 +/- 8.06e-16]']
         """
-        from sage.rings.real_arb import RealBallField
         R = normaliz_field
         if R is QQ:
             return None
+        from sage.rings.real_arb import RealBallField
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         emb = RealBallField(53)(R.gen(0))
         gen = 'a'
         R_a = PolynomialRing(QQ, gen)
@@ -2336,7 +2337,7 @@ class functions.
             ((t^4 + 3*t^3 + 8*t^2 + 3*t + 1)/(t + 1), (3*t^3 + 2*t^2 + 3*t)/(t + 1))
         """
         from sage.groups.conjugacy_classes import ConjugacyClassGAP
-        from sage.rings.all import CyclotomicField
+        from sage.rings.all import CyclotomicField, QQbar
         from sage.matrix.all import MatrixSpace
         from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         from sage.matrix.special import identity_matrix

src/sage/geometry/polyhedron/base.py

@@ -51,6 +51,7 @@
 
 from sage.misc.cachefunc import cached_method
 
+import sage.rings.abc
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.matrix.constructor import matrix

src/sage/geometry/polyhedron/base0.py

@@ -1366,13 +1366,9 @@ def cdd_Hrepresentation(self):
         try:
             cdd_type = self._cdd_type
         except AttributeError:
-            from sage.rings.integer_ring import ZZ
-            from sage.rings.rational_field import QQ
-            from sage.rings.real_double import RDF
-
             if self.base_ring() is ZZ or self.base_ring() is QQ:
                 cdd_type = 'rational'
-            elif self.base_ring() is RDF:
+            elif isinstance(self.base_ring(), sage.rings.abc.RealDoubleField):
                 cdd_type = 'real'
             else:
                 raise TypeError('the base ring must be ZZ, QQ, or RDF')
@@ -1431,13 +1427,9 @@ def cdd_Vrepresentation(self):
         try:
             cdd_type = self._cdd_type
         except AttributeError:
-            from sage.rings.integer_ring import ZZ
-            from sage.rings.rational_field import QQ
-            from sage.rings.real_double import RDF
-
             if self.base_ring() is ZZ or self.base_ring() is QQ:
                 cdd_type = 'rational'
-            elif self.base_ring() is RDF:
+            elif isinstance(self.base_ring(), sage.rings.abc.RealDoubleField):
                 cdd_type = 'real'
             else:
                 raise TypeError('the base ring must be ZZ, QQ, or RDF')

src/sage/geometry/polyhedron/base6.py

@@ -36,7 +36,6 @@
 from sage.modules.vector_space_morphism import linear_transformation
 from sage.matrix.constructor import matrix
 from sage.modules.free_module_element import vector
-from sage.rings.qqbar import AA
 from sage.geometry.convex_set import AffineHullProjectionData
 from .base5 import Polyhedron_base5
 
@@ -967,6 +966,7 @@ def _affine_hull_projection(self, *,
             except TypeError:
                 if not extend:
                     raise ValueError('the base ring needs to be extended; try with "extend=True"')
+                from sage.rings.qqbar import AA
                 M = matrix(AA, M)
                 A = M.gram_schmidt(orthonormal=orthonormal)[0]
                 if minimal:
@@ -1445,21 +1445,25 @@ def _test_affine_hull_projection(self, tester=None, verbose=False, **options):
             # Avoid very long doctests.
             return
 
-        data_sets = [None]*4
-        data_sets[0] = self.affine_hull_projection(return_all_data=True)
+        try:
+            from sage.rings.qqbar import AA
+        except ImportError:
+            AA = None
+
+        data_sets = []
+        data_sets.append(self.affine_hull_projection(return_all_data=True))
         if self.is_compact():
-            data_sets[1] = self.affine_hull_projection(return_all_data=True,
-                                                       orthogonal=True,
-                                                       extend=True)
-            data_sets[2] = self.affine_hull_projection(return_all_data=True,
-                                                       orthonormal=True,
-                                                       extend=True)
-            data_sets[3] = self.affine_hull_projection(return_all_data=True,
-                                                       orthonormal=True,
-                                                       extend=True,
-                                                       minimal=True)
-        else:
-            data_sets = data_sets[:1]
+            data_sets.append(self.affine_hull_projection(return_all_data=True,
+                                                         orthogonal=True,
+                                                         extend=True))
+            if AA is not None:
+                data_sets.append(self.affine_hull_projection(return_all_data=True,
+                                                             orthonormal=True,
+                                                             extend=True))
+                data_sets.append(self.affine_hull_projection(return_all_data=True,
+                                                             orthonormal=True,
+                                                             extend=True,
+                                                             minimal=True))
 
         for i, data in enumerate(data_sets):
             if verbose:

src/sage/geometry/polyhedron/base7.py

@@ -37,7 +37,6 @@
 from sage.modules.free_module_element import vector
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.rings.qqbar import AA
 from .base6 import Polyhedron_base6
 
 class Polyhedron_base7(Polyhedron_base6):
@@ -714,6 +713,7 @@ def volume(self, measure='ambient', engine='auto', **kwds):
             if Adet.is_square():
                 sqrt_Adet = Adet.sqrt()
             else:
+                from sage.rings.qqbar import AA
                 sqrt_Adet = AA(Adet).sqrt()
                 scaled_volume = AA(scaled_volume)
             return scaled_volume / sqrt_Adet
@@ -910,6 +910,7 @@ def integrate(self, function, measure='ambient', **kwds):
                 A = affine_hull_data.projection_linear_map.matrix()
                 Adet = (A.transpose() * A).det()
                 try:
+                    from sage.rings.qqbar import AA
                     Adet = AA.coerce(Adet)
                 except TypeError:
                     pass

src/sage/geometry/voronoi_diagram.py

@@ -15,7 +15,6 @@
 
 from sage.structure.sage_object import SageObject
 from sage.geometry.polyhedron.constructor import Polyhedron
-from sage.rings.qqbar import AA
 from sage.rings.rational_field import QQ
 import sage.rings.abc
 from sage.geometry.triangulation.point_configuration import PointConfiguration
@@ -103,7 +102,7 @@ def __init__(self, points):
         self._n = self._points.n_points()
         if not self._n or self._points.base_ring().is_subring(QQ):
             self._base_ring = QQ
-        elif isinstance(self._points.base_ring(), sage.rings.abc.RealDoubleField) or self._points.base_ring() == AA:
+        elif isinstance(self._points.base_ring(), (sage.rings.abc.RealDoubleField, sage.rings.abc.AlgebraicRealField)):
             self._base_ring = self._points.base_ring()
         elif isinstance(self._points.base_ring(), sage.rings.abc.RealField):
             from sage.rings.real_double import RDF