sage.rings.polynomial: Update from #35095

Author: Matthias Koeppe

src/sage/rings/polynomial/multi_polynomial_ring_base.pyx

@@ -22,7 +22,6 @@ from sage.arith.misc import binomial
 
 from sage.rings.integer_ring import ZZ
 
-from .polydict import PolyDict
 from . import polynomial_ring
 from .term_order import TermOrder
 from .polynomial_ring_constructor import (PolynomialRing,

src/sage/rings/polynomial/ore_polynomial_ring.py

@@ -23,6 +23,7 @@
 
 from sage.misc.prandom import randint
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.rings.infinity import Infinity
 from sage.structure.category_object import normalize_names
 
@@ -36,11 +37,12 @@
 from sage.rings.ring import _Fields
 
 from sage.categories.morphism import Morphism
-from sage.rings.derivation import RingDerivation
 
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.polynomial.ore_polynomial_element import OrePolynomialBaseringInjection
 
+lazy_import('sage.rings.derivation', 'RingDerivation')
+
 WORKING_CENTER_MAX_TRIES = 1000
 
 

src/sage/rings/polynomial/polynomial_ring.py

@@ -171,7 +171,6 @@
 import sage.rings.abc
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.finite_rings.element_base import FiniteRingElement
-from sage.rings.power_series_ring_element import PowerSeries
 from sage.rings.polynomial.polynomial_singular_interface import PolynomialRing_singular_repr
 from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
 from sage.rings.power_series_ring_element import PowerSeries
@@ -180,11 +179,6 @@
 
 import sage.interfaces.abc
 
-try:
-    from sage.interfaces.singular import SingularElement
-except ImportError:
-    SingularElement = ()
-
 
 def is_PolynomialRing(x):
     """
@@ -2088,8 +2082,8 @@ def _element_class():
                 return element_class
             if sparse:
                 from sage.rings.polynomial.polynomial_element_generic import Polynomial_generic_sparse_field
-                element_class = Polynomial_generic_sparse_field
-            elif isinstance(base_ring, rational_field.RationalField):
+                return Polynomial_generic_sparse_field
+            if isinstance(base_ring, rational_field.RationalField):
                 try:
                     from sage.rings.polynomial.polynomial_rational_flint import Polynomial_rational_flint
                     return Polynomial_rational_flint

src/sage/rings/polynomial/polynomial_singular_interface.py

@@ -167,7 +167,7 @@ def _do_singular_init_(singular, base_ring, char, _vars, order):
 
             return singular(f"std(ideal({base_ring.__minpoly}))", type='qring'), None
 
-    elif isinstance(base_ring, sage.rings.function_field.function_field_rational.RationalFunctionField) \
+    elif isinstance(base_ring, RationalFunctionField) \
             and base_ring.constant_field().is_prime_field():
         gen = str(base_ring.gen())
         return make_ring(f"({base_ring.characteristic()},{gen})"), None