Trac #32599: sage.structure, sage.sets: Remove hard dependencies on t…

…he symbolic ring / polynomial rings

(partially cherry-picked from #32432)

URL: https://trac.sagemath.org/32599
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Travis Scrimshaw

src/sage/sets/condition_set.py

@@ -19,9 +19,12 @@
 from sage.categories.enumerated_sets import EnumeratedSets
 from sage.misc.cachefunc import cached_method
 from sage.misc.misc import _stable_uniq
-from sage.symbolic.expression import is_Expression
-from sage.symbolic.callable import is_CallableSymbolicExpression
-from sage.symbolic.ring import SR
+
+try:
+    from sage.symbolic.expression import is_Expression
+    from sage.symbolic.callable import is_CallableSymbolicExpression
+except ImportError:
+    is_CallableSymbolicExpression = is_Expression = lambda x: False
 
 from .set import Set, Set_base, Set_boolean_operators, Set_add_sub_operators
 
@@ -169,6 +172,7 @@ def __classcall_private__(cls, universe, *predicates, vars=None, names=None, cat
                 if names is None:
                     raise TypeError('use callable symbolic expressions or provide variable names')
                 if vars is None:
+                    from sage.symbolic.ring import SR
                     vars = tuple(SR.var(name) for name in names)
                 callable_symbolic_predicates.append(predicate.function(*vars))
             else:
@@ -291,6 +295,7 @@ def arguments(self):
             sage: args[0].parent()
             Symbolic Ring
         """
+        from sage.symbolic.ring import SR
         return SR.var(self.variable_names())
 
     def _element_constructor_(self, *args, **kwds):

src/sage/structure/sequence.py

@@ -213,15 +213,19 @@ def Sequence(x, universe=None, check=True, immutable=False, cr=False, cr_str=Non
         ...
         TypeError: unable to convert a to an element of Integer Ring
     """
-    from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
-
-    if isinstance(x, Sequence_generic) and universe is None:
-        universe = x.universe()
-        x = list(x)
-
-    if isinstance(x, MPolynomialIdeal) and universe is None:
-        universe = x.ring()
-        x = x.gens()
+    if universe is None:
+        if isinstance(x, Sequence_generic):
+            universe = x.universe()
+            x = list(x)
+        else:
+            try:
+                from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
+            except ImportError:
+                pass
+            else:
+                if isinstance(x, MPolynomialIdeal):
+                    universe = x.ring()
+                    x = x.gens()
 
     if universe is None:
         orig_x = x
@@ -248,15 +252,18 @@ def Sequence(x, universe=None, check=True, immutable=False, cr=False, cr_str=Non
             if universe is None:   # no type errors raised.
                 universe = sage.structure.element.parent(x[len(x)-1])
 
-    from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence
-    from sage.rings.polynomial.pbori.pbori import BooleanMonomialMonoid
-    from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
-    from sage.rings.quotient_ring import is_QuotientRing
-
-    if is_MPolynomialRing(universe) or isinstance(universe, BooleanMonomialMonoid) or (is_QuotientRing(universe) and is_MPolynomialRing(universe.cover_ring())):
-        return PolynomialSequence(x, universe, immutable=immutable, cr=cr, cr_str=cr_str)
+    try:
+        from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence
+        from sage.rings.polynomial.pbori.pbori import BooleanMonomialMonoid
+        from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+        from sage.rings.quotient_ring import is_QuotientRing
+    except ImportError:
+        pass
     else:
-        return Sequence_generic(x, universe, check, immutable, cr, cr_str, use_sage_types)
+        if is_MPolynomialRing(universe) or isinstance(universe, BooleanMonomialMonoid) or (is_QuotientRing(universe) and is_MPolynomialRing(universe.cover_ring())):
+            return PolynomialSequence(x, universe, immutable=immutable, cr=cr, cr_str=cr_str)
+
+    return Sequence_generic(x, universe, check, immutable, cr, cr_str, use_sage_types)
 
 
 class Sequence_generic(sage.structure.sage_object.SageObject, list):