Trac #19436: fixup of 19431: convert asymptotic expansion to the symb…

…olic ring

#19431 changed `SymbolicRing._element_constructor_` which was not
needed. A method `_symbolic_` suffices in the !AsymptoticRing. An
additional parameter `R` in `.symbolic_expression` will be needed to
make it work.

URL: http://trac.sagemath.org/19436
Reported by: dkrenn
Ticket author(s): Daniel Krenn
Reviewer(s): Clemens Heuberger

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -2032,10 +2032,16 @@ def _substitute_(self, rules):
             substitute_raise_exception(self, e)
 
 
-    def symbolic_expression(self):
+    def symbolic_expression(self, R=None):
         r"""
         Return this asymptotic expansion as a symbolic expression.
 
+        INPUT:
+
+        - ``R`` -- (a subring of) the symbolic ring or ``None``.
+          The output is will be an element of ``R``. If ``None``,
+          then the symbolic ring is used.
+
         OUTPUT:
 
         A symbolic expression.
@@ -2057,11 +2063,26 @@ def symbolic_expression(self):
             Order((1/2)^z*x*sqrt(y)*sqrt(z)*sqrt(log(y)))
             sage: _.parent()
             Symbolic Ring
+
+        ::
+
+            sage: from sage.symbolic.ring import SymbolicRing
+            sage: class MySymbolicRing(SymbolicRing):
+            ....:     pass
+            sage: mySR = MySymbolicRing()
+            sage: a.symbolic_expression(mySR).parent() is mySR
+            True
         """
-        from sage.symbolic.ring import SR
-        return self.substitute(dict((g, SR.var(str(g)))
+        if R is None:
+            from sage.symbolic.ring import SR
+            R = SR
+
+        return self.substitute(dict((g, R(R.var(str(g))))
                                     for g in self.parent().gens()),
-                               domain=SR)
+                               domain=R)
+
+
+    _symbolic_ = symbolic_expression  # will be used by SR._element_constructor_
 
 
 class AsymptoticRing(Algebra, UniqueRepresentation):
@@ -2641,12 +2662,12 @@ def _element_constructor_(self, data, simplify=True, convert=True):
             return self.create_summand('exact', data)
 
         from misc import combine_exceptions
-        from sage.symbolic.ring import SR
+        from sage.symbolic.ring import SymbolicRing
         from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
         from sage.rings.polynomial.multi_polynomial_ring_generic import is_MPolynomialRing
         from sage.rings.power_series_ring import is_PowerSeriesRing
 
-        if P is SR:
+        if isinstance(P, SymbolicRing):
             from sage.symbolic.operators import add_vararg
             if data.operator() == add_vararg:
                 summands = []

src/sage/rings/asymptotic/growth_group.py

@@ -3014,13 +3014,13 @@ def _convert_(self, data):
             from sage.symbolic.ring import SR
             return self._convert_(SR(data))
 
-        from sage.symbolic.ring import SR
+        from sage.symbolic.ring import SymbolicRing
         from sage.rings.polynomial.polynomial_ring import PolynomialRing_general
         from sage.rings.polynomial.multi_polynomial_ring_generic import \
             MPolynomialRing_generic
         from sage.rings.power_series_ring import PowerSeriesRing_generic
         import operator
-        if P is SR:
+        if isinstance(P, SymbolicRing):
             if data.operator() == operator.pow:
                 base, exponent = data.operands()
                 if str(base) == var:
@@ -3636,25 +3636,25 @@ def _convert_(self, data):
             else:
                 return  # end of parsing
 
-        from sage.symbolic.ring import SR
+        from sage.symbolic.ring import SymbolicRing
         import operator
         from sage.symbolic.operators import mul_vararg
-        if P is SR:
+        if isinstance(P, SymbolicRing):
             op = data.operator()
             if op == operator.pow:
                 base, exponent = data.operands()
                 if str(exponent) == var:
                     return base
                 elif exponent.operator() == mul_vararg:
-                    return base ** (exponent / SR(var))
+                    return base ** (exponent / P(var))
             elif isinstance(op, sage.functions.log.Function_exp):
                 from sage.functions.log import exp
                 base = exp(1)
                 exponent = data.operands()[0]
                 if str(exponent) == var:
                     return base
                 elif exponent.operator() == mul_vararg:
-                    return base ** (exponent / SR(var))
+                    return base ** (exponent / P(var))
 
         elif data == 1:  # can be expensive, so let's put it at the end
             return self.base().one()

src/sage/rings/asymptotic/term_monoid.py

@@ -1843,8 +1843,8 @@ def _get_factors_(self, data):
         except AttributeError:
             return (data,)
 
-        from sage.symbolic.ring import SR
-        if P is SR:
+        from sage.symbolic.ring import SymbolicRing
+        if isinstance(P, SymbolicRing):
             from sage.symbolic.operators import mul_vararg
             if data.operator() == mul_vararg:
                 return tuple(data.operands())
@@ -2340,10 +2340,12 @@ def _substitute_(self, rules):
             pass
         else:
             from asymptotic_ring import AsymptoticRing
+            from sage.symbolic.ring import SymbolicRing
+
             if isinstance(P, AsymptoticRing):
                 return g.O()
 
-            elif P is sage.symbolic.ring.SR:
+            elif isinstance(P, SymbolicRing):
                 return g.Order()
 
         try:

src/sage/symbolic/ring.pyx

@@ -299,7 +299,6 @@ cdef class SymbolicRing(CommutativeRing):
 
         from sage.rings.infinity import (infinity, minus_infinity,
                                          unsigned_infinity)
-        from sage.rings.asymptotic.asymptotic_ring import AsymptoticExpansion
         from sage.structure.factorization import Factorization
 
         if isinstance(x, (Integer, RealNumber, float, long, complex)):
@@ -312,8 +311,6 @@ cdef class SymbolicRing(CommutativeRing):
             return new_Expression_from_GEx(self, g_mInfinity)
         elif x is unsigned_infinity:
             return new_Expression_from_GEx(self, g_UnsignedInfinity)
-        elif isinstance(x, AsymptoticExpansion):
-            return x.symbolic_expression()
         elif isinstance(x, (RingElement, Matrix)):
             GEx_construct_pyobject(exp, x)
         elif isinstance(x, Factorization):