Trac #24028: Held definite integrals don't translate to SymPy

{{{
sage: from sympy import sympify
sage: integral(x, x, 0, 1, hold=True)
integrate(x, x, 0, 1)
sage: sympify(_)
...
ValueError: Invalid limits given: (x, 0, 1)

sage: integral(x, x, 0, 1, hold=True)._sympy_()
...
ValueError: Invalid limits given: (x, 0, 1)
}}}

URL: https://trac.sagemath.org/24028
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Travis Scrimshaw

src/sage/interfaces/sympy.py

@@ -289,7 +289,7 @@ def _sympysage_integral(self):
         sage: sx = Symbol('x')
         sage: assert integral(x, x, hold=True)._sympy_() == Integral(sx, sx)
         sage: assert integral(x, x, hold=True) == Integral(sx, sx)._sage_()
-        sage: assert integral(x, x, 0, 1, hold=True)._sympy_() == Integral(sx, (sx,0,1)) # known bug
+        sage: assert integral(x, x, 0, 1, hold=True)._sympy_() == Integral(sx, (sx,0,1))
         sage: assert integral(x, x, 0, 1, hold=True) == Integral(sx, (sx,0,1))._sage_()
     """
     from sage.misc.functional import integral

src/sage/symbolic/integration/integral.py

@@ -137,7 +137,7 @@ def _print_latex_(self, f, x):
 class DefiniteIntegral(BuiltinFunction):
     def __init__(self):
         """
-        Symbolic function representing a definite integral.
+        The symbolic function representing a definite integral.
 
         EXAMPLES::
 
@@ -156,7 +156,7 @@ def __init__(self):
 
     def _eval_(self, f, x, a, b):
         """
-        Returns the results of symbolic evaluation of the integral
+        Return the results of symbolic evaluation of the integral
 
         EXAMPLES::
 
@@ -185,7 +185,7 @@ def _eval_(self, f, x, a, b):
 
     def _evalf_(self, f, x, a, b, parent=None, algorithm=None):
         """
-        Returns numerical approximation of the integral
+        Return a numerical approximation of the integral
 
         EXAMPLES::
 
@@ -209,7 +209,7 @@ def _evalf_(self, f, x, a, b, parent=None, algorithm=None):
 
     def _tderivative_(self, f, x, a, b, diff_param=None):
         """
-        Returns derivative of symbolic integration
+        Return the derivative of symbolic integration
 
         EXAMPLES::
 
@@ -233,7 +233,7 @@ def _tderivative_(self, f, x, a, b, diff_param=None):
 
     def _print_latex_(self, f, x, a, b):
         r"""
-        Returns LaTeX expression for integration of a symbolic function.
+        Convert this integral to LaTeX notation
 
         EXAMPLES::
 
@@ -254,6 +254,22 @@ def _print_latex_(self, f, x, a, b):
             dx_str = "{d %s}"%(latex(x))
         return "\\int_{%s}^{%s} %s\\,%s"%(latex(a), latex(b), latex(f), dx_str)
 
+    def _sympy_(self, f, x, a, b):
+        """
+        Convert this integral to the equivalent SymPy object
+
+        The resulting SymPy integral can be evaluated using ``doit()``.
+
+        EXAMPLES::
+
+            sage: integral(x, x, 0, 1, hold=True)._sympy_()
+            Integral(x, (x, 0, 1))
+            sage: _.doit()
+            1/2
+        """
+        from sympy.integrals import Integral
+        return Integral(f, (x, a, b))
+
 definite_integral = DefiniteIntegral()