InteractiveLPBackend: Change default base_ring to QQ

Author: Matthias Koeppe

src/sage/numerical/backends/generic_backend.pyx

@@ -1169,7 +1169,7 @@ def default_mip_solver(solver = None):
 
         - ``InteractiveLPProblem`` (``solver="InteractiveLP"``).  A didactical
           implementation of the revised simplex method in Sage.  It works over
-          any exact ordered field, the default is ``AA``.
+          any exact ordered field, the default is ``QQ``.
 
         ``solver`` should then be equal to one of ``"GLPK"``,
         ``"Coin"``, ``"CPLEX"``,  ``"CVXOPT"``, ``"Gurobi"``, ``"PPL"`, or
@@ -1294,7 +1294,7 @@ cpdef GenericBackend get_solver(constraint_generation = False, solver = None, ba
 
         - ``InteractiveLPProblem`` (``solver="InteractiveLP"``).  A didactical
           implementation of the revised simplex method in Sage.  It works over
-          any exact ordered field, the default is ``AA``.
+          any exact ordered field, the default is ``QQ``.
 
         ``solver`` should then be equal to one of ``"GLPK"``, ``"Coin"``,
         ``"CPLEX"``, ``"CVXOPT"``,``"Gurobi"``, ``"PPL"``, ``"InteractiveLP"``,

src/sage/numerical/backends/interactivelp_backend.pyx

@@ -66,8 +66,8 @@ cdef class InteractiveLPBackend:
         """
 
         if base_ring is None:
-            from sage.rings.all import AA
-            base_ring = AA
+            from sage.rings.all import QQ
+            base_ring = QQ
 
         self.lp = InteractiveLPProblem([], [], [], base_ring=base_ring)
         self.set_verbosity(0)
@@ -92,7 +92,7 @@ cdef class InteractiveLPBackend:
             sage: from sage.numerical.backends.generic_backend import get_solver
             sage: p = get_solver(solver = "InteractiveLP")
             sage: p.base_ring()
-            Algebraic Real Field
+            Rational Field
         """
         return self.lp.base_ring()
 
@@ -308,7 +308,7 @@ cdef class InteractiveLPBackend:
             sage: from sage.numerical.backends.generic_backend import get_solver
             sage: p = get_solver(solver = "InteractiveLP")
             sage: p._AbcxCVPRd()
-            ([], (), (), (), (), (), 'max', Algebraic Real Field, 0)
+            ([], (), (), (), (), (), 'max', Rational Field, 0)
         """
         A, b, c, x = self.lp.Abcx()
         constraint_types = self.lp.constraint_types()

src/sage/numerical/mip.pyx

@@ -598,7 +598,8 @@ cdef class MixedIntegerLinearProgram(SageObject):
             sage: p = MixedIntegerLinearProgram(solver='ppl')
             sage: p.base_ring()
             Rational Field
-            sage: p = MixedIntegerLinearProgram(solver='InteractiveLP')
+            sage: from sage.rings.all import AA
+            sage: p = MixedIntegerLinearProgram(solver='InteractiveLP', base_ring=AA)
             sage: p.base_ring()
             Algebraic Real Field
             sage: d = polytopes.dodecahedron()