get_solver: Add optional base_ring argument

src/sage/numerical/backends/generic_backend.pxd

@@ -50,4 +50,4 @@ cdef class GenericBackend:
 
     cdef object obj_constant_term
 
-cpdef GenericBackend get_solver(constraint_generation = ?, solver = ?)
+cpdef GenericBackend get_solver(constraint_generation = ?, solver = ?, base_ring = ?)

src/sage/numerical/backends/generic_backend.pyx

@@ -1237,7 +1237,7 @@ def default_mip_solver(solver = None):
     else:
         raise ValueError("'solver' should be set to 'GLPK', 'Coin', 'CPLEX', 'CVXOPT', 'Gurobi', 'PPL', 'InteractiveLP', or None.")
 
-cpdef GenericBackend get_solver(constraint_generation = False, solver = None):
+cpdef GenericBackend get_solver(constraint_generation = False, solver = None, base_ring = None):
     """
     Return a solver according to the given preferences
 
@@ -1271,7 +1271,9 @@ cpdef GenericBackend get_solver(constraint_generation = False, solver = None):
         ``solver`` should then be equal to one of ``"GLPK"``, ``"Coin"``,
         ``"CPLEX"``, ``"CVXOPT"``,``"Gurobi"``, ``"PPL"``, ``"InteractiveLP"``,
         or ``None``. If ``solver=None`` (default),
-        the default solver is used (see ``default_mip_solver`` method.
+        the default solver is used (see ``default_mip_solver`` method).
+
+    - ``base_ring`` -- Request a solver that works over this field.
 
     - ``constraint_generation`` -- Only used when ``solver=None``.
 
@@ -1286,14 +1288,40 @@ cpdef GenericBackend get_solver(constraint_generation = False, solver = None):
 
         - :func:`default_mip_solver` -- Returns/Sets the default MIP solver.
 
-    EXAMPLE::
+    EXAMPLES::
 
         sage: from sage.numerical.backends.generic_backend import get_solver
         sage: p = get_solver()
+        sage: p = get_solver(base_ring=RDF)
+        sage: p.base_ring()
+        Real Double Field
+        sage: p = get_solver(base_ring=QQ); p
+        <sage.numerical.backends.ppl_backend.PPLBackend object at ...>
+        sage: p.base_ring()
+        Rational Field
+        sage: p = get_solver(base_ring=AA); p
+        <sage.numerical.backends.interactivelp_backend.InteractiveLPBackend object at ...>
+        sage: p.base_ring()
+        Algebraic Real Field
+        sage: d = polytopes.dodecahedron()
+        sage: p = get_solver(base_ring=d.base_ring()); p
+        <sage.numerical.backends.interactivelp_backend.InteractiveLPBackend object at ...>
+        sage: p.base_ring()
+        Number Field in sqrt5 with defining polynomial x^2 - 5
     """
     if solver is None:
+
         solver = default_mip_solver()
 
+        if base_ring is not None:
+            from sage.rings.all import QQ, RDF
+            if base_ring is QQ:
+                solver = "Ppl"
+            elif solver in ["Interactivelp", "Ppl"] and not base_ring.is_exact():
+                solver = "Glpk"
+            elif base_ring is not RDF:
+                solver = "Interactivelp"
+
         # We do not want to use Coin for constraint_generation. It just does not
         # work
         if solver == "Coin" and constraint_generation:
@@ -1328,7 +1356,7 @@ cpdef GenericBackend get_solver(constraint_generation = False, solver = None):
 
     elif solver == "Interactivelp":
         from sage.numerical.backends.interactivelp_backend import InteractiveLPBackend
-        return InteractiveLPBackend()
+        return InteractiveLPBackend(base_ring=base_ring)
 
     else:
         raise ValueError("'solver' should be set to 'GLPK', 'Coin', 'CPLEX', 'CVXOPT', 'Gurobi', 'PPL', 'InteractiveLP', or None (in which case the default one is used).")