Make _repr_ of MILP more informative

Author: jdemeyer

src/sage/cpython/wrapperdescr.pyx

@@ -67,7 +67,7 @@ def wrapperdescr_call(slotwrapper, self, *args, **kwds):
         63/5
         sage: from sage.numerical.mip import MixedIntegerLinearProgram
         sage: wrapperdescr_call(type.__call__, MixedIntegerLinearProgram, maximization=False)
-        Mixed Integer Program  ( minimization, 0 variables, 0 constraints )
+        Mixed Integer Program (no objective, 0 variables, 0 constraints)
 
     TESTS::
 

src/sage/geometry/polyhedron/base.py

@@ -1145,7 +1145,7 @@ def to_linear_program(self, solver=None, return_variable=False, base_ring=None):
 
             sage: p = polytopes.cube()
             sage: p.to_linear_program()
-            Mixed Integer Program  ( maximization, 3 variables, 6 constraints )
+            Linear Program (no objective, 3 variables, 6 constraints)
             sage: lp, x = p.to_linear_program(return_variable=True)
             sage: lp.set_objective(2*x[0] + 1*x[1] + 39*x[2])
             sage: lp.solve()

src/sage/numerical/backends/cvxopt_backend.pyx

@@ -39,7 +39,7 @@ cdef class CVXOPTBackend(GenericBackend):
     :trac:`20332`::
 
         sage: p
-        Mixed Integer Program  ( maximization, 0 variables, 0 constraints )
+        Mixed Integer Program (no objective, 0 variables, 0 constraints)
 
     General backend testsuite::
 

src/sage/numerical/mip.pyx

@@ -528,28 +528,62 @@ cdef class MixedIntegerLinearProgram(SageObject):
     linear_function = __call__
 
     def _repr_(self):
-         r"""
-         Returns a short description of the ``MixedIntegerLinearProgram``.
+        r"""
+        Return a short description of the ``MixedIntegerLinearProgram``.
 
-         EXAMPLES::
+        EXAMPLES::
 
-             sage: p = MixedIntegerLinearProgram(solver='GLPK')
-             sage: v = p.new_variable(nonnegative=True)
-             sage: p.add_constraint(v[1] + v[2], max=2)
-             sage: print(p)
-             Mixed Integer Program ( maximization, 2 variables, 1 constraints )
-         """
-         cdef GenericBackend b = self._backend
+            sage: p = MixedIntegerLinearProgram(solver='GLPK')
+            sage: v = p.new_variable(binary=True)
+            sage: p.add_constraint(v[1] + v[2], max=1)
+            sage: p
+            Boolean Program (no objective, 2 variables, 1 constraint)
+        """
+        cdef GenericBackend b = self._backend
 
-         return ("Mixed Integer Program "+
+        cdef int nvars = b.ncols()
+        cdef int i
+
+        cdef int have_int = 0, have_bool = 0, have_cont = 0
+        for i in range(nvars):
+            if b.is_variable_binary(i):
+                have_bool = 1
+            elif b.is_variable_integer(i):
+                have_int = 1
+            else:
+                have_cont = 1
+
+        if have_cont:
+            if have_int or have_bool:
+                kind = "Mixed Integer Program"
+            else:
+                kind = "Linear Program"
+        elif have_int:
+            kind = "Integer Program"
+        elif have_bool:
+            kind = "Boolean Program"
+        else:
+            # We have no variables...
+            kind = "Mixed Integer Program"
+
+        if (all(b.objective_coefficient(i) == 0 for i in range(nvars))
+                and b.objective_constant_term() == 0):
+            minmax = "no objective"
+        elif b.is_maximization():
+            minmax = "maximization"
+        else:
+            minmax = "minimization"
 
-                 ( "\"" +self._backend.problem_name()+ "\""
-                   if (str(self._backend.problem_name()) != "") else "")+
+        def plural(num, noun):
+            if num != 1:
+                noun = noun + "s"
+            return f"{num} {noun}"
 
-                 " ( " + ("maximization" if b.is_maximization() else "minimization" ) +
+        name = b.problem_name()
+        if name:
+            kind += f' "{name}"'
 
-                 ", " + str(b.ncols()) + " variables, " +
-                 str(b.nrows()) + " constraints )")
+        return f"{kind} ({minmax}, {plural(b.ncols(), 'variable')}, {plural(b.nrows(), 'constraint')})"
 
     def __copy__(self):
         r"""
@@ -687,7 +721,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
             sage: p = MixedIntegerLinearProgram(solver='GLPK')
             sage: p.set_problem_name("Test program")
             sage: p
-            Mixed Integer Program "Test program" ( maximization, 0 variables, 0 constraints )
+            Mixed Integer Program "Test program" (no objective, 0 variables, 0 constraints)
         """
         self._backend.problem_name(name)