sage.numerical: Update # needs

src/sage/numerical/all.py

@@ -1,7 +1,7 @@
 from sage.misc.lazy_import import lazy_import
 lazy_import("sage.numerical.optimize",
             ["find_fit", "find_local_maximum", "find_local_minimum",
-             "find_root", "linear_program", "minimize", "minimize_constrained"])
+             "find_root", "minimize", "minimize_constrained"])
 lazy_import("sage.numerical.mip", ["MixedIntegerLinearProgram"])
 lazy_import("sage.numerical.sdp", ["SemidefiniteProgram"])
 lazy_import("sage.numerical.backends.generic_backend", ["default_mip_solver"])

src/sage/numerical/backends/cvxpy_backend.pyx

@@ -58,11 +58,11 @@ cdef class CVXPYBackend:
 
     Open-source solvers provided by optional packages::
 
-        sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK"); p.solve()            # optional - cvxopt
+        sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK"); p.solve()             # needs cvxopt
         0.0
-        sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK_MI"); p.solve()         # optional - cvxopt
+        sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK_MI"); p.solve()          # needs cvxopt
         0.0
-        sage: p = MixedIntegerLinearProgram(solver="CVXPY/CVXOPT"); p.solve()          # optional - cvxopt
+        sage: p = MixedIntegerLinearProgram(solver="CVXPY/CVXOPT"); p.solve()           # needs cvxopt
         0.0
         sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLOP"); p.solve()            # optional - ortools
         0.0

src/sage/numerical/backends/glpk_backend.pyx

@@ -1097,6 +1097,7 @@ cdef class GLPKBackend(GenericBackend):
         the result is not optimal. To do this, we try to compute the maximum
         number of disjoint balls (of diameter 1) in a hypercube::
 
+            sage: # needs sage.graphs
             sage: g = graphs.CubeGraph(9)
             sage: p = MixedIntegerLinearProgram(solver="GLPK")
             sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -1110,6 +1111,7 @@ cdef class GLPKBackend(GenericBackend):
 
         Same, now with a time limit::
 
+            sage: # needs sage.graphs
             sage: p.solver_parameter("mip_gap_tolerance",1)
             sage: p.solver_parameter("timelimit",3.0)
             sage: p.solve() # rel tol 100
@@ -1197,6 +1199,7 @@ cdef class GLPKBackend(GenericBackend):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: g = graphs.CubeGraph(9)
             sage: p = MixedIntegerLinearProgram(solver="GLPK")
             sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -1231,6 +1234,7 @@ cdef class GLPKBackend(GenericBackend):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: g = graphs.CubeGraph(9)
             sage: p = MixedIntegerLinearProgram(solver="GLPK")
             sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -1250,7 +1254,7 @@ cdef class GLPKBackend(GenericBackend):
         Just make sure that the variable *has* been defined, and is not just
         undefined::
 
-            sage: backend.get_relative_objective_gap() > 1
+            sage: backend.get_relative_objective_gap() > 1                              # needs sage.graphs
             True
         """
         return self.search_tree_data.mip_gap

src/sage/numerical/backends/glpk_graph_backend.pyx

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.graphs
 """
 GLPK Backend for access to GLPK graph functions
 

src/sage/numerical/backends/interactivelp_backend.pyx

@@ -53,17 +53,18 @@ cdef class InteractiveLPBackend:
 
         This backend can work with irrational algebraic numbers::
 
-            sage: poly = polytopes.dodecahedron(base_ring=AA)                                   # optional - sage.rings.number_field
-            sage: lp, x = poly.to_linear_program(solver='InteractiveLP', return_variable=True)  # optional - sage.rings.number_field
-            sage: lp.set_objective(x[0] + x[1] + x[2])                                          # optional - sage.rings.number_field
-            sage: lp.solve()                                                                    # optional - sage.rings.number_field
+            sage: # needs sage.rings.number_field
+            sage: poly = polytopes.dodecahedron(base_ring=AA)
+            sage: lp, x = poly.to_linear_program(solver='InteractiveLP', return_variable=True)
+            sage: lp.set_objective(x[0] + x[1] + x[2])
+            sage: lp.solve()
             2.291796067500631?
-            sage: lp.get_values(x[0], x[1], x[2])                                               # optional - sage.rings.number_field
+            sage: lp.get_values(x[0], x[1], x[2])
             [0.763932022500211?, 0.763932022500211?, 0.763932022500211?]
-            sage: lp.set_objective(x[0] - x[1] - x[2])                                          # optional - sage.rings.number_field
-            sage: lp.solve()                                                                    # optional - sage.rings.number_field
+            sage: lp.set_objective(x[0] - x[1] - x[2])
+            sage: lp.solve()
             2.291796067500631?
-            sage: lp.get_values(x[0], x[1], x[2])                                               # optional - sage.rings.number_field
+            sage: lp.get_values(x[0], x[1], x[2])
             [0.763932022500211?, -0.763932022500211?, -0.763932022500211?]
         """
 

src/sage/numerical/backends/ppl_backend.pyx

@@ -1,3 +1,4 @@
+# sage.doctest: optional - pplpy
 """
 PPL Backend
 
@@ -61,7 +62,7 @@ cdef class PPLBackend(GenericBackend):
 
         Raise an error if a ``base_ring`` is requested that is not supported::
 
-            sage: p = MixedIntegerLinearProgram(solver = "PPL", base_ring=AA)
+            sage: p = MixedIntegerLinearProgram(solver="PPL", base_ring=AA)             # needs sage.rings.number_field
             Traceback (most recent call last):
             ...
             TypeError: The PPL backend only supports rational data.

src/sage/numerical/gauss_legendre.pyx

@@ -79,11 +79,11 @@ def nodes_uncached(degree, prec):
 
         sage: from sage.numerical.gauss_legendre import nodes_uncached
         sage: L1 = nodes_uncached(24, 53)
-        sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x))
-        sage: Pdif = P.diff()
-        sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2)
+        sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x))            # needs sage.symbolic
+        sage: Pdif = P.diff()                                                           # needs sage.symbolic
+        sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2)                                  # needs sage.symbolic
         ....:        for r, _ in RR['x'](P).roots()]
-        sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9
+        sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9            # needs sage.symbolic
         ....:      for a, b in zip(L1, L2))
         True
 
@@ -188,11 +188,11 @@ def nodes(degree, prec):
 
         sage: from sage.numerical.gauss_legendre import nodes
         sage: L1 = nodes(24, 53)
-        sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x))
-        sage: Pdif = P.diff()
-        sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2)
+        sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x))            # needs sage.symbolic
+        sage: Pdif = P.diff()                                                           # needs sage.symbolic
+        sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2)                                  # needs sage.symbolic
         ....:        for r, _ in RR['x'](P).roots()]
-        sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9
+        sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9            # needs sage.symbolic
         ....:      for a, b in zip(L1, L2))
         True
 
@@ -343,8 +343,8 @@ def integrate_vector(f, prec, epsilon=None):
         sage: epsilon = K(2^(-prec + 4))
         sage: f = lambda t:V((1 + t^2, 1/(1 + t^2)))
         sage: I = integrate_vector(f, prec, epsilon=epsilon)
-        sage: J = V((4/3, pi/4))
-        sage: max(c.abs() for c in (I - J)) < epsilon
+        sage: J = V((4/3, pi/4))                                                        # needs sage.symbolic
+        sage: max(c.abs() for c in (I - J)) < epsilon                                   # needs sage.symbolic
         True
 
     We can also use complex-valued integrands::
@@ -354,10 +354,10 @@ def integrate_vector(f, prec, epsilon=None):
         sage: K = ComplexField(prec)
         sage: V = VectorSpace(K, 2)
         sage: epsilon = Kreal(2^(-prec + 4))
-        sage: f = lambda t: V((t, K(exp(2*pi*t*K.0))))
-        sage: I = integrate_vector(f, prec, epsilon=epsilon)
+        sage: f = lambda t: V((t, K(exp(2*pi*t*K.0))))                                  # needs sage.symbolic
+        sage: I = integrate_vector(f, prec, epsilon=epsilon)                            # needs sage.symbolic
         sage: J = V((1/2, 0))
-        sage: max(c.abs() for c in (I - J)) < epsilon
+        sage: max(c.abs() for c in (I - J)) < epsilon                                   # needs sage.symbolic
         True
     """
     results = []

src/sage/numerical/interactive_simplex_method.py

@@ -64,7 +64,7 @@
 
 Since it has only two variables, we can solve it graphically::
 
-    sage: P.plot()                                                                      # optional - sage.plot
+    sage: P.plot()                                                                      # needs sage.plot
     Graphics object consisting of 19 graphics primitives
 
 
@@ -298,9 +298,9 @@ def _latex_product(coefficients, variables,
 
         sage: from sage.numerical.interactive_simplex_method import \
         ....:       _latex_product
-        sage: var("x, y")
+        sage: var("x, y")                                                               # needs sage.symbolic
         (x, y)
-        sage: print(_latex_product([-1, 3], [x, y]))
+        sage: print(_latex_product([-1, 3], [x, y]))                                    # needs sage.symbolic
         - \mspace{-6mu}&\mspace{-6mu} x \mspace{-6mu}&\mspace{-6mu} + \mspace{-6mu}&\mspace{-6mu} 3 y
     """
     entries = []
@@ -1534,19 +1534,19 @@ def plot(self, *args, **kwds):
             sage: b = (1000, 1500)
             sage: c = (10, 5)
             sage: P = InteractiveLPProblem(A, b, c, ["C", "B"], variable_type=">=")
-            sage: p = P.plot()                                                          # optional - sage.plot
-            sage: p.show()                                                              # optional - sage.plot
+            sage: p = P.plot()                                                          # needs sage.plot
+            sage: p.show()                                                              # needs sage.plot
 
         In this case the plot works better with the following axes ranges::
 
-            sage: p = P.plot(0, 1000, 0, 1500)                                          # optional - sage.plot
-            sage: p.show()                                                              # optional - sage.plot
+            sage: p = P.plot(0, 1000, 0, 1500)                                          # needs sage.plot
+            sage: p.show()                                                              # needs sage.plot
 
         TESTS:
 
         We check that zero objective can be dealt with::
 
-            sage: InteractiveLPProblem(A, b, (0, 0), ["C", "B"], variable_type=">=").plot()         # optional - sage.plot
+            sage: InteractiveLPProblem(A, b, (0, 0), ["C", "B"], variable_type=">=").plot()         # needs sage.plot
             Graphics object consisting of 8 graphics primitives
         """
         FP = self.plot_feasible_set(*args, **kwds)
@@ -1611,13 +1611,13 @@ def plot_feasible_set(self, xmin=None, xmax=None, ymin=None, ymax=None,
             sage: b = (1000, 1500)
             sage: c = (10, 5)
             sage: P = InteractiveLPProblem(A, b, c, ["C", "B"], variable_type=">=")
-            sage: p = P.plot_feasible_set()                                             # optional - sage.plot
-            sage: p.show()                                                              # optional - sage.plot
+            sage: p = P.plot_feasible_set()                                             # needs sage.plot
+            sage: p.show()                                                              # needs sage.plot
 
         In this case the plot works better with the following axes ranges::
 
-            sage: p = P.plot_feasible_set(0, 1000, 0, 1500)                             # optional - sage.plot
-            sage: p.show()                                                              # optional - sage.plot
+            sage: p = P.plot_feasible_set(0, 1000, 0, 1500)                             # needs sage.plot
+            sage: p.show()                                                              # needs sage.plot
         """
         if self.n() != 2:
             raise ValueError("only problems with 2 variables can be plotted")

src/sage/numerical/knapsack.py

@@ -408,6 +408,7 @@ def is_superincreasing(self, seq=None):
 
         The sequence must contain only integers::
 
+            sage: # needs sage.symbolic
             sage: from sage.numerical.knapsack import Superincreasing
             sage: L = [1.0, 2.1, pi, 21, 69, 189, 376, 919]
             sage: Superincreasing(L).is_superincreasing()

src/sage/numerical/mip.pyx

@@ -315,6 +315,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
 
     Computation of a maximum stable set in Petersen's graph::
 
+         sage: # needs sage.graphs
          sage: g = graphs.PetersenGraph()
          sage: p = MixedIntegerLinearProgram(maximization=True, solver='GLPK')
          sage: b = p.new_variable(binary=True)
@@ -659,13 +660,15 @@ cdef class MixedIntegerLinearProgram(SageObject):
             sage: p = MixedIntegerLinearProgram(solver='ppl')
             sage: p.base_ring()
             Rational Field
-            sage: from sage.rings.qqbar import AA                                      # optional - sage.rings.number_field
-            sage: p = MixedIntegerLinearProgram(solver='InteractiveLP', base_ring=AA)  # optional - sage.rings.number_field
-            sage: p.base_ring()                                                        # optional - sage.rings.number_field
+            sage: from sage.rings.qqbar import AA                                       # needs sage.rings.number_field
+            sage: p = MixedIntegerLinearProgram(solver='InteractiveLP', base_ring=AA)   # needs sage.rings.number_field
+            sage: p.base_ring()                                                         # needs sage.rings.number_field
             Algebraic Real Field
-            sage: d = polytopes.dodecahedron()                                         # optional - sage.rings.number_field
-            sage: p = MixedIntegerLinearProgram(base_ring=d.base_ring())               # optional - sage.rings.number_field
-            sage: p.base_ring()                                                        # optional - sage.rings.number_field
+
+            sage: # needs sage.groups sage.rings.number_field
+            sage: d = polytopes.dodecahedron()
+            sage: p = MixedIntegerLinearProgram(base_ring=d.base_ring())
+            sage: p.base_ring()
             Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?
         """
         return self._backend.base_ring()
@@ -2629,6 +2632,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
 
          Computation of a maximum stable set in Petersen's graph::
 
+            sage: # needs sage.graphs
             sage: g = graphs.PetersenGraph()
             sage: p = MixedIntegerLinearProgram(maximization=True, solver='GLPK')
             sage: b = p.new_variable(nonnegative=True)
@@ -2823,14 +2827,15 @@ cdef class MixedIntegerLinearProgram(SageObject):
         are not recorded, and we can disable this feature providing an empty
         filename. This is currently working with CPLEX and Gurobi::
 
-            sage: p = MixedIntegerLinearProgram(solver="CPLEX")   # optional - CPLEX
-            sage: p.solver_parameter("logfile")                   # optional - CPLEX
+            sage: # optional - cplex
+            sage: p = MixedIntegerLinearProgram(solver="CPLEX")
+            sage: p.solver_parameter("logfile")
             ''
-            sage: p.solver_parameter("logfile", "/dev/null")      # optional - CPLEX
-            sage: p.solver_parameter("logfile")                   # optional - CPLEX
+            sage: p.solver_parameter("logfile", "/dev/null")
+            sage: p.solver_parameter("logfile")
             '/dev/null'
-            sage: p.solver_parameter("logfile", '')               # optional - CPLEX
-            sage: p.solver_parameter("logfile")                   # optional - CPLEX
+            sage: p.solver_parameter("logfile", '')
+            sage: p.solver_parameter("logfile")
             ''
 
         Solver-specific parameters:
@@ -2983,6 +2988,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: g = graphs.CubeGraph(9)
             sage: p = MixedIntegerLinearProgram(solver="GLPK")
             sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -3017,6 +3023,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: g = graphs.CubeGraph(9)
             sage: p = MixedIntegerLinearProgram(solver="GLPK")
             sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -3035,7 +3042,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
         Just make sure that the variable *has* been defined, and is not just
         undefined::
 
-            sage: p.get_relative_objective_gap() > 1
+            sage: p.get_relative_objective_gap() > 1                                    # needs sage.graphs
             True
         """
         return self._backend.get_relative_objective_gap()