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sagemathgh-36567: `sage.numerical`: Update `# needs` <!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes sagemath#1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> Also removing a function deprecated in sagemath#32226 <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes sagemath#12345". --> - In part cherry picked from sagemath#35095 - Part of sagemath#29705 <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [ ] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - sagemath#12345: short description why this is a dependency - sagemath#34567: ... --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: sagemath#36567 Reported by: Matthias Köppe Reviewer(s): David Coudert, Matthias Köppe
2 parents 964b9f9 + 1f0c2a2 commit a4a0c28

16 files changed

+999
-1000
lines changed

‎src/sage/numerical/all.py

+1-1
Original file line numberDiff line numberDiff line change
@@ -1,7 +1,7 @@
11
from sage.misc.lazy_import import lazy_import
22
lazy_import("sage.numerical.optimize",
33
["find_fit", "find_local_maximum", "find_local_minimum",
4-
"find_root", "linear_program", "minimize", "minimize_constrained"])
4+
"find_root", "minimize", "minimize_constrained"])
55
lazy_import("sage.numerical.mip", ["MixedIntegerLinearProgram"])
66
lazy_import("sage.numerical.sdp", ["SemidefiniteProgram"])
77
lazy_import("sage.numerical.backends.generic_backend", ["default_mip_solver"])

‎src/sage/numerical/backends/cvxopt_backend.pyx

+208-198
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‎src/sage/numerical/backends/cvxopt_sdp_backend.pyx

+69-68
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‎src/sage/numerical/backends/cvxpy_backend.pyx

+3-3
Original file line numberDiff line numberDiff line change
@@ -58,11 +58,11 @@ cdef class CVXPYBackend:
5858
5959
Open-source solvers provided by optional packages::
6060
61-
sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK"); p.solve() # optional - cvxopt
61+
sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK"); p.solve() # needs cvxopt
6262
0.0
63-
sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK_MI"); p.solve() # optional - cvxopt
63+
sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLPK_MI"); p.solve() # needs cvxopt
6464
0.0
65-
sage: p = MixedIntegerLinearProgram(solver="CVXPY/CVXOPT"); p.solve() # optional - cvxopt
65+
sage: p = MixedIntegerLinearProgram(solver="CVXPY/CVXOPT"); p.solve() # needs cvxopt
6666
0.0
6767
sage: p = MixedIntegerLinearProgram(solver="CVXPY/GLOP"); p.solve() # optional - ortools
6868
0.0

‎src/sage/numerical/backends/generic_backend.pyx

+337-291
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‎src/sage/numerical/backends/generic_sdp_backend.pyx

+159-143
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‎src/sage/numerical/backends/glpk_backend.pyx

+5-1
Original file line numberDiff line numberDiff line change
@@ -1097,6 +1097,7 @@ cdef class GLPKBackend(GenericBackend):
10971097
the result is not optimal. To do this, we try to compute the maximum
10981098
number of disjoint balls (of diameter 1) in a hypercube::
10991099
1100+
sage: # needs sage.graphs
11001101
sage: g = graphs.CubeGraph(9)
11011102
sage: p = MixedIntegerLinearProgram(solver="GLPK")
11021103
sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -1110,6 +1111,7 @@ cdef class GLPKBackend(GenericBackend):
11101111
11111112
Same, now with a time limit::
11121113
1114+
sage: # needs sage.graphs
11131115
sage: p.solver_parameter("mip_gap_tolerance",1)
11141116
sage: p.solver_parameter("timelimit",3.0)
11151117
sage: p.solve() # rel tol 100
@@ -1197,6 +1199,7 @@ cdef class GLPKBackend(GenericBackend):
11971199
11981200
EXAMPLES::
11991201
1202+
sage: # needs sage.graphs
12001203
sage: g = graphs.CubeGraph(9)
12011204
sage: p = MixedIntegerLinearProgram(solver="GLPK")
12021205
sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -1231,6 +1234,7 @@ cdef class GLPKBackend(GenericBackend):
12311234
12321235
EXAMPLES::
12331236
1237+
sage: # needs sage.graphs
12341238
sage: g = graphs.CubeGraph(9)
12351239
sage: p = MixedIntegerLinearProgram(solver="GLPK")
12361240
sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -1250,7 +1254,7 @@ cdef class GLPKBackend(GenericBackend):
12501254
Just make sure that the variable *has* been defined, and is not just
12511255
undefined::
12521256
1253-
sage: backend.get_relative_objective_gap() > 1
1257+
sage: backend.get_relative_objective_gap() > 1 # needs sage.graphs
12541258
True
12551259
"""
12561260
return self.search_tree_data.mip_gap

‎src/sage/numerical/backends/glpk_graph_backend.pyx

+1
Original file line numberDiff line numberDiff line change
@@ -1,3 +1,4 @@
1+
# sage.doctest: needs sage.graphs
12
"""
23
GLPK Backend for access to GLPK graph functions
34

‎src/sage/numerical/backends/interactivelp_backend.pyx

+9-8
Original file line numberDiff line numberDiff line change
@@ -53,17 +53,18 @@ cdef class InteractiveLPBackend:
5353
5454
This backend can work with irrational algebraic numbers::
5555
56-
sage: poly = polytopes.dodecahedron(base_ring=AA) # optional - sage.rings.number_field
57-
sage: lp, x = poly.to_linear_program(solver='InteractiveLP', return_variable=True) # optional - sage.rings.number_field
58-
sage: lp.set_objective(x[0] + x[1] + x[2]) # optional - sage.rings.number_field
59-
sage: lp.solve() # optional - sage.rings.number_field
56+
sage: # needs sage.rings.number_field
57+
sage: poly = polytopes.dodecahedron(base_ring=AA)
58+
sage: lp, x = poly.to_linear_program(solver='InteractiveLP', return_variable=True)
59+
sage: lp.set_objective(x[0] + x[1] + x[2])
60+
sage: lp.solve()
6061
2.291796067500631?
61-
sage: lp.get_values(x[0], x[1], x[2]) # optional - sage.rings.number_field
62+
sage: lp.get_values(x[0], x[1], x[2])
6263
[0.763932022500211?, 0.763932022500211?, 0.763932022500211?]
63-
sage: lp.set_objective(x[0] - x[1] - x[2]) # optional - sage.rings.number_field
64-
sage: lp.solve() # optional - sage.rings.number_field
64+
sage: lp.set_objective(x[0] - x[1] - x[2])
65+
sage: lp.solve()
6566
2.291796067500631?
66-
sage: lp.get_values(x[0], x[1], x[2]) # optional - sage.rings.number_field
67+
sage: lp.get_values(x[0], x[1], x[2])
6768
[0.763932022500211?, -0.763932022500211?, -0.763932022500211?]
6869
"""
6970

‎src/sage/numerical/backends/ppl_backend.pyx

+2-1
Original file line numberDiff line numberDiff line change
@@ -1,3 +1,4 @@
1+
# sage.doctest: optional - pplpy
12
"""
23
PPL Backend
34
@@ -61,7 +62,7 @@ cdef class PPLBackend(GenericBackend):
6162
6263
Raise an error if a ``base_ring`` is requested that is not supported::
6364
64-
sage: p = MixedIntegerLinearProgram(solver = "PPL", base_ring=AA)
65+
sage: p = MixedIntegerLinearProgram(solver="PPL", base_ring=AA) # needs sage.rings.number_field
6566
Traceback (most recent call last):
6667
...
6768
TypeError: The PPL backend only supports rational data.

‎src/sage/numerical/gauss_legendre.pyx

+13-13
Original file line numberDiff line numberDiff line change
@@ -79,11 +79,11 @@ def nodes_uncached(degree, prec):
7979
8080
sage: from sage.numerical.gauss_legendre import nodes_uncached
8181
sage: L1 = nodes_uncached(24, 53)
82-
sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x))
83-
sage: Pdif = P.diff()
84-
sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2)
82+
sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x)) # needs sage.symbolic
83+
sage: Pdif = P.diff() # needs sage.symbolic
84+
sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2) # needs sage.symbolic
8585
....: for r, _ in RR['x'](P).roots()]
86-
sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9
86+
sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9 # needs sage.symbolic
8787
....: for a, b in zip(L1, L2))
8888
True
8989
@@ -188,11 +188,11 @@ def nodes(degree, prec):
188188
189189
sage: from sage.numerical.gauss_legendre import nodes
190190
sage: L1 = nodes(24, 53)
191-
sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x))
192-
sage: Pdif = P.diff()
193-
sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2)
191+
sage: P = RR['x'](sage.functions.orthogonal_polys.legendre_P(24, x)) # needs sage.symbolic
192+
sage: Pdif = P.diff() # needs sage.symbolic
193+
sage: L2 = [((r + 1)/2, 1/(1 - r^2)/Pdif(r)^2) # needs sage.symbolic
194194
....: for r, _ in RR['x'](P).roots()]
195-
sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9
195+
sage: all((a[0] - b[0]).abs() < 1e-15 and (a[1] - b[1]).abs() < 1e-9 # needs sage.symbolic
196196
....: for a, b in zip(L1, L2))
197197
True
198198
@@ -343,8 +343,8 @@ def integrate_vector(f, prec, epsilon=None):
343343
sage: epsilon = K(2^(-prec + 4))
344344
sage: f = lambda t:V((1 + t^2, 1/(1 + t^2)))
345345
sage: I = integrate_vector(f, prec, epsilon=epsilon)
346-
sage: J = V((4/3, pi/4))
347-
sage: max(c.abs() for c in (I - J)) < epsilon
346+
sage: J = V((4/3, pi/4)) # needs sage.symbolic
347+
sage: max(c.abs() for c in (I - J)) < epsilon # needs sage.symbolic
348348
True
349349
350350
We can also use complex-valued integrands::
@@ -354,10 +354,10 @@ def integrate_vector(f, prec, epsilon=None):
354354
sage: K = ComplexField(prec)
355355
sage: V = VectorSpace(K, 2)
356356
sage: epsilon = Kreal(2^(-prec + 4))
357-
sage: f = lambda t: V((t, K(exp(2*pi*t*K.0))))
358-
sage: I = integrate_vector(f, prec, epsilon=epsilon)
357+
sage: f = lambda t: V((t, K(exp(2*pi*t*K.0)))) # needs sage.symbolic
358+
sage: I = integrate_vector(f, prec, epsilon=epsilon) # needs sage.symbolic
359359
sage: J = V((1/2, 0))
360-
sage: max(c.abs() for c in (I - J)) < epsilon
360+
sage: max(c.abs() for c in (I - J)) < epsilon # needs sage.symbolic
361361
True
362362
"""
363363
results = []

‎src/sage/numerical/interactive_simplex_method.py

+12-12
Original file line numberDiff line numberDiff line change
@@ -64,7 +64,7 @@
6464
6565
Since it has only two variables, we can solve it graphically::
6666
67-
sage: P.plot() # optional - sage.plot
67+
sage: P.plot() # needs sage.plot
6868
Graphics object consisting of 19 graphics primitives
6969
7070
@@ -298,9 +298,9 @@ def _latex_product(coefficients, variables,
298298
299299
sage: from sage.numerical.interactive_simplex_method import \
300300
....: _latex_product
301-
sage: var("x, y")
301+
sage: var("x, y") # needs sage.symbolic
302302
(x, y)
303-
sage: print(_latex_product([-1, 3], [x, y]))
303+
sage: print(_latex_product([-1, 3], [x, y])) # needs sage.symbolic
304304
- \mspace{-6mu}&\mspace{-6mu} x \mspace{-6mu}&\mspace{-6mu} + \mspace{-6mu}&\mspace{-6mu} 3 y
305305
"""
306306
entries = []
@@ -1534,19 +1534,19 @@ def plot(self, *args, **kwds):
15341534
sage: b = (1000, 1500)
15351535
sage: c = (10, 5)
15361536
sage: P = InteractiveLPProblem(A, b, c, ["C", "B"], variable_type=">=")
1537-
sage: p = P.plot() # optional - sage.plot
1538-
sage: p.show() # optional - sage.plot
1537+
sage: p = P.plot() # needs sage.plot
1538+
sage: p.show() # needs sage.plot
15391539
15401540
In this case the plot works better with the following axes ranges::
15411541
1542-
sage: p = P.plot(0, 1000, 0, 1500) # optional - sage.plot
1543-
sage: p.show() # optional - sage.plot
1542+
sage: p = P.plot(0, 1000, 0, 1500) # needs sage.plot
1543+
sage: p.show() # needs sage.plot
15441544
15451545
TESTS:
15461546
15471547
We check that zero objective can be dealt with::
15481548
1549-
sage: InteractiveLPProblem(A, b, (0, 0), ["C", "B"], variable_type=">=").plot() # optional - sage.plot
1549+
sage: InteractiveLPProblem(A, b, (0, 0), ["C", "B"], variable_type=">=").plot() # needs sage.plot
15501550
Graphics object consisting of 8 graphics primitives
15511551
"""
15521552
FP = self.plot_feasible_set(*args, **kwds)
@@ -1611,13 +1611,13 @@ def plot_feasible_set(self, xmin=None, xmax=None, ymin=None, ymax=None,
16111611
sage: b = (1000, 1500)
16121612
sage: c = (10, 5)
16131613
sage: P = InteractiveLPProblem(A, b, c, ["C", "B"], variable_type=">=")
1614-
sage: p = P.plot_feasible_set() # optional - sage.plot
1615-
sage: p.show() # optional - sage.plot
1614+
sage: p = P.plot_feasible_set() # needs sage.plot
1615+
sage: p.show() # needs sage.plot
16161616
16171617
In this case the plot works better with the following axes ranges::
16181618
1619-
sage: p = P.plot_feasible_set(0, 1000, 0, 1500) # optional - sage.plot
1620-
sage: p.show() # optional - sage.plot
1619+
sage: p = P.plot_feasible_set(0, 1000, 0, 1500) # needs sage.plot
1620+
sage: p.show() # needs sage.plot
16211621
"""
16221622
if self.n() != 2:
16231623
raise ValueError("only problems with 2 variables can be plotted")

‎src/sage/numerical/knapsack.py

+1
Original file line numberDiff line numberDiff line change
@@ -408,6 +408,7 @@ def is_superincreasing(self, seq=None):
408408
409409
The sequence must contain only integers::
410410
411+
sage: # needs sage.symbolic
411412
sage: from sage.numerical.knapsack import Superincreasing
412413
sage: L = [1.0, 2.1, pi, 21, 69, 189, 376, 919]
413414
sage: Superincreasing(L).is_superincreasing()

‎src/sage/numerical/mip.pyx

+20-13
Original file line numberDiff line numberDiff line change
@@ -315,6 +315,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
315315
316316
Computation of a maximum stable set in Petersen's graph::
317317
318+
sage: # needs sage.graphs
318319
sage: g = graphs.PetersenGraph()
319320
sage: p = MixedIntegerLinearProgram(maximization=True, solver='GLPK')
320321
sage: b = p.new_variable(binary=True)
@@ -659,13 +660,15 @@ cdef class MixedIntegerLinearProgram(SageObject):
659660
sage: p = MixedIntegerLinearProgram(solver='ppl')
660661
sage: p.base_ring()
661662
Rational Field
662-
sage: from sage.rings.qqbar import AA # optional - sage.rings.number_field
663-
sage: p = MixedIntegerLinearProgram(solver='InteractiveLP', base_ring=AA) # optional - sage.rings.number_field
664-
sage: p.base_ring() # optional - sage.rings.number_field
663+
sage: from sage.rings.qqbar import AA # needs sage.rings.number_field
664+
sage: p = MixedIntegerLinearProgram(solver='InteractiveLP', base_ring=AA) # needs sage.rings.number_field
665+
sage: p.base_ring() # needs sage.rings.number_field
665666
Algebraic Real Field
666-
sage: d = polytopes.dodecahedron() # optional - sage.rings.number_field
667-
sage: p = MixedIntegerLinearProgram(base_ring=d.base_ring()) # optional - sage.rings.number_field
668-
sage: p.base_ring() # optional - sage.rings.number_field
667+
668+
sage: # needs sage.groups sage.rings.number_field
669+
sage: d = polytopes.dodecahedron()
670+
sage: p = MixedIntegerLinearProgram(base_ring=d.base_ring())
671+
sage: p.base_ring()
669672
Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?
670673
"""
671674
return self._backend.base_ring()
@@ -2629,6 +2632,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
26292632
26302633
Computation of a maximum stable set in Petersen's graph::
26312634
2635+
sage: # needs sage.graphs
26322636
sage: g = graphs.PetersenGraph()
26332637
sage: p = MixedIntegerLinearProgram(maximization=True, solver='GLPK')
26342638
sage: b = p.new_variable(nonnegative=True)
@@ -2823,14 +2827,15 @@ cdef class MixedIntegerLinearProgram(SageObject):
28232827
are not recorded, and we can disable this feature providing an empty
28242828
filename. This is currently working with CPLEX and Gurobi::
28252829
2826-
sage: p = MixedIntegerLinearProgram(solver="CPLEX") # optional - CPLEX
2827-
sage: p.solver_parameter("logfile") # optional - CPLEX
2830+
sage: # optional - cplex
2831+
sage: p = MixedIntegerLinearProgram(solver="CPLEX")
2832+
sage: p.solver_parameter("logfile")
28282833
''
2829-
sage: p.solver_parameter("logfile", "/dev/null") # optional - CPLEX
2830-
sage: p.solver_parameter("logfile") # optional - CPLEX
2834+
sage: p.solver_parameter("logfile", "/dev/null")
2835+
sage: p.solver_parameter("logfile")
28312836
'/dev/null'
2832-
sage: p.solver_parameter("logfile", '') # optional - CPLEX
2833-
sage: p.solver_parameter("logfile") # optional - CPLEX
2837+
sage: p.solver_parameter("logfile", '')
2838+
sage: p.solver_parameter("logfile")
28342839
''
28352840
28362841
Solver-specific parameters:
@@ -2983,6 +2988,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
29832988
29842989
EXAMPLES::
29852990
2991+
sage: # needs sage.graphs
29862992
sage: g = graphs.CubeGraph(9)
29872993
sage: p = MixedIntegerLinearProgram(solver="GLPK")
29882994
sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -3017,6 +3023,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
30173023
30183024
EXAMPLES::
30193025
3026+
sage: # needs sage.graphs
30203027
sage: g = graphs.CubeGraph(9)
30213028
sage: p = MixedIntegerLinearProgram(solver="GLPK")
30223029
sage: p.solver_parameter("mip_gap_tolerance",100)
@@ -3035,7 +3042,7 @@ cdef class MixedIntegerLinearProgram(SageObject):
30353042
Just make sure that the variable *has* been defined, and is not just
30363043
undefined::
30373044
3038-
sage: p.get_relative_objective_gap() > 1
3045+
sage: p.get_relative_objective_gap() > 1 # needs sage.graphs
30393046
True
30403047
"""
30413048
return self._backend.get_relative_objective_gap()

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