gh-36950: sage.plot: Update # needs, doctest cosmetics; fix `sig_…

…on_count` doctest dataflow warnings

    
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Fixes #36920

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In part cherry picked from:
- #35095
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- [ ] I have created tests covering the changes.
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### ⌛ Dependencies

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- #12345: short description why this is a dependency
- #34567: ...
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- Depends on #36905 (merged here)

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URL: #36950
Reported by: Matthias Köppe
Reviewer(s): David Coudert

src/sage/doctest/sources.py

@@ -238,7 +238,7 @@ def _process_doc(self, doctests, doc, namespace, start):
                 # Line number refers to the end of the docstring
                 sigon = doctest.Example(sig_on_count_doc_doctest, "0\n", lineno=docstring.count("\n"))
                 sigon.sage_source = sig_on_count_doc_doctest
-                sigon.optional_tags = frozenset()
+                sigon.optional_tags = frozenset(self.file_optional_tags)
                 sigon.probed_tags = frozenset()
                 dt.examples.append(sigon)
             doctests.append(dt)

src/sage/libs/ntl/ntl_ZZ_pEX_linkage.pxi

@@ -332,7 +332,7 @@ cdef inline int celement_pow(ZZ_pEX_c* res, ZZ_pEX_c* x, long e, ZZ_pEX_c *modul
         sage: (x+1)^(-2)
         1/(x^2 + 2*x + 1)
         sage: f = x+(a+1)
-        sage: f**50 == sum(binomial(50,i)*(a+1)**i*x**(50-i) for i in range(51))
+        sage: f**50 == sum(binomial(50,i)*(a+1)**i*x**(50-i) for i in range(51))        # needs sage.symbolic
         True
 
     TESTS:

src/sage/misc/converting_dict.py

@@ -25,7 +25,7 @@
 This is used e.g. in the result of a variety, to allow access to the
 result no matter how a generator is identified::
 
-    sage: # needs sage.rings.number_field
+    sage: # needs sage.libs.singular sage.rings.number_field
     sage: K.<x,y> = QQ[]
     sage: I = ideal([x^2 + 2*y - 5, x + y + 3])
     sage: V = sorted(I.variety(AA), key=str)

src/sage/misc/replace_dot_all.py

@@ -298,7 +298,7 @@ def process_line(location, line, replacements, row_index, verbose=False):
         sage: from sage.misc.replace_dot_all import *
         sage: location = os.path.join(sage.env.SAGE_SRC, 'sage/plot/arc.py')
         sage: replacements = find_replacements(location, package_regex='sage[.]plot[.]all', verbose=True); replacements
-        [[476, 24, 'from sage.plot.graphics import Graphics']]
+        [[477, 24, 'from sage.plot.graphics import Graphics']]
         sage: with open(location, "r") as file:
         ....:     lines = file.readlines()
         sage: row_index, col_number, *_ = replacements[0]

src/sage/misc/table.py

@@ -293,7 +293,7 @@ def __eq__(self, other):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.plot
+            sage: # needs sage.modules sage.plot sage.symbolic
             sage: rows = [['a', 'b', 'c'], [1,plot(sin(x)),3], [4,5,identity_matrix(2)]]
             sage: T = table(rows, header_row=True)
             sage: T2 = table(rows, header_row=True)

src/sage/plot/animate.py

@@ -453,7 +453,8 @@ def make_image(self, frame, filename, **kwds):
             ....:                         floor(G.ymin()), ceil(G.ymax()))
             ....:        G.save_image(filename, **kwds)
 
-            sage: B = MyAnimation([graphs.CompleteGraph(n) for n in range(7,11)], figsize=5)
+            sage: B = MyAnimation([graphs.CompleteGraph(n)
+            ....:                  for n in range(7,11)], figsize=5)
             sage: d = B.png()
             sage: v = os.listdir(d); v.sort(); v
             ['00000000.png', '00000001.png', '00000002.png', '00000003.png']

src/sage/plot/arc.py

@@ -56,6 +56,7 @@ def __init__(self, x, y, r1, r2, angle, s1, s2, options):
 
         EXAMPLES::
 
+            sage: # needs sage.symbolic
             sage: A = arc((2,3),1,1,pi/4,(0,pi))
             sage: A[0].x == 2
             True

src/sage/plot/colors.py

@@ -215,7 +215,7 @@ def mod_one(x):
         0.0
         sage: mod_one(-11/7)
         0.4285714285714286
-        sage: mod_one(pi) + mod_one(-pi)
+        sage: mod_one(pi) + mod_one(-pi)                                                # needs sage.symbolic
         1.0
     """
     x = float(x)
@@ -1146,9 +1146,10 @@ def hue(h, s=1, v=1):
     This function makes it easy to sample a broad range of colors for
     graphics::
 
+        sage: # needs sage.symbolic
         sage: p = Graphics()
         sage: for phi in xsrange(0, 2 * pi, 1 / pi):
-        ....:     p += plot(sin(x + phi), (x, -7, 7), rgbcolor = hue(phi))
+        ....:     p += plot(sin(x + phi), (x, -7, 7), rgbcolor=hue(phi))
         sage: p
         Graphics object consisting of 20 graphics primitives
 

src/sage/plot/ellipse.py

@@ -220,7 +220,7 @@ def plot3d(self):
         TESTS::
 
             sage: from sage.plot.ellipse import Ellipse
-            sage: Ellipse(0,0,2,1,pi/4,{}).plot3d()
+            sage: Ellipse(0,0,2,1,pi/4,{}).plot3d()                                     # needs sage.symbolic
             Traceback (most recent call last):
             ...
             NotImplementedError

src/sage/plot/graphics.py

@@ -64,7 +64,7 @@ def is_Graphics(x):
         sage: from sage.plot.graphics import is_Graphics
         sage: is_Graphics(1)
         False
-        sage: is_Graphics(disk((0.0, 0.0), 1, (0, pi/2)))
+        sage: is_Graphics(disk((0.0, 0.0), 1, (0, pi/2)))                               # needs sage.symbolic
         True
     """
     return isinstance(x, Graphics)
@@ -1359,6 +1359,7 @@ def _set_scale(self, subplot, scale=None, base=None):
 
         EXAMPLES::
 
+            sage: # needs sage.symbolic
             sage: p = plot(x, 1, 10)
             sage: fig = p.matplotlib()
             sage: ax = fig.get_axes()[0]
@@ -1373,6 +1374,7 @@ def _set_scale(self, subplot, scale=None, base=None):
 
         TESTS::
 
+            sage: # needs sage.symbolic
             sage: p._set_scale(ax, 'log')
             Traceback (most recent call last):
             ...
@@ -1797,7 +1799,7 @@ def show(self, **kwds):
 
         ::
 
-            sage: G.show(scale='semilogy', base=(3,2)) # base ignored for x-axis        # needs sage.symbolic
+            sage: G.show(scale='semilogy', base=(3,2))  # base ignored for x-axis       # needs sage.symbolic
 
         The scale can be also given as a 2-tuple or a 3-tuple.::
 

src/sage/plot/histogram.py

@@ -274,8 +274,8 @@ def histogram(datalist, **options):
 
         sage: nv = normalvariate
         sage: H = histogram([nv(0, 1) for _ in range(1000)], bins=20, density=True, range=[-5, 5])
-        sage: P = plot(1/sqrt(2*pi)*e^(-x^2/2), (x, -5, 5), color='red', linestyle='--')
-        sage: H+P
+        sage: P = plot(1/sqrt(2*pi)*e^(-x^2/2), (x, -5, 5), color='red', linestyle='--')            # needs sage.symbolic
+        sage: H + P                                                                     # needs sage.symbolic
         Graphics object consisting of 2 graphics primitives
 
     .. PLOT::

src/sage/plot/line.py

@@ -559,6 +559,7 @@ def line2d(points, **options):
 
     A purple plot of the Riemann zeta function `\zeta(1/2 + it)`, `0 < t < 30`::
 
+        sage: # needs sage.libs.pari sage.rings.complex_double
         sage: i = CDF.gen()
         sage: v = [zeta(0.5 + n/10 * i) for n in range(300)]
         sage: L = [(z.real(), z.imag()) for z in v]
@@ -590,6 +591,7 @@ def line2d(points, **options):
 
     A red, blue, and green "cool cat"::
 
+        sage: # needs sage.symbolic
         sage: G = plot(-cos(x), -2, 2, thickness=5, rgbcolor=(0.5,1,0.5))
         sage: P = polygon([[1,2], [5,6], [5,0]], rgbcolor=(1,0,0))
         sage: Q = polygon([(-x,y) for x,y in P[0]], rgbcolor=(0,0,1))

src/sage/plot/matrix_plot.py

@@ -535,7 +535,7 @@ def matrix_plot(mat, xrange=None, yrange=None, **options):
 
     ::
 
-        sage: matrix_plot([[sin(x), cos(x)], [1, 0]])
+        sage: matrix_plot([[sin(x), cos(x)], [1, 0]])                                   # needs sage.symbolic
         Traceback (most recent call last):
         ...
         TypeError: mat must be a Matrix or a two dimensional array

src/sage/plot/plot.py

@@ -1763,7 +1763,7 @@ def b(n): return lambda x: bessel_J(n, x) + 0.5*(n-1)
 
     .. PLOT::
 
-        g = plot(sin(pi*x), (x, -8, 8), ticks=[[-7,-3,0,3,7],[-1/2,0,1/2]])
+        g = plot(sin(pi*x), (x, -8, 8), ticks=[[-7,-3,0,3,7], [-1/2,0,1/2]])
         sphinx_plot(g)
 
     ::
@@ -1799,7 +1799,7 @@ def b(n): return lambda x: bessel_J(n, x) + 0.5*(n-1)
 
     .. PLOT::
 
-        g = plot(x**2, (x,0,3), ticks=[[1,2.5],[0.5,1,2]], tick_formatter=[["$x_1$","$x_2$"],["$y_1$","$y_2$","$y_3$"]])
+        g = plot(x**2, (x,0,3), ticks=[[1,2.5],[0.5,1,2]], tick_formatter=[["$x_1$","$x_2$"], ["$y_1$","$y_2$","$y_3$"]])
         sphinx_plot(g)
 
     You can force Type 1 fonts in your figures by providing the relevant
@@ -1891,7 +1891,7 @@ def f(x): return (floor(x)+0.5) / (1-(x-0.5)**2)
 
         sage: plot(arcsec(x/2), -2, 2)  # plot should be empty; no valid points
         Graphics object consisting of 0 graphics primitives
-        sage: plot(sqrt(x^2-1), -2, 2)  # [-1, 1] is excluded automatically
+        sage: plot(sqrt(x^2 - 1), -2, 2)  # [-1, 1] is excluded automatically
         Graphics object consisting of 2 graphics primitives
 
     .. PLOT::
@@ -2573,7 +2573,7 @@ def parametric_plot(funcs, *args, **kwargs):
     is 1, so that circles look like circles. ::
 
         sage: t = var('t')
-        sage: parametric_plot( (cos(t), sin(t)), (t, 0, 2*pi))
+        sage: parametric_plot((cos(t), sin(t)), (t, 0, 2*pi))
         Graphics object consisting of 1 graphics primitive
 
     .. PLOT::
@@ -2613,23 +2613,25 @@ def parametric_plot(funcs, *args, **kwargs):
 
     .. PLOT::
 
-        t =var('t')
+        t = var('t')
         g = parametric_plot((t, t**2), (t, -4, 4), fill=True)
         sphinx_plot(g)
 
     A filled Hypotrochoid::
 
-        sage: parametric_plot([cos(x) + 2 * cos(x/4), sin(x) - 2 * sin(x/4)], (x,0, 8*pi), fill=True)
+        sage: parametric_plot([cos(x) + 2 * cos(x/4), sin(x) - 2 * sin(x/4)],
+        ....:                 (x, 0, 8*pi), fill=True)
         Graphics object consisting of 2 graphics primitives
 
     .. PLOT::
 
-        g = parametric_plot([cos(x) + 2 * cos(x/4), sin(x) - 2 * sin(x/4)], (x,0, 8*pi), fill=True)
+        g = parametric_plot([cos(x) + 2 * cos(x/4), sin(x) - 2 * sin(x/4)], (x, 0, 8*pi), fill=True)
         sphinx_plot(g)
 
     ::
 
-        sage: parametric_plot( (5*cos(x), 5*sin(x), x), (x,-12, 12), plot_points=150, color="red") # long time
+        sage: parametric_plot((5*cos(x), 5*sin(x), x), (x, -12, 12),  # long time
+        ....:                 plot_points=150, color="red")
         Graphics3d Object
 
     .. PLOT::
@@ -2829,7 +2831,8 @@ def polar_plot(funcs, *args, **kwds):
 
     Fill the area between two functions::
 
-        sage: polar_plot(cos(4*x) + 1.5, 0, 2*pi, fill=0.5 * cos(4*x) + 2.5, fillcolor='orange')
+        sage: polar_plot(cos(4*x) + 1.5, 0, 2*pi, fill=0.5 * cos(4*x) + 2.5,
+        ....:            fillcolor='orange')
         Graphics object consisting of 2 graphics primitives
 
     .. PLOT::
@@ -2839,7 +2842,8 @@ def polar_plot(funcs, *args, **kwds):
 
     Fill the area between several spirals::
 
-        sage: polar_plot([(1.2+k*0.2)*log(x) for k in range(6)], 1, 3 * pi, fill={0: [1], 2: [3], 4: [5]})
+        sage: polar_plot([(1.2+k*0.2)*log(x) for k in range(6)], 1, 3 * pi,
+        ....:            fill={0: [1], 2: [3], 4: [5]})
         Graphics object consisting of 9 graphics primitives
 
     .. PLOT::
@@ -2895,7 +2899,7 @@ def list_plot(data, plotjoined=False, **kwargs):
 
     EXAMPLES::
 
-        sage: list_plot([i^2 for i in range(5)]) # long time
+        sage: list_plot([i^2 for i in range(5)])  # long time
         Graphics object consisting of 1 graphics primitive
 
     .. PLOT::
@@ -3008,7 +3012,9 @@ def list_plot(data, plotjoined=False, **kwargs):
         sage: list_plot(x_coords, y_coords)
         Traceback (most recent call last):
         ...
-        TypeError: The second argument 'plotjoined' should be boolean (True or False).  If you meant to plot two lists 'x' and 'y' against each other, use 'list_plot(list(zip(x,y)))'.
+        TypeError: The second argument 'plotjoined' should be boolean (True or False).
+        If you meant to plot two lists 'x' and 'y' against each other,
+        use 'list_plot(list(zip(x,y)))'.
 
     Dictionaries with numeric keys and values can be plotted::
 
@@ -3055,12 +3061,12 @@ def list_plot(data, plotjoined=False, **kwargs):
 
         Instead this will work. We drop the point `(0,1)`.::
 
-            sage: list_plot(list(zip(range(1,len(yl)), yl[1:])), scale='loglog') # long time
+            sage: list_plot(list(zip(range(1,len(yl)), yl[1:])), scale='loglog')  # long time
             Graphics object consisting of 1 graphics primitive
 
     We use :func:`list_plot_loglog` and plot in a different base.::
 
-        sage: list_plot_loglog(list(zip(range(1,len(yl)), yl[1:])), base=2) # long time
+        sage: list_plot_loglog(list(zip(range(1,len(yl)), yl[1:])), base=2)  # long time
         Graphics object consisting of 1 graphics primitive
 
     .. PLOT::
@@ -3267,22 +3273,22 @@ def plot_semilogy(funcs, *args, **kwds):
 
     EXAMPLES::
 
-        sage: plot_semilogy(exp, (1,10)) # long time # plot in semilogy scale, base 10
+        sage: plot_semilogy(exp, (1, 10))  # long time # plot in semilogy scale, base 10
         Graphics object consisting of 1 graphics primitive
 
     .. PLOT::
 
-        g = plot_semilogy(exp, (1,10)) # long time # plot in semilogy scale, base 10
+        g = plot_semilogy(exp, (1,10))  # long time # plot in semilogy scale, base 10
         sphinx_plot(g)
 
     ::
 
-        sage: plot_semilogy(exp, (1,10), base=2) # long time # with base 2
+        sage: plot_semilogy(exp, (1, 10), base=2)  # long time # with base 2
         Graphics object consisting of 1 graphics primitive
 
     .. PLOT::
 
-        g = plot_semilogy(exp, (1,10), base=2) # long time # with base 2
+        g = plot_semilogy(exp, (1,10), base=2)  # long time # with base 2
         sphinx_plot(g)
 
     """
@@ -3505,13 +3511,14 @@ def reshape(v, n, m):
 
     ::
 
-        sage: M = [[plot(sin(k*x),(x,-pi,pi)) for k in range(3)],[plot(cos(j*x),(x,-pi,pi)) for j in [3..5]]]
+        sage: M = [[plot(sin(k*x), (x,-pi,pi)) for k in range(3)],
+        ....:      [plot(cos(j*x), (x,-pi,pi)) for j in [3..5]]]
         sage: graphics_array(M,6,1)  # long time (up to 4s on sage.math, 2012)
         Graphics Array of size 6 x 1
 
     TESTS::
 
-        sage: L = [plot(sin(k*x),(x,-pi,pi)) for k in [1..3]]
+        sage: L = [plot(sin(k*x), (x,-pi,pi)) for k in [1..3]]
         sage: graphics_array(L,0,-1) # indirect doctest
         Traceback (most recent call last):
         ...
@@ -3620,6 +3627,7 @@ def h(x): return sin(4*x)
     It is possible to use ``figsize`` to change the size of the plot
     as a whole::
 
+        sage: x = var('x')
         sage: L = [plot(sin(k*x), (x,-pi,pi)) for k in [1..3]]
         sage: ga = graphics_array(L)
         sage: ga.show(figsize=[5,3])  # smallish and compact
@@ -3860,7 +3868,8 @@ def adaptive_refinement(f, p1, p2, adaptive_tolerance=0.01,
     TESTS::
 
         sage: from sage.plot.plot import adaptive_refinement
-        sage: adaptive_refinement(sin, (0,0), (pi,0), adaptive_tolerance=0.01, adaptive_recursion=0)
+        sage: adaptive_refinement(sin, (0,0), (pi,0), adaptive_tolerance=0.01,
+        ....:                     adaptive_recursion=0)
         []
         sage: adaptive_refinement(sin, (0,0), (pi,0), adaptive_tolerance=0.01)
         [(0.125*pi, 0.3826834323650898), (0.1875*pi, 0.5555702330196022),
@@ -3881,7 +3890,8 @@ def adaptive_refinement(f, p1, p2, adaptive_tolerance=0.01,
         sage: f(x) = sin(1/x)
         sage: n1 = len(adaptive_refinement(f, (0,0), (pi,0), adaptive_tolerance=0.01)); n1
         15
-        sage: n2 = len(adaptive_refinement(f, (0,0), (pi,0), adaptive_recursion=10, adaptive_tolerance=0.01)); n2
+        sage: n2 = len(adaptive_refinement(f, (0,0), (pi,0), adaptive_recursion=10,
+        ....:                              adaptive_tolerance=0.01)); n2
         79
         sage: n3 = len(adaptive_refinement(f, (0,0), (pi,0), adaptive_tolerance=0.001)); n3
         26

src/sage/plot/plot3d/base.pyx

@@ -1998,9 +1998,10 @@ end_scene""".format(
 
         This works when faces have more then 3 sides::
 
-            sage: P = polytopes.dodecahedron()                                          # needs sage.geometry.polyhedron
-            sage: Q = P.plot().all[-1]                                                  # needs sage.geometry.polyhedron
-            sage: print(Q.stl_binary()[:40].decode('ascii'))                            # needs sage.geometry.polyhedron
+            sage: # needs sage.geometry.polyhedron sage.groups
+            sage: P = polytopes.dodecahedron()
+            sage: Q = P.plot().all[-1]
+            sage: print(Q.stl_binary()[:40].decode('ascii'))
             STL binary file / made by SageMath / ###
         """
         import struct
@@ -2060,9 +2061,10 @@ end_scene""".format(
 
         Now works when faces have more then 3 sides::
 
-            sage: P = polytopes.dodecahedron()                                          # needs sage.geometry.polyhedron
-            sage: Q = P.plot().all[-1]                                                  # needs sage.geometry.polyhedron
-            sage: print(Q.stl_ascii_string().splitlines()[:7])                          # needs sage.geometry.polyhedron
+            sage: # needs sage.geometry.polyhedron sage.groups
+            sage: P = polytopes.dodecahedron()
+            sage: Q = P.plot().all[-1]
+            sage: print(Q.stl_ascii_string().splitlines()[:7])
             ['solid surface',
              'facet normal 0.0 0.5257311121191338 0.8506508083520399',
              '    outer loop',

src/sage/plot/plot3d/list_plot3d.py

@@ -530,7 +530,8 @@ def list_plot3d_tuples(v, interpolation_type, **kwds):
 
     .. PLOT::
 
-        sphinx_plot(list_plot3d([[1, 1, 1], [1, 2, 1], [0, 1, 3], [1, 0, 4]], point_list=True))
+        sphinx_plot(list_plot3d([[1, 1, 1], [1, 2, 1], [0, 1, 3], [1, 0, 4]],
+                                point_list=True))
 
     ::
 

src/sage/plot/plot3d/revolution_plot3d.py

@@ -1,4 +1,4 @@
-# sage.doctest: needs sage.plot
+# sage.doctest: needs sage.plot sage.symbolic
 """
 Surfaces of revolution