sage.plot: More # optional

Author: Matthias Koeppe

src/sage/plot/animate.py

@@ -1,4 +1,4 @@
-# -*- coding: utf-8 -*-
+# sage.doctest: optional - sage.symbolic
 r"""
 Animated plots
 
@@ -31,7 +31,8 @@
 The sine function::
 
     sage: x = SR.var("x")
-    sage: sines = [plot(c*sin(x), (-2*pi,2*pi), color=Color(c,0,0), ymin=-1, ymax=1) for c in sxrange(0,1,.2)]
+    sage: sines = [plot(c*sin(x), (-2*pi,2*pi), color=Color(c,0,0), ymin=-1, ymax=1)
+    ....:          for c in sxrange(0,1,.2)]
     sage: a = animate(sines)
     sage: print(a)
     Animation with 5 frames
@@ -48,24 +49,32 @@
 
 An animated :class:`sage.plot.multigraphics.GraphicsArray` of rotating ellipses::
 
-    sage: E = animate((graphics_array([[ellipse((0,0),a,b,angle=t,xmin=-3,xmax=3)+circle((0,0),3,color='blue') for a in range(1,3)] for b in range(2,4)]) for t in sxrange(0,pi/4,.15)))
+    sage: E = animate((graphics_array([[ellipse((0,0), a, b, angle=t, xmin=-3, xmax=3)
+    ....:                                + circle((0,0), 3, color='blue')
+    ....:                               for a in range(1,3)]
+    ....:                              for b in range(2,4)])
+    ....:              for t in sxrange(0, pi/4, .15)))
     sage: str(E)    # animations produced from a generator do not have a known length
     'Animation with unknown number of frames'
     sage: E.show()                  # long time  # optional -- ImageMagick
 
 A simple animation of a circle shooting up to the right::
 
-    sage: c = animate([circle((i,i), 1-1/(i+1), hue=i/10) for i in srange(0,2,0.2)],
-    ....:               xmin=0,ymin=0,xmax=2,ymax=2,figsize=[2,2])
+    sage: c = animate([circle((i,i), 1 - 1/(i+1), hue=i/10)
+    ....:              for i in srange(0, 2, 0.2)],
+    ....:             xmin=0, ymin=0, xmax=2, ymax=2, figsize=[2,2])
     sage: c.show()                  # long time  # optional -- ImageMagick
 
 
 Animations of 3d objects::
 
     sage: s,t = SR.var("s,t")
     sage: def sphere_and_plane(x):
-    ....:     return sphere((0,0,0),1,color='red',opacity=.5)+parametric_plot3d([t,x,s],(s,-1,1),(t,-1,1),color='green',opacity=.7)
-    sage: sp = animate([sphere_and_plane(x) for x in sxrange(-1,1,.3)])
+    ....:     return (sphere((0,0,0), 1, color='red', opacity=.5)
+    ....:              + parametric_plot3d([t,x,s], (s,-1,1), (t,-1,1),
+    ....:                                  color='green', opacity=.7))
+    sage: sp = animate([sphere_and_plane(x)
+    ....:               for x in sxrange(-1, 1, .3)])
     sage: sp[0]      # first frame
     Graphics3d Object
     sage: sp[-1]     # last frame
@@ -74,9 +83,13 @@
 
     sage: (x,y,z) = SR.var("x,y,z")
     sage: def frame(t):
-    ....:     return implicit_plot3d((x^2 + y^2 + z^2), (x, -2, 2), (y, -2, 2), (z, -2, 2), plot_points=60, contour=[1,3,5], region=lambda x,y,z: x<=t or y>=t or z<=t)
-    sage: a = animate([frame(t) for t in srange(.01,1.5,.2)])
-    sage: a[0]       # long time
+    ....:     return implicit_plot3d((x^2 + y^2 + z^2),
+    ....:                            (x, -2, 2), (y, -2, 2), (z, -2, 2),
+    ....:                            plot_points=60, contour=[1,3,5],
+    ....:                            region=lambda x,y,z: x<=t or y>=t or z<=t)
+    sage: a = animate([frame(t)
+    ....:              for t in srange(.01,1.5,.2)])
+    sage: a[0]                      # long time
     Graphics3d Object
     sage: a.show()                  # long time  # optional -- ImageMagick
 
@@ -86,7 +99,8 @@
 illustrated by the following example::
 
     sage: t = SR.var("t")
-    sage: a = animate((sin(c*pi*t) for c in sxrange(1,2,.2)))
+    sage: a = animate((sin(c*pi*t)
+    ....:              for c in sxrange(1, 2, .2)))
     sage: a.show()                  # long time  # optional -- ImageMagick
 
 
@@ -135,7 +149,8 @@ def animate(frames, **kwds):
     EXAMPLES::
 
         sage: t = SR.var("t")
-        sage: a = animate((cos(c*pi*t) for c in sxrange(1,2,.2)))
+        sage: a = animate((cos(c*pi*t)
+        ....:              for c in sxrange(1, 2, .2)))
         sage: a.show()              # long time  # optional -- ImageMagick
 
     See also :mod:`sage.plot.animate` for more examples.
@@ -149,22 +164,23 @@ class Animation(WithEqualityById, SageObject):
     INPUT:
 
 
-    - ``v`` - iterable of Sage objects. These should preferably be
-      graphics objects, but if they aren't then :meth:`make_image` is
+    - ``v`` -- iterable of Sage objects. These should preferably be
+      graphics objects, but if they aren't, then :meth:`make_image` is
       called on them.
 
-    - ``xmin, xmax, ymin, ymax`` - the ranges of the x and y axes.
+    - ``xmin, xmax, ymin, ymax`` -- the ranges of the x and y axes.
 
-    - ``**kwds`` - all additional inputs are passed onto the rendering
-      command. E.g., use figsize to adjust the resolution and aspect
+    - ``**kwds`` -- all additional inputs are passed onto the rendering
+      command. E.g., use ``figsize`` to adjust the resolution and aspect
       ratio.
 
 
     EXAMPLES::
 
         sage: x = SR.var("x")
-        sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.3)],
-        ....:                xmin=0, xmax=2*pi, figsize=[2,1])
+        sage: a = animate([sin(x + float(k))
+        ....:              for k in srange(0, 2*pi, 0.3)],
+        ....:             xmin=0, xmax=2*pi, figsize=[2,1])
         sage: print(a)
         Animation with 21 frames
         sage: print(a[:5])
@@ -185,9 +201,9 @@ class Animation(WithEqualityById, SageObject):
         sage: step = 0.1
         sage: L = Graphics()
         sage: v = []
-        sage: for i in srange(0,1,step):
-        ....:       L += line([(i,i^2),(i+step,(i+step)^2)], rgbcolor=(1,0,0), thickness=2)
-        ....:       v.append(L)
+        sage: for i in srange(0, 1, step):
+        ....:     L += line([(i,i^2),(i+step,(i+step)^2)], rgbcolor=(1,0,0), thickness=2)
+        ....:     v.append(L)
         sage: a = animate(v, xmin=0, ymin=0)
         sage: a.show()              # long time  # optional -- ImageMagick
         sage: show(L)
@@ -427,7 +443,9 @@ def make_image(self, frame, filename, **kwds):
             sage: t = SR.var("t")
             sage: x = lambda t: cos(t)
             sage: y = lambda n,t: sin(t)/n
-            sage: B = MyAnimation([([x(t), y(i+1,t)],(t,0,1), {'color':Color((1,0,i/4)), 'aspect_ratio':1, 'ymax':1}) for i in range(4)])
+            sage: B = MyAnimation([([x(t), y(i+1,t)], (t,0,1),
+            ....:                   {'color':Color((1,0,i/4)), 'aspect_ratio':1, 'ymax':1})
+            ....:                  for i in range(4)])
 
             sage: d = B.png(); v = os.listdir(d); v.sort(); v  # long time
             ['00000000.png', '00000001.png', '00000002.png', '00000003.png']
@@ -436,10 +454,12 @@ def make_image(self, frame, filename, **kwds):
             sage: class MyAnimation(Animation):
             ....:    def make_image(self, frame, filename, **kwds):
             ....:        G = frame.plot()
-            ....:        G.set_axes_range(floor(G.xmin()),ceil(G.xmax()),floor(G.ymin()),ceil(G.ymax()))
+            ....:        G.set_axes_range(floor(G.xmin()), ceil(G.xmax()),
+            ....:                         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']
@@ -506,26 +526,27 @@ def graphics_array(self, ncols=3):
 
         EXAMPLES::
 
-            sage: E = EllipticCurve('37a')
-            sage: v = [E.change_ring(GF(p)).plot(pointsize=30) for p in [97, 101, 103]]
-            sage: a = animate(v, xmin=0, ymin=0, axes=False)
-            sage: print(a)
+            sage: E = EllipticCurve('37a')                                              # optional - sage.schemes
+            sage: v = [E.change_ring(GF(p)).plot(pointsize=30)                          # optional - sage.rings.finite_rings sage.schemes
+            ....:      for p in [97, 101, 103]]
+            sage: a = animate(v, xmin=0, ymin=0, axes=False)                            # optional - sage.rings.finite_rings sage.schemes
+            sage: print(a)                                                              # optional - sage.rings.finite_rings sage.schemes
             Animation with 3 frames
-            sage: a.show()  # optional -- ImageMagick
+            sage: a.show()  # optional -- ImageMagick                                   # optional - sage.rings.finite_rings sage.schemes
 
         Modify the default arrangement of array::
 
-            sage: g = a.graphics_array(); print(g)
+            sage: g = a.graphics_array(); print(g)                                      # optional - sage.rings.finite_rings sage.schemes
             Graphics Array of size 1 x 3
-            sage: g.show(figsize=[6,3])
+            sage: g.show(figsize=[6,3])                                                 # optional - sage.rings.finite_rings sage.schemes
 
         Specify different arrangement of array and save it with a given file name::
 
-            sage: g = a.graphics_array(ncols=2); print(g)
+            sage: g = a.graphics_array(ncols=2); print(g)                               # optional - sage.rings.finite_rings sage.schemes
             Graphics Array of size 2 x 2
-            sage: f = tmp_filename(ext='.png'); print(f)
+            sage: f = tmp_filename(ext='.png'); print(f)                                # optional - sage.rings.finite_rings sage.schemes
             ...png
-            sage: g.save(f)
+            sage: g.save(f)                                                             # optional - sage.rings.finite_rings sage.schemes
 
         Frames can be specified as a generator too; it is internally converted to a list::
 
@@ -580,16 +601,21 @@ def gif(self, delay=20, savefile=None, iterations=0, show_path=False,
         EXAMPLES::
 
             sage: x = SR.var("x")
-            sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
+            sage: a = animate([sin(x + float(k))
+            ....:              for k in srange(0,2*pi,0.7)],
             ....:             xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1])
             sage: td = tmp_dir()
             sage: a.gif()              # not tested
-            sage: a.gif(savefile=td + 'my_animation.gif', delay=35, iterations=3)             # long time  # optional -- ImageMagick
-            sage: with open(td + 'my_animation.gif', 'rb') as f: print(b'GIF8' in f.read())   # long time  # optional -- ImageMagick
+            sage: a.gif(savefile=td + 'my_animation.gif',               # long time  # optional -- ImageMagick
+            ....:       delay=35, iterations=3)
+            sage: with open(td + 'my_animation.gif', 'rb') as f:        # long time  # optional -- ImageMagick
+            ....:     print(b'GIF8' in f.read())
             True
-            sage: a.gif(savefile=td + 'my_animation.gif', show_path=True)                     # long time  # optional -- ImageMagick
+            sage: a.gif(savefile=td + 'my_animation.gif',               # long time  # optional -- ImageMagick
+            ....:       show_path=True)
             Animation saved to .../my_animation.gif.
-            sage: a.gif(savefile=td + 'my_animation_2.gif', show_path=True, use_ffmpeg=True)  # long time  # optional -- ffmpeg
+            sage: a.gif(savefile=td + 'my_animation_2.gif',             # long time  # optional -- ffmpeg
+            ....:       show_path=True, use_ffmpeg=True)
             Animation saved to .../my_animation_2.gif.
 
         .. NOTE::
@@ -810,8 +836,9 @@ def show(self, delay=None, iterations=None, **kwds):
         EXAMPLES::
 
             sage: x = SR.var("x")
-            sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
-            ....:                xmin=0, xmax=2*pi, figsize=[2,1])
+            sage: a = animate([sin(x + float(k))
+            ....:              for k in srange(0,2*pi,0.7)],
+            ....:             xmin=0, xmax=2*pi, figsize=[2,1])
             sage: a.show()                              # long time  # optional -- ImageMagick
 
         The preceding will loop the animation forever. If you want to show
@@ -922,7 +949,8 @@ def ffmpeg(self, savefile=None, show_path=False, output_format=None,
         EXAMPLES::
 
             sage: x = SR.var("x")
-            sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
+            sage: a = animate([sin(x + float(k))
+            ....:              for k in srange(0, 2*pi, 0.7)],
             ....:             xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1])
             sage: td = tmp_dir()
             sage: a.ffmpeg(savefile=td + 'new.mpg')                  # long time  # optional -- ffmpeg
@@ -1042,8 +1070,9 @@ def apng(self, savefile=None, show_path=False, delay=20, iterations=0):
         EXAMPLES::
 
             sage: x = SR.var("x")
-            sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
-            ....:                xmin=0, xmax=2*pi, figsize=[2,1])
+            sage: a = animate([sin(x + float(k))
+            ....:              for k in srange(0,2*pi,0.7)],
+            ....:             xmin=0, xmax=2*pi, figsize=[2,1])
             sage: dir = tmp_dir()
             sage: a.apng(show_path=True)  # long time
             Animation saved to ....png.
@@ -1053,7 +1082,8 @@ def apng(self, savefile=None, show_path=False, delay=20, iterations=0):
 
         If the individual frames have different sizes, an error will be raised::
 
-            sage: a = animate([plot(sin(x), (x, 0, k)) for k in range(1,4)],
+            sage: a = animate([plot(sin(x), (x, 0, k))
+            ....:              for k in range(1,4)],
             ....:             ymin=-1, ymax=1, aspect_ratio=1, figsize=[2,1])
             sage: a.apng()  # long time
             Traceback (most recent call last):
@@ -1111,7 +1141,8 @@ def save(self, filename=None, show_path=False, use_ffmpeg=False, **kwds):
         EXAMPLES::
 
             sage: x = SR.var("x")
-            sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
+            sage: a = animate([sin(x + float(k))
+            ....:              for k in srange(0, 2*pi, 0.7)],
             ....:             xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1])
             sage: td = tmp_dir()
             sage: a.save()         # not tested
@@ -1194,7 +1225,8 @@ def interactive(self, **kwds):
         EXAMPLES::
 
             sage: x = SR.var("x")
-            sage: frames = [point3d((sin(x), cos(x), x)) for x in (0, pi/16, .., 2*pi)]
+            sage: frames = [point3d((sin(x), cos(x), x))
+            ....:           for x in (0, pi/16, .., 2*pi)]
             sage: animate(frames).interactive(online=True)
             Graphics3d Object
 
@@ -1245,16 +1277,16 @@ class APngAssembler():
 
     INPUT:
 
-        - ``out`` -- a file opened for binary writing to which the data
-          will be written
+    - ``out`` -- a file opened for binary writing to which the data
+      will be written
 
-        - ``num_frames`` -- the number of frames in the animation
+    - ``num_frames`` -- the number of frames in the animation
 
-        - ``num_plays`` -- how often to iterate, 0 means infinitely
+    - ``num_plays`` -- how often to iterate, 0 means infinitely
 
-        - ``delay`` -- numerator of the delay fraction in seconds
+    - ``delay`` -- numerator of the delay fraction in seconds
 
-        - ``delay_denominator`` -- denominator of the delay in seconds
+    - ``delay_denominator`` -- denominator of the delay in seconds
 
     EXAMPLES::
 

src/sage/plot/arrow.py

@@ -586,7 +586,8 @@ def arrow2d(tailpoint=None, headpoint=None, path=None, **options):
 
     A pretty circle of arrows::
 
-        sage: sum([arrow2d((0,0), (cos(x),sin(x)), hue=x/(2*pi)) for x in [0..2*pi,step=0.1]])
+        sage: sum(arrow2d((0,0), (cos(x),sin(x)), hue=x/(2*pi))                         # optional - sage.symbolic
+        ....:     for x in [0..2*pi, step=0.1])
         Graphics object consisting of 63 graphics primitives
 
     .. PLOT::

src/sage/plot/bezier_path.py

@@ -168,9 +168,9 @@ def plot3d(self, z=0, **kwds):
         EXAMPLES::
 
             sage: b = bezier_path([[(0,0),(0,1),(1,0)]])
-            sage: A = b.plot3d()
-            sage: B = b.plot3d(z=2)
-            sage: A + B
+            sage: A = b.plot3d()                                                        # optional - sage.symbolic
+            sage: B = b.plot3d(z=2)                                                     # optional - sage.symbolic
+            sage: A + B                                                                 # optional - sage.symbolic
             Graphics3d Object
 
         .. PLOT::
@@ -182,7 +182,7 @@ def plot3d(self, z=0, **kwds):
 
         ::
 
-            sage: bezier3d([[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]])
+            sage: bezier3d([[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]])                         # optional - sage.symbolic
             Graphics3d Object
 
         .. PLOT::