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Trac #32993: add pictures to line.py documentation
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The examples lacked their plot counterpart

URL: https://trac.sagemath.org/32993
Reported by: jhonrubia6
Ticket author(s): Javier Honrubia González
Reviewer(s): Kwankyu Lee
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Release Manager committed Feb 12, 2022
2 parents 3834fde + 9d5eea3 commit 69d9945
Showing 1 changed file with 126 additions and 21 deletions.
147 changes: 126 additions & 21 deletions src/sage/plot/line.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,7 +2,7 @@
Line Plots
"""

#*****************************************************************************
# *****************************************************************************
# Copyright (C) 2006 Alex Clemesha <[email protected]>,
# William Stein <[email protected]>,
# 2008 Mike Hansen <[email protected]>,
Expand All @@ -17,11 +17,12 @@
# The full text of the GPL is available at:
#
# http://www.gnu.org/licenses/
#*****************************************************************************
# *****************************************************************************
from sage.plot.primitive import GraphicPrimitive_xydata
from sage.misc.decorators import options, rename_keyword
from sage.plot.colors import to_mpl_color


class Line(GraphicPrimitive_xydata):
"""
Primitive class that initializes the line graphics type.
Expand Down Expand Up @@ -73,19 +74,19 @@ def _allowed_options(self):
('thickness', 'How thick the line is.'),
('zorder', 'The layer level in which to draw')]
"""
return {'alpha':'How transparent the line is.',
'legend_color':'The color of the legend text.',
'legend_label':'The label for this item in the legend.',
'thickness':'How thick the line is.',
'rgbcolor':'The color as an RGB tuple.',
'hue':'The color given as a hue.',
'linestyle':"The style of the line, which is one of '--' (dashed), '-.' (dash dot), '-' (solid), 'steps', ':' (dotted).",
'marker':"the marker symbol (see documentation for line2d for details)",
'markersize':'the size of the marker in points',
'markeredgecolor':'the color of the marker edge',
'markeredgewidth':'the size of the marker edge in points',
'markerfacecolor':'the color of the marker face',
'zorder':'The layer level in which to draw'
return {'alpha': 'How transparent the line is.',
'legend_color': 'The color of the legend text.',
'legend_label': 'The label for this item in the legend.',
'thickness': 'How thick the line is.',
'rgbcolor': 'The color as an RGB tuple.',
'hue': 'The color given as a hue.',
'linestyle': "The style of the line, which is one of '--' (dashed), '-.' (dash dot), '-' (solid), 'steps', ':' (dotted).",
'marker': "the marker symbol (see documentation for line2d for details)",
'markersize': 'the size of the marker in points',
'markeredgecolor': 'the color of the marker edge',
'markeredgewidth': 'the size of the marker edge in points',
'markerfacecolor': 'the color of the marker face',
'zorder': 'The layer level in which to draw'
}

def _plot3d_options(self, options=None):
Expand Down Expand Up @@ -118,7 +119,7 @@ def _plot3d_options(self, options=None):
del options['zorder']
if 'linestyle' in options:
if options['linestyle'] not in ('-', 'solid'):
raise NotImplementedError("Invalid 3d line style: '%s'"%
raise NotImplementedError("Invalid 3d line style: '%s'" %
(options['linestyle']))
del options['linestyle']
options_3d.update(GraphicPrimitive_xydata._plot3d_options(self, options))
Expand All @@ -134,6 +135,13 @@ def plot3d(self, z=0, **kwds):
sage: F = EllipticCurve('37a').plot(thickness=5).plot3d(z=2)
sage: E + F # long time (5s on sage.math, 2012)
Graphics3d Object
.. PLOT::
E = EllipticCurve('37a').plot(thickness=5).plot3d()
F = EllipticCurve('37a').plot(thickness=5).plot3d(z=2)
sphinx_plot(E+F)
"""
from sage.plot.plot3d.shapes2 import line3d
options = self._plot3d_options()
Expand All @@ -150,7 +158,7 @@ def _repr_(self):
sage: Line([-1,2,3,3], [17,4,0,2], {})._repr_()
'Line defined by 4 points'
"""
return "Line defined by %s points"%len(self)
return "Line defined by %s points" % len(self)

def __getitem__(self, i):
"""
Expand Down Expand Up @@ -265,6 +273,7 @@ def _render_on_subplot(self, subplot):
return_type='short'))
subplot.add_line(p)


def line(points, **kwds):
"""
Returns either a 2-dimensional or 3-dimensional line depending
Expand All @@ -283,10 +292,20 @@ def line(points, **kwds):
sage: line([(0,0), (1,1)])
Graphics object consisting of 1 graphics primitive
.. PLOT::
E = line([(0,0), (1,1)])
sphinx_plot(E)
::
sage: line([(0,0,1), (1,1,1)])
Graphics3d Object
.. PLOT::
E = line([(0,0,1), (1,1,1)])
sphinx_plot(E)
"""
try:
return line2d(points, **kwds)
Expand All @@ -296,8 +315,8 @@ def line(points, **kwds):


@rename_keyword(color='rgbcolor')
@options(alpha=1, rgbcolor=(0,0,1), thickness=1, legend_label=None,
legend_color=None, aspect_ratio ='automatic')
@options(alpha=1, rgbcolor=(0, 0, 1), thickness=1, legend_label=None,
legend_color=None, aspect_ratio='automatic')
def line2d(points, **options):
r"""
Create the line through the given list of points.
Expand Down Expand Up @@ -387,13 +406,23 @@ def line2d(points, **options):
sage: line([(0,0),(1,1)], legend_label='line')
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(line([(0,0),(1,1)], legend_label='line'))
Lines with different colors in the legend text::
sage: p1 = line([(0,0),(1,1)], legend_label='line')
sage: p2 = line([(1,1),(2,4)], legend_label='squared', legend_color='red')
sage: p1 + p2
Graphics object consisting of 2 graphics primitives
.. PLOT::
p1 = line([(0,0),(1,1)], legend_label='line')
p2 = line([(1,1),(2,4)], legend_label='squared', legend_color='red')
sphinx_plot(p1 + p2)
Extra options will get passed on to show(), as long as they are valid::
sage: line([(0,1), (3,4)], figsize=[10, 2])
Expand All @@ -405,6 +434,10 @@ def line2d(points, **options):
sage: line([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='loglog',base=2)
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(line([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='loglog',base=2))
Many more examples below!
A blue conchoid of Nicomedes::
Expand All @@ -413,38 +446,73 @@ def line2d(points, **options):
sage: line(L, rgbcolor=(1/4,1/8,3/4))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[1+5*cos(pi/2+pi*i/100), tan(pi/2+pi*i/100)*(1+5*cos(pi/2+pi*i/100))] for i in range(1,100)]
sphinx_plot(line(L, rgbcolor=(1/4,1/8,3/4)))
A line with 2 complex points::
sage: i = CC.0
sage: i = CC(0,1)
sage: line([1+i, 2+3*i])
Graphics object consisting of 1 graphics primitive
.. PLOT::
i = CC(0,1)
o = line([1+i, 2+3*i])
sphinx_plot(o)
A blue hypotrochoid (3 leaves)::
sage: n = 4; h = 3; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: line(L, rgbcolor=(1/4,1/4,3/4))
Graphics object consisting of 1 graphics primitive
.. PLOT::
n = 4
h = 3
b = 2
L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
o = line(L, rgbcolor=(1/4,1/4,3/4))
sphinx_plot(o)
A blue hypotrochoid (4 leaves)::
sage: n = 6; h = 5; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: line(L, rgbcolor=(1/4,1/4,3/4))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,101)]
sphinx_plot(line(L, rgbcolor=(1,1/4,1/2)))
A red limacon of Pascal::
sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,101)]
sage: line(L, rgbcolor=(1,1/4,1/2))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,101)]
sphinx_plot(line(L, rgbcolor=(1,1/4,1/2)))
A light green trisectrix of Maclaurin::
sage: L = [[2*(1-4*cos(-pi/2+pi*i/100)^2),10*tan(-pi/2+pi*i/100)*(1-4*cos(-pi/2+pi*i/100)^2)] for i in range(1,100)]
sage: line(L, rgbcolor=(1/4,1,1/8))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[2*(1-4*cos(-pi/2+pi*i/100)**2),10*tan(-pi/2+pi*i/100)*(1-4*cos(-pi/2+pi*i/100)**2)] for i in range(1,100)]
sphinx_plot(line(L, rgbcolor=(1/4,1,1/8)))
A green lemniscate of Bernoulli::
sage: cosines = [cos(-pi/2+pi*i/100) for i in range(201)]
Expand All @@ -453,19 +521,35 @@ def line2d(points, **options):
sage: line(L, rgbcolor=(1/4,3/4,1/8))
Graphics object consisting of 1 graphics primitive
.. PLOT::
cosines = [cos(-pi/2+pi*i/100) for i in range(201)]
v = [(1/c, tan(-pi/2+pi*i/100)) for i,c in enumerate(cosines) if c != 0]
L = [(a/(a**2+b**2), b/(a**2+b**2)) for a,b in v]
sphinx_plot(line(L, rgbcolor=(1/4,3/4,1/8)))
A red plot of the Jacobi elliptic function `\text{sn}(x,2)`, `-3 < x < 3`::
sage: L = [(i/100.0, real_part(jacobi('sn', i/100.0, 2.0))) for i in
....: range(-300, 300, 30)]
sage: line(L, rgbcolor=(3/4, 1/4, 1/8))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [(i/100.0, real_part(jacobi('sn', i/100.0, 2.0))) for i in range(-300, 300, 30)]
sphinx_plot(line(L, rgbcolor=(3/4, 1/4, 1/8)))
A red plot of `J`-Bessel function `J_2(x)`, `0 < x < 10`::
sage: L = [(i/10.0, bessel_J(2,i/10.0)) for i in range(100)]
sage: line(L, rgbcolor=(3/4,1/4,5/8))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [(i/10.0, bessel_J(2,i/10.0)) for i in range(100)]
sphinx_plot(line(L, rgbcolor=(3/4,1/4,5/8)))
A purple plot of the Riemann zeta function `\zeta(1/2 + it)`, `0 < t < 30`::
Expand All @@ -475,6 +559,13 @@ def line2d(points, **options):
sage: line(L, rgbcolor=(3/4,1/2,5/8))
Graphics object consisting of 1 graphics primitive
.. PLOT::
i = CDF.gen()
v = [zeta(0.5 + n/10 * i) for n in range(300)]
L = [(z.real(), z.imag()) for z in v]
sphinx_plot(line(L, rgbcolor=(3/4,1/2,5/8)))
A purple plot of the Hasse-Weil `L`-function `L(E, 1 + it)`, `-1 < t < 10`::
sage: E = EllipticCurve('37a')
Expand All @@ -483,6 +574,13 @@ def line2d(points, **options):
sage: line(L, rgbcolor=(3/4,1/2,5/8))
Graphics object consisting of 1 graphics primitive
.. PLOT ::
E = EllipticCurve('37a')
vals = E.lseries().values_along_line(1-I, 1+10*I, 100) # critical line
L = [(z[1].real(), z[1].imag()) for z in vals]
sphinx_plot(line(L, rgbcolor=(3/4,1/2,5/8)))
A red, blue, and green "cool cat"::
sage: G = plot(-cos(x), -2, 2, thickness=5, rgbcolor=(0.5,1,0.5))
Expand All @@ -491,6 +589,13 @@ def line2d(points, **options):
sage: G + P + Q # show the plot
Graphics object consisting of 3 graphics primitives
.. PLOT::
G = plot(-cos(x), -2, 2, thickness=5, rgbcolor=(0.5,1,0.5))
P = polygon([[1,2], [5,6], [5,0]], rgbcolor=(1,0,0))
Q = polygon([(-x,y) for x,y in P[0]], rgbcolor=(0,0,1))
sphinx_plot(G + P + Q)
TESTS:
Check that :trac:`13690` is fixed. The legend label should have circles
Expand All @@ -501,7 +606,7 @@ def line2d(points, **options):
"""
from sage.plot.all import Graphics
from sage.plot.plot import xydata_from_point_list
points = list(points) # make sure points is a python list
points = list(points) # make sure points is a python list
if not points:
return Graphics()
xdata, ydata = xydata_from_point_list(points)
Expand Down

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