Points¶
- class sage.plot.point.Point(xdata, ydata, options)[source]¶
- Bases: - GraphicPrimitive_xydata- Primitive class for the point graphics type. See point?, point2d? or point3d? for information about actually plotting points. - INPUT: - xdata– list of x values for points in Point object
- ydata– list of y values for points in Point object
- options– dictionary of valid plot options to pass to constructor
 - EXAMPLES: - Note this should normally be used indirectly via - point()and friends:- sage: from sage.plot.point import Point sage: P = Point([1,2],[2,3],{'alpha':.5}) sage: P Point set defined by 2 point(s) sage: P.options()['alpha'] 0.500000000000000 sage: P.xdata [1, 2] - >>> from sage.all import * >>> from sage.plot.point import Point >>> P = Point([Integer(1),Integer(2)],[Integer(2),Integer(3)],{'alpha':RealNumber('.5')}) >>> P Point set defined by 2 point(s) >>> P.options()['alpha'] 0.500000000000000 >>> P.xdata [1, 2] - plot3d(z=0, **kwds)[source]¶
- Plots a two-dimensional point in 3-D, with default height zero. - INPUT: - z– (optional) 3D height above \(xy\)-plane; may be a list if- selfis a list of points
 - EXAMPLES: - One point: - sage: A = point((1, 1)) sage: a = A[0]; a Point set defined by 1 point(s) sage: b = a.plot3d() - >>> from sage.all import * >>> A = point((Integer(1), Integer(1))) >>> a = A[Integer(0)]; a Point set defined by 1 point(s) >>> b = a.plot3d() - One point with a height: - sage: A = point((1, 1)) sage: a = A[0]; a Point set defined by 1 point(s) sage: b = a.plot3d(z=3) sage: b.loc[2] 3.0 - >>> from sage.all import * >>> A = point((Integer(1), Integer(1))) >>> a = A[Integer(0)]; a Point set defined by 1 point(s) >>> b = a.plot3d(z=Integer(3)) >>> b.loc[Integer(2)] 3.0 - Multiple points: - sage: P = point([(0, 0), (1, 1)]) sage: p = P[0]; p Point set defined by 2 point(s) sage: q = p.plot3d(size=22) - >>> from sage.all import * >>> P = point([(Integer(0), Integer(0)), (Integer(1), Integer(1))]) >>> p = P[Integer(0)]; p Point set defined by 2 point(s) >>> q = p.plot3d(size=Integer(22)) - Multiple points with different heights: - sage: P = point([(0, 0), (1, 1)]) sage: p = P[0] sage: q = p.plot3d(z=[2,3]) sage: q.all[0].loc[2] 2.0 sage: q.all[1].loc[2] 3.0 - >>> from sage.all import * >>> P = point([(Integer(0), Integer(0)), (Integer(1), Integer(1))]) >>> p = P[Integer(0)] >>> q = p.plot3d(z=[Integer(2),Integer(3)]) >>> q.all[Integer(0)].loc[Integer(2)] 2.0 >>> q.all[Integer(1)].loc[Integer(2)] 3.0 - Note that keywords passed must be valid point3d options: - sage: A = point((1, 1), size=22) sage: a = A[0]; a Point set defined by 1 point(s) sage: b = a.plot3d() sage: b.size 22 sage: b = a.plot3d(pointsize=23) # only 2D valid option sage: b.size 22 sage: b = a.plot3d(size=23) # correct keyword sage: b.size 23 - >>> from sage.all import * >>> A = point((Integer(1), Integer(1)), size=Integer(22)) >>> a = A[Integer(0)]; a Point set defined by 1 point(s) >>> b = a.plot3d() >>> b.size 22 >>> b = a.plot3d(pointsize=Integer(23)) # only 2D valid option >>> b.size 22 >>> b = a.plot3d(size=Integer(23)) # correct keyword >>> b.size 23 
 
- sage.plot.point.point(points, **kwds)[source]¶
- Return either a 2-dimensional or 3-dimensional point or sum of points. - INPUT: - points– either a single point (as a tuple), a list of points, a single complex number, or a list of complex numbers
 - For information regarding additional arguments, see either point2d? or point3d?. - EXAMPLES: - sage: point((1, 2)) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point((Integer(1), Integer(2))) Graphics object consisting of 1 graphics primitive - sage: point((1, 2, 3)) Graphics3d Object - >>> from sage.all import * >>> point((Integer(1), Integer(2), Integer(3))) Graphics3d Object - sage: point([(0, 0), (1, 1)]) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point([(Integer(0), Integer(0)), (Integer(1), Integer(1))]) Graphics object consisting of 1 graphics primitive - sage: point([(0, 0, 1), (1, 1, 1)]) Graphics3d Object - >>> from sage.all import * >>> point([(Integer(0), Integer(0), Integer(1)), (Integer(1), Integer(1), Integer(1))]) Graphics3d Object - Extra options will get passed on to show(), as long as they are valid: - sage: point([(cos(theta), sin(theta)) # needs sage.symbolic ....: for theta in srange(0, 2*pi, pi/8)], frame=True) Graphics object consisting of 1 graphics primitive sage: point([(cos(theta), sin(theta)) # These are equivalent # needs sage.symbolic ....: for theta in srange(0, 2*pi, pi/8)]).show(frame=True) - >>> from sage.all import * >>> point([(cos(theta), sin(theta)) # needs sage.symbolic ... for theta in srange(Integer(0), Integer(2)*pi, pi/Integer(8))], frame=True) Graphics object consisting of 1 graphics primitive >>> point([(cos(theta), sin(theta)) # These are equivalent # needs sage.symbolic ... for theta in srange(Integer(0), Integer(2)*pi, pi/Integer(8))]).show(frame=True) 
- sage.plot.point.point2d(points, alpha=1, aspect_ratio='automatic', faceted=False, legend_color=None, legend_label=None, marker='o', markeredgecolor=None, rgbcolor=(0, 0, 1), size=10, **options)[source]¶
- A point of size - sizedefined by point = \((x, y)\).- INPUT: - points– either a single point (as a tuple), a list of points, a single complex number, or a list of complex numbers
- alpha– how transparent the point is
- faceted– if- True, color the edge of the point (only for 2D plots)
- hue– the color given as a hue
- legend_color– the color of the legend text
- legend_label– the label for this item in the legend
- marker– the marker symbol for 2D plots only (see documentation of- plot()for details)
- markeredgecolor– the color of the marker edge (only for 2D plots)
- rgbcolor– the color as an RGB tuple
- size– how big the point is (i.e., area in points^2=(1/72 inch)^2)
- zorder– the layer level in which to draw
 - EXAMPLES: - A purple point from a single tuple of coordinates: - sage: point((0.5, 0.5), rgbcolor=hue(0.75)) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point((RealNumber('0.5'), RealNumber('0.5')), rgbcolor=hue(RealNumber('0.75'))) Graphics object consisting of 1 graphics primitive - Points with customized markers and edge colors: - sage: r = [(random(), random()) for _ in range(10)] sage: point(r, marker='d', markeredgecolor='red', size=20) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> r = [(random(), random()) for _ in range(Integer(10))] >>> point(r, marker='d', markeredgecolor='red', size=Integer(20)) Graphics object consisting of 1 graphics primitive - Passing an empty list returns an empty plot: - sage: point([]) Graphics object consisting of 0 graphics primitives sage: import numpy; point(numpy.array([])) Graphics object consisting of 0 graphics primitives - >>> from sage.all import * >>> point([]) Graphics object consisting of 0 graphics primitives >>> import numpy; point(numpy.array([])) Graphics object consisting of 0 graphics primitives - If you need a 2D point to live in 3-space later, this is possible: - sage: A = point((1, 1)) sage: a = A[0]; a Point set defined by 1 point(s) sage: b = a.plot3d(z=3) - >>> from sage.all import * >>> A = point((Integer(1), Integer(1))) >>> a = A[Integer(0)]; a Point set defined by 1 point(s) >>> b = a.plot3d(z=Integer(3)) - This is also true with multiple points: - sage: P = point([(0, 0), (1, 1)]) sage: p = P[0] sage: q = p.plot3d(z=[2,3]) - >>> from sage.all import * >>> P = point([(Integer(0), Integer(0)), (Integer(1), Integer(1))]) >>> p = P[Integer(0)] >>> q = p.plot3d(z=[Integer(2),Integer(3)]) - Here are some random larger red points, given as a list of tuples: - sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), size=30) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point(((RealNumber('0.5'), RealNumber('0.5')), (Integer(1), Integer(2)), (RealNumber('0.5'), RealNumber('0.9')), (-Integer(1), -Integer(1))), rgbcolor=hue(Integer(1)), size=Integer(30)) Graphics object consisting of 1 graphics primitive - And an example with a legend: - sage: point((0, 0), rgbcolor='black', pointsize=40, legend_label='origin') Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point((Integer(0), Integer(0)), rgbcolor='black', pointsize=Integer(40), legend_label='origin') Graphics object consisting of 1 graphics primitive - The legend can be colored: - sage: P = points([(0, 0), (1, 0)], pointsize=40, ....: legend_label='origin', legend_color='red') sage: P + plot(x^2, (x, 0, 1), legend_label='plot', legend_color='green') # needs sage.symbolic Graphics object consisting of 2 graphics primitives - >>> from sage.all import * >>> P = points([(Integer(0), Integer(0)), (Integer(1), Integer(0))], pointsize=Integer(40), ... legend_label='origin', legend_color='red') >>> P + plot(x**Integer(2), (x, Integer(0), Integer(1)), legend_label='plot', legend_color='green') # needs sage.symbolic Graphics object consisting of 2 graphics primitives - Extra options will get passed on to show(), as long as they are valid: - sage: point([(cos(theta), sin(theta)) # needs sage.symbolic ....: for theta in srange(0, 2*pi, pi/8)], frame=True) Graphics object consisting of 1 graphics primitive sage: point([(cos(theta), sin(theta)) # These are equivalent # needs sage.symbolic ....: for theta in srange(0, 2*pi, pi/8)]).show(frame=True) - >>> from sage.all import * >>> point([(cos(theta), sin(theta)) # needs sage.symbolic ... for theta in srange(Integer(0), Integer(2)*pi, pi/Integer(8))], frame=True) Graphics object consisting of 1 graphics primitive >>> point([(cos(theta), sin(theta)) # These are equivalent # needs sage.symbolic ... for theta in srange(Integer(0), Integer(2)*pi, pi/Integer(8))]).show(frame=True) - For plotting data, we can use a logarithmic scale, as long as we are sure not to include any nonpositive points in the logarithmic direction: - sage: point([(1, 2),(2, 4),(3, 4),(4, 8),(4.5, 32)], scale='semilogy', base=2) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point([(Integer(1), Integer(2)),(Integer(2), Integer(4)),(Integer(3), Integer(4)),(Integer(4), Integer(8)),(RealNumber('4.5'), Integer(32))], scale='semilogy', base=Integer(2)) Graphics object consisting of 1 graphics primitive - Since Sage Version 4.4 (Issue #8599), the size of a 2d point can be given by the argument - sizeinstead of- pointsize. The argument- pointsizeis still supported:- sage: point((3, 4), size=100) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point((Integer(3), Integer(4)), size=Integer(100)) Graphics object consisting of 1 graphics primitive - sage: point((3, 4), pointsize=100) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point((Integer(3), Integer(4)), pointsize=Integer(100)) Graphics object consisting of 1 graphics primitive - We can plot a single complex number: - sage: point(1 + I, pointsize=100) # needs sage.symbolic Graphics object consisting of 1 graphics primitive sage: point(sqrt(2) + I, pointsize=100) # needs sage.symbolic Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point(Integer(1) + I, pointsize=Integer(100)) # needs sage.symbolic Graphics object consisting of 1 graphics primitive >>> point(sqrt(Integer(2)) + I, pointsize=Integer(100)) # needs sage.symbolic Graphics object consisting of 1 graphics primitive - We can also plot a list of complex numbers: - sage: point([I, 1 + I, 2 + 2*I], pointsize=100) # needs sage.symbolic Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point([I, Integer(1) + I, Integer(2) + Integer(2)*I], pointsize=Integer(100)) # needs sage.symbolic Graphics object consisting of 1 graphics primitive 
- sage.plot.point.points(points, **kwds)[source]¶
- Return either a 2-dimensional or 3-dimensional point or sum of points. - INPUT: - points– either a single point (as a tuple), a list of points, a single complex number, or a list of complex numbers
 - For information regarding additional arguments, see either point2d? or point3d?. - EXAMPLES: - sage: point((1, 2)) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point((Integer(1), Integer(2))) Graphics object consisting of 1 graphics primitive - sage: point((1, 2, 3)) Graphics3d Object - >>> from sage.all import * >>> point((Integer(1), Integer(2), Integer(3))) Graphics3d Object - sage: point([(0, 0), (1, 1)]) Graphics object consisting of 1 graphics primitive - >>> from sage.all import * >>> point([(Integer(0), Integer(0)), (Integer(1), Integer(1))]) Graphics object consisting of 1 graphics primitive - sage: point([(0, 0, 1), (1, 1, 1)]) Graphics3d Object - >>> from sage.all import * >>> point([(Integer(0), Integer(0), Integer(1)), (Integer(1), Integer(1), Integer(1))]) Graphics3d Object - Extra options will get passed on to show(), as long as they are valid: - sage: point([(cos(theta), sin(theta)) # needs sage.symbolic ....: for theta in srange(0, 2*pi, pi/8)], frame=True) Graphics object consisting of 1 graphics primitive sage: point([(cos(theta), sin(theta)) # These are equivalent # needs sage.symbolic ....: for theta in srange(0, 2*pi, pi/8)]).show(frame=True) - >>> from sage.all import * >>> point([(cos(theta), sin(theta)) # needs sage.symbolic ... for theta in srange(Integer(0), Integer(2)*pi, pi/Integer(8))], frame=True) Graphics object consisting of 1 graphics primitive >>> point([(cos(theta), sin(theta)) # These are equivalent # needs sage.symbolic ... for theta in srange(Integer(0), Integer(2)*pi, pi/Integer(8))]).show(frame=True)