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Commonly Used Sage Commands

2D Plotting

Command		Notes
plot(f(x),(x,xmin,xmax), options)	::	plots the function f(x) ( or f) with some of the options shown below; ymin = number ymax = number color = 'red', 'green', 'blue', 'black', 'yellow', 'purple', ... use the command sorted(colors) to get an alphabetized list of possible colors, or one can use HTML color such as '#aabbcc' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches
list_plot(list, options)	::	plots a list of numbers, a list of tuples, a numpy array, or a dictionary with some of the options shown below. If given a list of numbers (that is, not a list of tuples or lists), list_plot forms a list of tuples (i, x_i) where i goes from 0 to len(data)-1 and x_i is the i-th data value, and puts points at those tuple values. Use zip(x_coords,y_coords) to create a single list of ordered pairs. plotjoined = True (or False) to include a line between adjacent points color = 'red', 'green', 'blue', 'black', 'yellow', 'purple', ... use the command sorted(colors) to get an alphabetized list of possible colors, or one can use HTML color such as '#aabbcc' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches
parametric_plot((f(t),g(t)),(t,tmin,tmax), options)	::	a parametric plot of x = f(t) and y = g(t) in the x-y plane with some of the options shown below; color = 'red', 'green', 'blue', 'black', 'yellow', 'purple' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches

3D Plotting

Command		Notes
plot3d(f(x,y),(x,xmin,xmax),(y,ymin,ymax), options)	::	plots the function z = f(x,y) ( or f) with some of the options shown below; color = 'red', 'green', 'blue', 'black', 'yellow', 'purple' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches
implicit_plot(f(x,y) == value,(x,xmin,xmax),(y,ymin,ymax), options)	::	plots the level curve of f(x,y) equal to value with some of the options shown below; color = 'red', 'green', 'blue', 'black', 'yellow', 'purple' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches axes = True (or False)
contour_plot(f(x,y),(x,xmin,xmax),(y,ymin,ymax), options)	::	plots the contours of the surface z=f(x,y) with some of the options shown below; contours = number, where number is the number of contour to plot, default is 10 contours = [c1,c2, ..., cn], a list of contours is specified fill = True (or False), space between contours either filled or not labels = True (or False), contours labeled or not label_fmt='%1.0f', format for the contour labels. The number after the decimal is equal to the number of decimals given in the label color = 'red', 'green', 'blue', 'black', 'yellow', 'purple' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches axes = True (or False)
parametric_plot3d((f(t),g(t),h(t)),(t,tmin,tmax), options)	::	a parametric plot of the path x=f(t), y=g(t), and z=h(t) in the xyz space with some of the options shown below; color = 'red', 'green', 'blue', 'black', 'yellow', 'purple' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 linestyle = '-' or 'solid', '- -' or 'dashed', '-.' or 'dash dot', ':' or 'dotted' thickness = the number of pixels axes_labels = ('x label','y label') aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches opacity = o, where 0 $\le$ o $\le$ 1 mesh = True or False (default = False)
parametric_plot3d((f(u,v),g(u,v),h(u,v)),(u,umin,umax),(v,vmin,vmax), options)	::	a parametric plot of a surface in xyz space with some of the options shown below; color = 'red', 'green', 'blue', 'black', 'yellow', 'purple' rgbcolor = (r,g,b), where r,g,b are numbers between 0 and 1 aspect_ratio = number, where number is the length to height ratio figsize = [w,h], where w and h are in inches opacity = o, where 0 $\le$ o $\le$ 1 mesh = True or False (default = False)

Simplifying

Command Notes

.simplify_full().simplify_trig() :: simplifies the expression