Sage / SageMath Wrapper: Graphing with x-y values in a table
Below is some, as yet unrefactored, wrapper code that I wrote to generate plots, that are aware of asymptotes, using Sage that include corresponding x and y values in the form a table. Below is an image (here a polynomial function) and then the code.
# handle division by zero
# http://stackoverflow.com/questions/1528237/how-can-i-handle-exceptions-in-a-list-comprehension-in-python
def catch(func, handle=lambda e : e, *args, **kwargs):
try:
return func(*args, **kwargs)
except Exception as e:
#return handle(e)
return NaN
# graphic, table, labeled points, point of interest
def go(fx=0, gx=0, xmin=-3, xmax=3, ymin=None, ymax=None, step=1, x1=None, label=True, simple=False, rotation=0):
"""Show a graph, table of values, and points of interest """
import numpy as np # for arange
x = var('x'); fn = 'plot' + str(int(random()*10000)) + '.png'
f(x) = fx
g(x) = gx
if simple == True:
s = abs(xmin/ceil(step))
else:
s = step
# data
fv = [(i, catch(lambda: f(i).n())) for i in np.arange(xmin,xmax,s)] # include xmax
gv = [(i, catch(lambda: g(i).n())) for i in np.arange(xmin,xmax,s)] # include xmax
# plot with points
G = plot(f(x),(x,xmin,xmax), ymin=ymin, ymax=ymax, detect_poles='show', color='green');
G += plot(g(x),(x,xmin,xmax),ymin=ymin, ymax=ymax, detect_poles='show', color='red');
G += points(fv+gv,pointsize=40,color='black');
for p in fv+gv: # label points
if label:
if math.isnan(p[1])==False: # don't plot NaNs
G += text(' (%.1f,%.1f)'%(p[0],p[1]),p,horizontal_alignment='left',rotation=rotation,color='black',fontsize=10, fontweight='normal')
if math.isnan(p[1]): # plot NaNs
q=(p[0],.5)
G += text(' (%.1f,Div0)'%q[0],q,horizontal_alignment='left',rotation=rotation,color='black',fontsize=10, fontweight='normal')
G += points(q,pointsize=40,color='blue');
# horizontal asymptotes
a1 = limit(f,x=+infinity)
a2 = limit(f,x=-infinity)
G += line([(-100,a1),(100,a2)], xmin=xmin,xmax=xmax,ymin=ymin, ymax=ymax, color='gray', linestyle='dashed')
if x1:
p1 = (x1, catch(lambda: f(x1))) # point of interest
G += points(p1,pointsize=40,color='blue')
G += text(' (%.1f,%.1f)'%(p1[0],p1[1]),p1,horizontal_alignment='left',rotation=rotation,color='blue',fontsize=10, fontweight='bold')
else:
p1 = (None, None)
G.save(DATA + fn) # required due to Sage object caching
html('<div style="float:left;">')
html("<img src="+fn+"></img>")
html('</div><div style="float:left; padding-left:50px;">Green Graph')
html.table([["$x$", f]] + fv, header = True)
html('</div><div style="float:left; padding-left:50px;">Red Graph')
html.table([["$x$", g]] + gv, header = True)
html('</div><div style="float:left; padding-left:50px;">Interesting Points')
html.table([["$x$", "$y$"]] + [p1], header = True)
html('</div>') # html
import time; time.sleep(1); os.remove(DATA + fn) # cleanup
returnExample of how to use it
NOTE: The 4 comma-separated numbers following f(x), g(x) are the minimum x and y values.
f(x)=3*x^2/(x^2+2)
g(x)=f(x)+1
go(f(x),g(x),-5,5,0,6,x1=.5)
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