## Tuesday, January 31, 2012

### Sage - 2D plot - simple plot, more than one function on the same plot, axes limits, change color of function in graph

There are many options when plotting in Sage.  Here is a simple example.

alpha = 30*pi/180
show(alpha)
show(float(alpha))
f = (arcsin(alpha))^2 + log(tan(alpha/2)) - arcsin(alpha)*arctan(alpha)
show(f)
show(float(f))
g = (1/(0.7*sin(x)))*sqrt(1 + ((pi)^(-2))*((0.7*sin(x))^2)*(f - csc(x)*tan(x/2) - log(tan(x/2))))
p = plot(g, (0, alpha))
show(p, ymin = 0, ymax = 20)

In Sage, the variable x is automatically known/defined.  I then create a simple function similar to how I created alpha and f.  I next equal p to the plot since I wanted to change the y axis range manually which you can do through the show command (or this can also be done in the plot command as well).

Here is another example of a 2D plot.  This one shows how to plot a couple of functions.

alpha = 30*pi/180
show(alpha)
show(float(alpha))
z = 0.5
r_max = z*tan(alpha)
show(r_max)
show(float(r_max))
lamb_da = (csc(alpha))^2 - (cot(alpha))*(csc(alpha)) + log(tan(alpha/2))
show(float(lamb_da))
cig_ma_c = 1
r = var('r')

psee = (1/2*pi)*(cig_ma_c)*(r^2)*(lamb_da + (z/r)*sqrt(1 + (z/r)^2) - log(sqrt(1 + (z/r)^2) - z/r) - 1 - (z/r)^2)

lamb_da_bi = (csc(alpha))^2 - (cot(alpha))*(csc(alpha)) + log(tan(alpha)/2)

show(float(lamb_da_bi))

psee_bi = (1/2*pi)*(cig_ma_c)*(r^2)*(lamb_da_bi + (z/r)*sqrt(1 + (z/r)^2) - log(r/(2*z)) - 1 - (z/r)^2)

p1 = plot(psee, (r, 0, r_max))

p2 = plot(psee_bi, (r, 0, r_max), color ='green')

show(p1 + p2)