4706.sagews

# 2d vector plot
f(x,y)=(1.25*x-0.25*x*y, 0.05*x*y-0.1*y)
show(plot_vector_field(f, (x, 0, 10), (y, 0, 10)))

# 3d vector plot
g(x,y,z)=(x,y,z)
show(plot_vector_field3d(g, (x,-3,3),(y,-3,3),(z,-3,3)))

# interactive sin plot
@interact
def fun(a=(0,5),b=(0,5)):
    show(plot(sin(a*x)+sin(b*x),(x,0,10)))

# interactive vector plot
@interact
def fun(r=(1,4), a=(0.01,0.5), c=(0.01,0.5), d=(0.01,0.5)):
    f(x,y)=(r*x - a*x*y, a*c*x*y - d*y)
    show(plot_vector_field(f,(x,0,10),(y,0,10)))

from sage.calculus.desolvers import desolve_odeint
N=var("N")
t=srange(0,100,0.01)
log_sol=desolve_odeint(0.1*N*(1-N/1000.0), 10, t, N)
list_plot(zip(t,log_sol))

x,y=var('x,y')
f=[x*(1-y),-y*(1-x)]
t=srange(0,20,0.01)
sol=desolve_odeint(f,[0.5,2],t,[x,y])
p1=list_plot(zip(t,sol[:,0]))
p2=list_plot(zip(t,sol[:,1]), color="red")
show(p1+p2)

list_plot(zip(sol[:,0],sol[:,1]))