f(x)=cos(x)
w1=[-1,0,1]
w2 = [-sqrt(3)/2, 0 , sqrt(3)/2]
w2n = [(-sqrt(3)/2).n(), 0 , (sqrt(3)/2).n()]
#print range (-1,2)
#print srange(-1,2,1/2)
punkty = [(xp,f(xp).n()) for xp in w1]
punkty2 = [(xp, f(xp)) for xp in w2]
#print punkty
y1 = [f(xp).n() for xp in w1]
y2 = [f(xp).n() for xp in w2]
#print y1

import numpy
wi= numpy.poly1d(numpy.polyfit(w1, y1, len(w1)-1))
wi2= numpy.poly1d(numpy.polyfit(w2n, y2, len(w2n)-1))
plot(wi, (x,-1.1, 1.1), figsize=4, aspect_ratio=1) + \
points(punkty[1:3], color="red", size=30) + \
points(punkty[1:3], color="magenta", size=30) + \
plot(f, (x,-1.1,1.1), color="green") + \
plot(wi2, (x,-1.1,1.1), color="black")

wi0 = numpy.poly1d(numpy.polyfit(w1, y1, 0))
wi1 = numpy.poly1d(numpy.polyfit(w1, y1, 1))
wi2 = numpy.poly1d(numpy.polyfit(w1, y1, 2))
wi3 = numpy.poly1d(numpy.polyfit(w1, y1, 3))
wi4 = numpy.poly1d(numpy.polyfit(w1, y1, 4))
print wi1
print wi2
print wi3

plot(wi0, (x,-1.1,1.1), aspect_ratio=1) +\
plot(wi1, (x,-1.1,1.1), color = "green") +\
plot(wi2, (x,-1.1,1.1), color = "black") +\
plot(wi3, (x,-1.1,1.1), color = "magenta") +\
plot(wi4, (x,-1.1,1.1), color = "red")