File:Bernstein Polynomials.svg

# adapted from file without sum of Bernstein Polynomials by Kilom691
# http://commons.wikimedia.org/wiki/File:Bernstein_poly_4.svg

N = 4

rnb = rainbow(N + 1)
pt1 = sum(
        plot(
    	    binomial(N, i) * x ** i * (1 - x) ** (N - i),
    	    0, 1,
            legend_label=r'$B^{}_{}(u)$'.format(N, i),
            color=rnb[i],
            thickness=3,
            aspect_ratio=1
            )
	    for i in range(N + 1)
        )
almostOne = 0.99999 # bug in sagemath, put it to 1.0 and BSum plot will vanish
var('i')
BSum = sum( binomial(N, i) * x ** i * (1 - x) ** (N - i), i, 0, 3 ) \
            + binomial(N, 4) * x ** 4 * (1 - x) ** (N - 4) * almostOne
pt2 = plot(
        BSum,
        0, 1,
        legend_label='$\sum_{i=0}^{4} \, B^{4}_{i}(u)$', # code between $ .. $ uses LaTeX math commands to format equation
        color='orange',
        thickness=3
        )
pt2.set_legend_options(loc=(0.37,0.5))

show( pt1 + pt2, figsize=6 )