def f(x): return RDF(1 / (1 + 25 * x^2)) def runge(): R = PolynomialRing(RDF, 'x') g = plot(f, -1, 1, rgbcolor='red', thickness=1) polynom = [] for i, n in enumerate([6, 8, 10, 12]): data = [(x, f(x)) for x in xsrange(-1, 1, 2 / (n - 1), include_endpoint=True)] polynom.append(R.lagrange_polynomial(data)) g += list_plot(data, rgbcolor='black', pointsize=5) g += plot(polynom, -1, 1, fill=f, fillalpha=0.2, thickness=0) return g runge()