| 1 | r""" |
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| 2 | |
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| 3 | sage: g = plot(x * sin(1/x), x, -2, 2, plot_points=500) |
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| 4 | sage: def p(x, n): return(taylor(sin(x), x, 0, n)) |
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| 5 | sage: xmax = 15 ; n = 15 |
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| 6 | sage: g = plot(sin(x), x, -xmax, xmax) |
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| 7 | sage: for d in range(n): |
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| 8 | ... g += plot(p(x, 2 * d + 1), x, -xmax, xmax,\ |
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| 9 | ... color=(1.7*d/(2*n), 1.5*d/(2*n), 1-3*d/(4*n))) |
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| 10 | sage: # g.show(ymin=-2, ymax=2) |
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| 11 | |
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| 12 | """ |
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| 13 | |
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| 14 | |
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| 15 | r""" |
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| 16 | |
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| 17 | sage: a = animate([[sin(x), taylor(sin(x), x, 0, 2*k+1)]\ |
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| 18 | ... for k in range(0, 14)], xmin=-14, xmax=14,\ |
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| 19 | ... ymin=-3, ymax=3, figsize=[8, 4]) |
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| 20 | sage: # a.show() |
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| 21 | |
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| 22 | """ |
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| 23 | |
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| 24 | |
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| 25 | r""" |
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| 26 | |
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| 27 | sage: f2(x) = 1; f1(x) = -1 |
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| 28 | sage: f = Piecewise([[(-pi,0),f1],[(0,pi),f2]]) |
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| 29 | sage: S = f.fourier_series_partial_sum(20,pi); S |
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| 30 | 4/3*sin(3*x)/pi + 4/5*sin(5*x)/pi + 4/7*sin(7*x)/pi + 4/9*sin(9*x)/pi + 4/11*sin(11*x)/pi + 4/13*sin(13*x)/pi + 4/15*sin(15*x)/pi + 4/17*sin(17*x)/pi + 4/19*sin(19*x)/pi + 4*sin(x)/pi |
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| 31 | sage: g = plot(S, x, -8, 8, color='blue') |
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| 32 | sage: scie(x) = x - 2 * pi * floor((x + pi) / (2 * pi)) |
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| 33 | sage: g += plot(scie(x) / abs(scie(x)), x, -8, 8, color='red') |
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| 34 | |
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| 35 | """ |
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| 36 | |
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| 37 | |
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| 38 | r""" |
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| 39 | |
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| 40 | sage: t = var('t') |
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| 41 | sage: x = cos(t) + cos(7*t)/2 + sin(17*t)/3 |
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| 42 | sage: y = sin(t) + sin(7*t)/2 + cos(17*t)/3 |
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| 43 | sage: g = parametric_plot( (x, y), (t, 0, 2*pi)) |
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| 44 | sage: # g.show(aspect_ratio=1) |
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| 45 | |
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| 46 | """ |
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| 47 | |
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| 48 | |
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| 49 | r""" |
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| 50 | |
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| 51 | sage: t = var('t'); e, n = 2, 20/19 |
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| 52 | sage: g1 = polar_plot(1+e*cos(n*t),(t,0,n*38*pi),plot_points=5000) |
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| 53 | sage: e, n = 1/3, 20/19 |
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| 54 | sage: g2 = polar_plot(1+e*cos(n*t),(t,0,n*38*pi),plot_points=5000) |
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| 55 | sage: # g1.show(aspect_ratio=1); g2.show(aspect_ratio=1) |
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| 56 | |
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| 57 | """ |
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| 58 | |
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| 59 | |
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| 60 | r""" |
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| 61 | |
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| 62 | sage: z = var('z'); g1 = complex_plot(abs(cos(z^4)) - 1,\ |
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| 63 | ... (-3, 3), (-3, 3), plot_points=400) |
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| 64 | sage: f = lambda x, y : (abs(cos((x + I * y) ** 4)) - 1) |
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| 65 | sage: g2 = implicit_plot(f, (-3, 3), (-3, 3), plot_points=400) # long time (~300 seconds) |
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| 66 | sage: # g1.show(aspect_ratio=1); g2.show(aspect_ratio=1) |
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| 67 | sage: f(z) = z^5 + z - 1 + 1/z |
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| 68 | sage: g = complex_plot(f, (-3, 3), (-3, 3)) # long time |
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| 69 | |
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| 70 | |
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| 71 | """ |
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| 72 | |
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