Polar and Parametric Coordinate Systems

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def tf1(i,k,t): 

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    f1=(1/k[0]+sin(k[1]+k[2]*t))*(1/k[0]+cos(k[1]+k[2]*t))

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    f2=(1/k[0]-sin(k[1]+k[2]*t)^3)*(1/k[1]-cos(k[1]+k[2]*t)^3)

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    return [i*f1*f2*cos(t),i*f1*f2*sin(t)]

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def tf2(i,k,t): 

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    return [(i+cos(i*k[0]*t)+cos(k[0]*t))*cos(t)/k[1]/k[2],

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            (i+cos(i*k[0]*t)+cos(k[0]*t))*sin(t)/k[1]/k[2]]

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var('t'); K=[randint(2,16) for i in range(3)]

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p1=sum([parametric_plot(tf1(i,K,t),(t,0,2*pi),color=hue(i/6)) 

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        for i in range(1,5)])

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p2=sum([parametric_plot(tf2(i,K,t),(t,0,2*pi),color=hue(i/6)) 

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        for i in range(1,5)])

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(p1+p2).show(title=K,axes=False,figsize=6)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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