Conditional Functions

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@interact

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def _(N=[1,2,3]):

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    def rho(phi):

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        if N==1: 

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            return sqrt(2*cos(2*phi)) \

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            if 2*cos(2*phi)>=0 else 0

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        if N==2: 

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            return 4*cos(2*phi-pi/4)^2

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        if N==3: 

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            return 6*cos(2*phi) \

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            if 6*cos(2*phi)>=3 else 0

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    var('phi')

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    p=polar_plot(rho,(phi,0,2*pi),

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                 fill=True,fillcolor='#3636ff')

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    p.show(figsize=(5,5),gridlines=True)

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