412.sagews

omg = 10
def wave0(t): return sin(omg*t)
    
def wave1(t): return 1/3*sin(3*omg*t)
    
def wave2(t): return 1/5*sin(5*omg*t)
    
def wave3(t): return 1/7*sin(7*omg*t)

def wavesum(t): return wave0(t) + wave1(t) + wave2(t) + wave3(t)

plotRange = (-2*pi/omg,2*pi/omg)
plot0 = plot(wave0,plotRange,color='black')
plot1 = plot(wave1,plotRange,color='red')
plot2 = plot(wave2,plotRange,color='green')
plot3 = plot(wave3,plotRange,color='orange')
plotsum = plot(wavesum,plotRange,color='blue')
show(plot0+plot1+plot2+plotsum)

def waveTerm(t, i): return sin(i*omg*t)/i

def waveS(t): return sum((waveTerm(t,i) for i in xrange(1,39,2)))

plot(waveS, plotRange)