A friend just asked me about piecewise functions in Sage (how to
construct, plot, differentiate, integrate, etc., them). I came up with
two answers for plotting:
* use python functions:
def f(t):
return t^2*(0<=t<=1) + (t-1)*(1<t<=2)+(sin(t))*(2<t<=3)
plot(f, (0,5), exclude=(0,1,2,3))
* Use unit_step or heaviside:
def interval(x,a,b):
return unit_step(x-a)*unit_step(b-x)
f(t)=(t^2-2*t+1)*interval(t,1,2)+(t-1)*interval(t,2,3)+sin(t^2)*interval(t,3,4)
show(plot(f,(t,0,5),exclude=range(5),fill=True))
show(integrate(f,(t,0,5)))
show(diff(f,t))
Is there something better? I tried to get piecewise to work, but I
couldn't plot, integrate, etc., the function.
f=piecewise([((1,2), x^2), ((2,3), sin(x))])
plot(f, (x,0,3)) # error, but plot(f) works...
integrate(f, (x,1,3)) # error, but integrate(f) works
diff(f,x) # error, but diff(f) gives a warning and an output
Thanks,
Jason
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