How to define a piecewise map in sage

Question

I want to define in Sage the following map. I've attempted to use the following code in Sage:

gamma=function('gamma')
gamma(t)=piecewise([(t>0,(t,0,e^(-1/t^2))),(t==0,(0,0,0)),(t<0,(t,e^(-1/t^2),0))])

This, however, gives me the error TypeError: unable to convert (t, 0, e^(-1/t^2)) to a symbolic expression. How could I change it to create such a type of map?

Answer 1

It seems piecewise does not support vector-valued functions.

Possible workaround: define each coordinate as a piecewise function.

sage: gamma(t) = (t,
....:             piecewise([(t <= 0, 0), (t > 0, exp(-t^-2))]),
....:             piecewise([(t < 0, exp(-t^-2)), (t > 0, 0)]))
....:
sage: gamma
t |--> (t,
        piecewise(t|-->0 on (-oo, 0], t|-->e^(-1/t^2) on (0, +oo); t),
        piecewise(t|-->e^(-1/t^2) on (-oo, 0), t|-->0 on (0, +oo); t))
sage: parametric_plot(gamma, (t, -1, 1))
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