Can you please help with the construction of the piecewise function specified in the details and its plotting?
I want to define and then plot a piecewise function on [-2,2] which is 0.0 on [-2,-1] and on [1,2], and which is (in LaTeX notation) $\exp(-x^2/(1-x^2))$ on (-1,1). I am newcomer to SAGE and tried several variants according to the Reference manual, but failed every time. Some of the error messages are posted below. Can you please offer a SAGE solution for defining of functions in SAGE which are calculated with more than two expression on more than two respective intervals, and such that some of the expression may not be polynomials? Please note that for my purposes I will need to create parametric plots in 3D with parametrizations where the fx, fy and fz will be piecewise functions of the above-said type. I already know how to create the respective 3D plots in SAGE if fx, fy, and fz are well-defined in SAGE.