Let \(f\colon S^4\to S^4\) be defined by \[ f(x,y,z,w)=\frac{1}{\sqrt{x^4+y^4+z^4+w^4}}\,(x^2,y^2,z^2,w^2). \] Compute the degree of \(f\).
The source prints \(S^4\), but the formula has four coordinates, so it defines a self-map of the unit sphere \(S^3\subset\mathbb R^4\).