Sentence:  The 1-dimensional semialgebraic set \mathcal{S}:={x>0,xy=1} is the image of the <WSD>regular map</WSD> / :: f: \R^2\rightarrow \R^2, (x,y)\mapsto \left ((xy-1)^2+x^2, \frac{1}{(xy-1)^2+x^2}\right ). 
Meaning of the word marked with <WSD> tags:  A morphism between algebraic varieties.