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Nov 6, 2010 at 15:22 comment added Sergei Ivanov The $y$ is here to make the values non-regular (ok, formally they are not regular for the map of a line either, but it is even more confusing then). With rational coefficients, it can be made a polynomial map of a circle. The length of the image can be large but then the degree is large too, this is what I wanted to say.
Nov 6, 2010 at 4:34 comment added John Jiang Thanks. I guess by degree I really meant the smallest possible degree of the polynomial representation of the algebraic map. Also in my application $M$ can be assumed to be compact and also equipped with a Riemannian metric.
Nov 6, 2010 at 4:07 history edited Sergei Ivanov CC BY-SA 2.5
acknowledged the error
Nov 6, 2010 at 3:55 history edited Sergei Ivanov CC BY-SA 2.5
edited body
Nov 6, 2010 at 1:59 history edited Sergei Ivanov CC BY-SA 2.5
edited body
Nov 6, 2010 at 0:40 history answered Sergei Ivanov CC BY-SA 2.5