On Wednesday, January 4, 2017 at 9:06:44 PM UTC, Eric Gourgoulhon wrote: > > Le mercredi 4 janvier 2017 21:47:00 UTC+1, Dima Pasechnik a écrit : >> >> >> >> It's because I need to consider sqrt(-z), so that I cannot stay with >>> rational functions. >>> >> >> I woud have picked one more variable, w, and set w^2=-z. >> Now everything is polynomial again... >> >> > But z is not a variable: it is (minus) the determinant of the > Tomimatsu-Sato metric w.r.t. to the coordinates (x,y,phi), which turns out > to be a rational function in (x,y). For further computations, the explicit > expression of the volume element sqrt(-z) in terms of (x,y) is required. > So I don't see how I could use something like w^2=-z with w being a > function of (x,y) without taking a square root. > and, indeed, it will be there, as w=sqrt(-z), no? That is, in effect you'd be computing in the polynomial ring modulo the ideal generated by w^2+z.
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