Le mercredi 4 janvier 2017 23:41:00 UTC+1, Dima Pasechnik a écrit : > > > > 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. > > Thanks for your suggestion; however, I am not sure if this could fully work: some computations require to take derivatives, i.e. to evaluate d/dx (sqrt(-z)), where z is the rational function of (x,y) discussed above. Could this work in our framework?
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