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Substitution of polynomial powers

Hi,

I would like to make a "square root" substitution in a particular multivariate polynomial to obtain another multivariate polynomial. For instance, if I have

f(x,y) = x^2 + x^4 y + y^3 + 1 and want to replace x^2 with u, then the resulting polynomial should be g(u,y) = u + u^2 y + y^3 + 1. I tried using subs but didn't work properly. Any ideas how to do this in sage?