On Tuesday, March 10, 2020 at 6:22:45 AM UTC-7, Dima Pasechnik wrote: > > Suppose I have > > R.<x,y,z>=QQ[] > K.<u,v>=QQ[] > f=R.hom([u*v,u^2,v^2-u^2]) > > then for any even degree p in K one can compute > a preimage under f (e.g. u^4-u*v goes to y^2+x, etc) >
I think the general way (which should be pretty performant for such a nice example) is to do it via reduction wrt. the graph ideal: sage: R.<u,v,x,y,z>=PolynomialRing(QQ,order="degrevlex(2),degrevlex(3)") sage: I=R.ideal([x-u^2,y-u*v,z-v^2]) sage: inv=lambda f:QQ['x,y,z']((I.reduce(f))) sage: inv(u^2) x Obviously, the term order chosen will dictate what representative you get back, if the map isn't injective. You should of course choose an elimination order. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/3e738cad-5167-4add-a28a-a1c0d52ba008%40googlegroups.com.
