Timeline for irreducible elements in a ideal of $R[x_1,x_2]$

8 events

when toggle format	what		by	license	comment
Apr 8, 2012 at 16:25	history	edited	Emil Jeřábek	CC BY-SA 3.0	Make the bounds tight. (You can interpolate $n$ points by a degree $n-1$ polynomial.)
Apr 7, 2012 at 0:03	comment	added	Will Sawin		@Daniel: Let $y,f(x)$ be as before and $g(x)$ vanish at the $x$ coordinates of the set of points, then $(y-f(x))^2+g(x)^2$ is irreducible in $\mathbb R[x,y]$, because it splits in $\mathbb C[x,y]$ into $(y-f(x)+ig(x))(y-f(x)-ig(x))$, neither of which is in $\mathbb R[x,y]$
Apr 6, 2012 at 15:32	comment	added	Daniel		@J.C. Ottem I have a question, how can I put in the coefficients the conditions of being irreducible?
Apr 6, 2012 at 15:31	comment	added	Daniel		@Will Sawin Your polynomials has other roots right? ( Not just the finite points, What can I do to find a polynomial that only has that finite points and it´s also irreducible)?
Apr 6, 2012 at 7:15	comment	added	Georges Elencwajg		I would never have thought there was such a beautifully elementary solution: congratulations, Will !
Apr 6, 2012 at 5:46	comment	added	Daniel		Ah and I forgot something, not only must cancel on this points, and be irreducible, also has only that roots , and no more!
Apr 6, 2012 at 2:39	history	edited	Will Sawin	CC BY-SA 3.0	added 477 characters in body
Apr 6, 2012 at 2:28	history	answered	Will Sawin	CC BY-SA 3.0