Legh's profile - activity

Thanks, I actually finished the task I needed this for using something else, so now this just a curiosity to me. You are right $\mathbb{Q}$ extended by $\sqrt{2}$ could give a useful answer, but since this is not vital to me anymore I don't have a reason to try. I'll just leave the post here to see if someone has an answer to this problem, if possible. To be honest at this point I'm not sure anymore there is one, since this morning I tried to do the same thing using python and didn't work out. Thanks again.

No, I can't. Thanks for the concern but I'd like to solve the problem, not go around it. I'm sure there is a way to work with intersections and Groebner basis of ideals over the Real numbers field

Thanks for your answer, i see what is happening with the $\sqrt{2}$, hope someone can help me solve the intersection problem.

I am trying to compute the intersection of Ideals over $\mathbb{R}[x,y]$, but I get problems from the coefficient $\frac{1}{\sqrt{2}}$. This is my code:

R.<x,y>=PolynomialRing(RR,order='lex')

I=Ideal([(x^2+y^2-1),(x*y),(y^3-y)])

I5=Ideal([x-1/sqrt(2),y-1/sqrt(2)])

I6=Ideal([x+1/sqrt(2),y-1/sqrt(2)])

I7=Ideal([x+1/sqrt(2),y+1/sqrt(2)])

I8=Ideal([x-1/sqrt(2),y+1/sqrt(2)])

J=I.intersection(I5,I6,I7,I8)

and this is the error I get:

TypeError: Intersection is only available for ideals of the same ring.

So when I ask if

I5 in R

the answer is False. I also tried with QQbar but same result, can someone explain this? Thanks!

EDIT: I also tried with $\frac{\sqrt{2}}{2}$ instead of $\frac{1}{\sqrt{2}}$ and I get the same error.