I tried doing some calculations that involve integral closures, but I seem to run into problems:
Say I define a ring as a quotient ring: for example the quotient ring $\mathbb{C}[x,y]/(y^3-x^2)$. Then if I use the integral_closure option, he rejects me. As far as I can tell this is because he treats quotient rings as Commutative Rings rather than, say, integral domains, and so it doesn't have the option of integral closures.
I'm sure there's a way to do such things. What is it? Is the idea that we have to apply some functor so that that ring would be treated as an object in a different category?
