Oliver's profile - activity

I don't think this is easy, or even possible, to do in native Sage. The GAP AllSmallGroups function might be helpful - you can access GAP by doing gap_console() in the Sage command line, choosing 'gap' from the system choices in the notebook, or doing sage -gap when you lauch Sage.

However, I don't think this is wrapped in Sage at this time.

I want to check if a certain statement is correct about groups, but it is very hard to check it by hand (and even harder to prove). Is it possible to run over isomorphism classes of groups (for any specific cardinality), so as to check that statement?

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?

Say I want to look at the field extension $Quot(\mathbb{Q}[x,y]/y^7-x)$ over $\mathbb{Q}(x)$ and then compute its Galois closure. How do I do that?

Ideally it could be done on the scheme-level (to define the scheme-morphism: (the projectivization of the affine plane curve $y^7-x$) mapping to (the projective $x$-line); and then compute its Galois closure -- a scheme!). But I don't know how to implement either version.