> Maybe an alternative viewpoint  (perhaps taken by Axiom, and maybe
> Sage) is
>
> (a) if you want to use a computer algebra system (especially one
> accessed through Sage) effectively  then
> (b) you should know something about "modern algebra", at least so as
> to be conversant with the notions
> of ring, field, polynomial, ...  and preliminary notions.  This could
> take about an hour of reading,
> especially if you leave out proofs.

Not at all.  The viewpoint is rather related to a different thread:

(1) The people who develop most functionality originally are
mathematicians who do know about such things, and that was sufficient
for most purposes then, but

(2) Now we need to make those more user-accessible, and no one is
doing it for function X.

I agree this isn't ideal, but (as you know) open source software is
developed in a very different way, so we make the best of it rather
than giving up.

But there aren't really too many places where this comes in with
respect to "rings" etc.; it's really more of a system-wide thing where
there are options which you would know if you knew the underlying
software but aren't well-enough exposed at the Sage level (including
many Maxima ones Robert Marik has done an excellent job of uncovering
and making Pythonic syntax for).

- kcrisman

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