Hi Nils and Eggart,

On 29 Jul., 01:20, Nils Bruin <[email protected]> wrote:
> The term "Goppa polynomial" leads me to suspect that the OP had coding
> theoretic and hence probably quite algebraic intentions, so he/she
> probably is better off looking at polynomial rings rather than
> "symbolic expressions".

Yes, that was my original impression, too.

My second impression was, since (s)he talked about vars = var('x'); g
= function('g',x); g(x)=goppapolynomial(F,x); dg = diff(g,x), that it
was not so much about algebra.

Anyway.
My third impression is that the question "algebra or calculus" is less
important in this case than the question of "finding out what can be
done how". So:

If you have an object X and don't know how to deal with it, you may
do
    X?
which shows you the documentation of X

Available methods can be found with "tab completion": type X. and then
hit the tab key -- it will show you all method names.

In your case, you thought you need "diff" or "differential" or so. So,
if X is a polynomial, then X.diff<TAB> will show you that the
polynomial indeed has no method whose name starts with "diff". If you
are lucky, you try X.d<TAB>, which will show you all method names
starting with "d" -- and then, the method "derivative" might catch
your attention.

Also dir(X) can show you all available methods. That's usually a long
list, but in my experience it can be helpful.

Now, if "derivative" sounds like what you need, try X.derivative? to
get the documentation.

After all, I think it is not needed to read all 5000+ pages of
reference - the references provide search. Also there are several
search commands in Sage, such as search_def, search_src, search_doc,
and then search_def? or search_src? will tell you how too use these
search commands.

Cheers,
Simon

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