On Sep 18, 9:42 am, niels <niels.lub...@gmail.com> wrote:
> > Does find_root take general symbolic expressions (i.e., x==x^2)? ...
> > sage:solve(x^5+x^3+17*x+1,x) ...
>
> I think it should at least be clear over what ring the user wants to
> solve, then it is also clear which method should be used.
>
> * If the coefficients are algebraic/transcendental over QQ then
> symbolic algebraic are often preferred
>
> * Over finite fields probably just try everything (but maybe something
> better)
>
> * Over RR or CC a numerical solver is often preferred (since already
> the input coefficients are probably not precise, and more geometrical
> methods are used)
Try sage: x.roots? for documentation about specifying rings to solve
over; most or even all of what you suggest is possible if you do that.
>
> I think that symbolic expressions don't mean so much if the ring is
> not specified (or is it?).
> This is in my opinion very confusing.
>
I don't know if there is a way to get at where coefficients of
elements in SR come from; they all just become symbolic expressions.
Even with the .coeffs() method, they still end up coming out as
symbolic expressions. Burcin or others will clarify, but probably the
idea was that symbolic means just that - symbolic, with no reference
to other things. If you really want polynomials, you need to do
something like
sage: R.<x> = CC[]
sage: x^2+1
and go from there, I think. That is occasionally annoying to those of
us who primarily teach undergraduates, but essential for many of the
applications of Sage.
- kcrisman
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