Hi Georg,

On 2015-06-02, ggrafendorfer <georg.grafendor...@gmail.com> wrote:
> sage: g(x) = x^2 - 26*x -9
> sage: g.factor()
> x^2 - 26*x - 9

First of all, what you create is a symbolic function, so, factorisation
doesn't really make sense.

  sage: g(x) = x^2-26*x-9
  sage: g
  x |--> x^2 - 26*x - 9

What you probably want to factor is a symbolic expression that isn't a
function. Let's see if it works:

  sage: g = x^2-26*x-9
  sage: g
  x^2 - 26*x - 9
  sage: g.factor()
  x^2 - 26*x - 9

This time, the reason is that your expression lives in the symbolic
ring, which is so large that the notion of factorisation doesn't really
make sense (you could factor g as, say sin(x)*(g/sin(x))).

  sage: g.parent()
  Symbolic Ring

So, instead of working with general symbolic expressions, you should
work with actual polynomials, living in a polynomial ring with
prescribed coefficient domain.

Of course, the factorisation of your polynomial will depend on the
coefficient domain:

  sage: R.<x> = ZZ[]
  sage: R
  Univariate Polynomial Ring in x over Integer Ring
  sage: g = x^2-26*x-9
  sage: g.factor()
  x^2 - 26*x - 9

but when you work over the algebraic completion of QQ or if you work in
RR or some other large enough coefficient domain, then g factors:

  sage: R.<x> = QQbar[]
  sage: g = x^2-26*x-9
  sage: g.factor()
  (x - 26.34166406412634?) * (x + 0.3416640641263338?)
  sage: R.<x> = RR[]
  sage: g = x^2-26*x-9
  sage: g.factor()
  (x - 26.3416640641263) * (x + 0.341664064126334)

Best regards,
Simon

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