On Sunday, December 30, 2018 at 10:30:53 AM UTC-8, Peter Luschny wrote:
>
> > In the mean time, you can accomplish your computations without using SR:
> > sage: R.<x>=QQ[[]]
> > sage: (1 - x - sqrt(1 - 6*x + x^2))/(2*x)
> > 1 + 2*x + 6*x^2 + 22*x^3 + 90*x^4 + 394*x^5 + ...
>
> Does this only work in interactive mode? As soon as I try to
> capture it in a function it doesn't work anymore.
>
> Given
sage: var('x')
sage: f=sqrt(1+x)
sage: R.<t>=QQ[[]]
you'd hope that f(x=t) would do the trick, but unfortunately that tries to
put t into SR rather than try to evaluate it in R. A workaround:
sage: F=fast_callable(f,vars=[x])
sage: f_as_power_series = F(t)
It depends a bit on how you want to give f to begin with. If you want to
start with an expression in SR then the approach is fairly efficient. If
you know you'll be working in Q[[t]] anyway, you might as well start with
creating f in that ring.
> def SERIES(s):
> R.<x> = QQ[[]]
> return s
>
By definining R.<x>, you don't change s, so you just get the object s back
that you passed in.
What people use depends on their background: I guess that someone
> who comes from Maple or Mathematica almost automatically writes
> 'series' and thinks in terms of SR.
>
Indeed. What I meant was, given that "series" is so poor in sage presently,
people cannot be using it. So apparently, people who use series in sage do
so via other means. Indeed, the algebra of series is fairly well-supported
via power series rings. It would be great if the pynac series would be
better supported in sage (and if not, we should probably remove them
entirely, because your example shows they are very misleading), but then
one has to think: who's going to do the work and why hasn't it happened
yet? Apparently, people have been sufficiently happy with the other means.
That said, checking if a ticket exists and, if not, filing one would be
good. Perhaps someone likes to work on it (you?).
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