Re: repeated series expansion

Vladimir Skokov <[email protected]> writes:

> Dear all,=C2=A0
>
> I have only started to learn axiom. Could you help me please?=C2=A0
> I have an expression, say sin(x+y). How could I perform expansion=C2=A0
> withe respect ot x and than to y?=C2=A0
>
> i.e.=C2=A0
>
> series( =C2=A0series( =C2=A0sin(x+y),x=3D0 =C2=A0),y=3D0 =C2=A0 )
>
> thank you in advance=C2=A0

In axiom there is another option:

(1) -> x :=3D 'X::TS FRAC INT; y :=3D 'Y::TS FRAC INT;

                                        Type: TaylorSeries(Fraction(Integer=
))
(2) -> sin(x+y)

                     1  3   1    2   1  2    1  3
   (2)  (Y + X) + (- - Y  - - X Y  - - X Y - - X ) + O(5)
                     6      2        2       6
                                        Type: TaylorSeries(Fraction(Integer=
))

However, currently there is no domain for generalised multivariate
Taylor series.  I don't know how difficult that would be, and I didn't
think the maths through either.

Martin