Re: [Axiom-math] repeated series expansion

[Martin Rubey]

Vladimir Skokov <address@hidden> writes:

> Dear all, 
>
> I have only started to learn axiom. Could you help me please? 
> I have an expression, say sin(x+y). How could I perform expansion 
> withe respect ot x and than to y? 
>
> i.e. 
>
> series(  series(  sin(x+y),x=0  ),y=0   )
>
> thank you in advance 

In axiom there is another option:

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