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Re: [Axiom-math] repeated series expansion


From: Raymond Rogers
Subject: Re: [Axiom-math] repeated series expansion
Date: Fri, 16 Jul 2010 16:47:29 -0500
User-agent: Thunderbird 2.0.0.24 (X11/20100411)

Martin Rubey wrote:
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.

  
That's interesting.  How does "MultivariateTaylorSeriesCategory()" from bookvol 10.2 page 1026  fall short?
I have never used it; but it seemed relevant to the above.

Ray

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