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Re: [Axiom-math] repeated series expansion


From: Ralf Hemmecke
Subject: Re: [Axiom-math] repeated series expansion
Date: Fri, 16 Jul 2010 22:50:47 +0200
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.9.2.4) Gecko/20100608 Thunderbird/3.1

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))

Thanks, Martin. That is exactly the representation with the (homogeneous) polynomial coefficients I was talking about here...
http://lists.nongnu.org/archive/html/axiom-math/2010-07/msg00003.html

However, currently there is no domain for generalised multivariate
Taylor series.

Could you say, what you actually mean by "generalized multivariate TS"?

Ralf



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