Thanks, Martin.
On Nov 10, 8:07 pm, Martin Rubey <[EMAIL PROTECTED]> wrote:
> Alex Raichev <[EMAIL PROTECTED]> writes:
> > Hi all:
>
> > Is there Sage function that computes Taylor expansions for
> > multivariate functions?
>
> If you are willing to install the optional fricas package:
>
> sage: reset()
> sage: X=axiom('x::TS FRAC INT')
> sage: Y=axiom('y::TS FRAC INT')
> sage: axiom._eval_line(')set str cal 3')
> sage: sin(X+Y)
>
> 1 3 1 2 1 2 1 3
> (y + x) + (- - y - - x y - - x y - - x ) + O(4)
> 6 2 2 6
> sage: axiom.coefficient(sin(X+Y), 5)
>
> 1 5 1 4 1 2 3 1 3 2 1 4 1 5
> --- y + -- x y + -- x y + -- x y + -- x y + --- x
> 120 24 12 12 24 120
> -----------------------------------------------------------------------------
>
> I guess I should provide some details. x and y are at first symbols, then via
> "::" coerced to TaylorSeries Fraction Integer (short: TS FRAC INT, both
> works).
>
> The third line instructs FriCAS to calculate series only up to order 3, note
> that FriCAS's series really are lazy formal power series. Note that these are
> *not* just iterated power series, as eg. in Mathematica :-)
>
> The next line applies sin to the TaylorSeries X+Y.
>
> Unfortunately, the interface to FriCAS is currently rather weak - there is a
> problem with pexpect, there is not sage wrapper for the most important
> function
> "::" of FriCAS, and there is still a lot of work to do to convert FriCAS
> objects to Sage objects. (although a lot has been done under the hood,
> already)
>
> An alternative route would be to extend the Mike Hansen / Ralf Hemmecke lazy
> power series.
>
> Hope this helps.
>
> Martin
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