Jonathan Hanke <jonha...@gmail.com> writes:
> Hi,
>
> I was wondering if there is (or is planned) support for natural multivariate
> power series ring constructions (with say
> fixed precision for each variable) similar to that of polynomal rings? It
> would be nice to be able to say something like
>
> S = PowerSeriesRing(QQ, 'x,y', [15, 20])
> or
> S.<x,y> = PowerSeriesRing(QQ, [15, 20])
There is (in my opinion) quite good support for multivariate series in
FriCAS. I think the design is worth copying, assuming that fricas will
not become a standard part of Sage. Example: (sorry for the ASCII art,
read with fixed width font please...) Note that these are lazy power
series.
Martin
(1) -> x := 'x::TS FRAC INT
(1) x
Type: TaylorSeries(Fraction(Integer))
(2) -> y := 'y::TS FRAC INT
(2) y
Type: TaylorSeries(Fraction(Integer))
(3) -> cos(x+y)
(3)
1 2 1 2
1 + (- - y - x y - - x )
2 2
+
1 4 1 3 1 2 2 1 3 1 4
(-- y + - x y + - x y + - x y + -- x ) + O(5)
24 6 4 6 24
Type: TaylorSeries(Fraction(Integer))
(4) -> cos x * cos y - sin x * sin y - %
(4) O(5)
Type: TaylorSeries(Fraction(Integer))
(5) -> recip sqrt((cos x)^2 + (sin y)^2)
1 2 1 2 13 4 3 2 2 5 4
(5) 1 + (- - y + - x ) + (-- y - - x y + -- x ) + O(5)
2 2 24 4 24
Type: Union(TaylorSeries(Fraction(Integer)),...)
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