Curious behavior of Taylor series

"Igor Khavkine" <[email protected]>
Newsgroups gmane.comp.mathematics.axiom.general
Message-ID <[email protected]>
Can someone explain the following behavior of Taylor series in Axiom?

(113) -> y := taylor x
   (113)  x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
(114) -> x*y
   (114)  x x
                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
(115) -> coefficient(%,1)
   (115)  x
                                                     Type: Expression Integer

The same behavior does not occur if the coefficient ring is changed to
say the rationals:

(118) -> y := (taylor x) :: UTS(FRAC INT,x,0)
   (118)  x
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
(119) -> x*y
           2
   (119)  x
                           Type: UnivariateTaylorSeries(Fraction Integer,x,0)
(120) -> coefficient(%,2)
   (120)  1
                                                       Type: Fraction Integer

I've been trying to write a routine that takes some expression f(x,y),
but possibly containing other symbolic constants, and then solves the
implicit equation f(x,y)=0 for y as a Taylor series in x. The above
behavior has proved to be an obstacle.

Thanks.

Igor
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